A thin uniform rod \( A B \) of mass \( m= \)
1 kg moves translationally with
acceleration \( a=2 m / s^{2} \) due to two anti
parallel forces \( F_{1} \) and \( F_{2} \) The distance between the points at which these
forces are applied is equal to \( l=20 c m \)
Besides, it is known that \( F_{2}=5 N \). Find
the length of the rod (in meteres)


Unit of density and relative density are
same.
A . True
B. False


Find the equation of the curve for which
the normal at any point \( (x, y) \) passes through the origin. The curve represents
\( \mathbf{a}: \)
A . ellipse
B. rectange
c. circle
D. hyperbola


Two crosses between the same pair of genotypes or phenotypes in which the sources of the gametes are reversed in one cross, is known as
A. Test cross
B. Reciprocal cross
c. Dihybrid cross
D. Reverse cross


Bakelite polymer is formed by the polymerization of:
A. methanol and salicyladehyde
B. methanal and hydroxy benzene
c. ethanal and hydroxy benzene
D. ethanal and cinnamic acid


For \( i^{2}=-1 \) find the value of \( i^{253} \)


A man has a strange ability to jump
from any height to another with ease
The manjumps to P then to Q, R, S, T
and then into water. For which jump will he require the. highest energy?
A. Land to
B. s to
\( c \cdot Q \) to \( R \)
D. R to


\( \int \frac{2 x-1}{2 x^{2}+2 x+1} d x= \)
\( \mathbf{A} \cdot \frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|+2 \tan ^{-1}(2 x+1)+c \)
B \( \cdot-\frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|-2 \tan ^{-1}(2 x+1)+c \)
C \( -\frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|+2 \tan ^{-1}(2 x+1)+c \)
D \( \cdot \frac{1}{2} \ln \left|2 x^{2}+2 x+1\right|-2 \tan ^{-1}(2 x+1)+c \)


The IUPAC name of
\( \boldsymbol{K}_{2}\left[\boldsymbol{C r}(\boldsymbol{C N})_{2} \boldsymbol{O}_{2}\left(\boldsymbol{O}_{2}\right) \boldsymbol{N} \boldsymbol{H}_{3}\right] \) is:
A. potassium amminedicyanotetraoxo chrominum (III)
B. potassium amminedicyanodioxygendioxo chromate \( (1 v) \)
c. potassium amminedicyanosuperoxoperoxo chromate
(III)
D. potassium amminedicyanodioxoperoxo chromate (VI)


Define atomic mass unit.


A compound which is insoluble in cold water but soluble in excess of ammonia
solution is :
A. sulphur
B. sulphate
C. silver chloride
D. hydrogen chloride


The ratio of the sum of first 3 terms to
that of the first 6 terms of a \( G . P . \) is
\( 125: 152 . \) Find their common ratio's.


The energy gap \( E_{G} \) of a semi-conductor decreases with rise in temperature.
A. True
B. False


The heat of combustion of carbon to
\( C O_{2} \) is \( -393.5 \mathrm{kJ} / \mathrm{mol} \). What is the heat
released upon formation of 35.2 g of \( C O_{2} \) from carbon and oxygen gas?


The relative permeability of silicon is 0.99837 and that of palladium is
\( 1.00692, \) choose the correct option from the following:
A. silicon is paramagnetic and palladium is ferromagnetic
B. silicon is ferromagnetic and palladium is paramagnetic
c. silicon is diamagnetic and palladium is paramagnetic
D. Both are paramagnetic


Examination or observation of tissues
is done using a
A. Microscope
B. Magnifying glass
c. seen through naked eye
D. None of the above


Exa is used as prefix in SI system. True =
\( 1, \) false \( =0 \)


For weak electrolytes, van't Hoff factor 'i
is a measure of the degree of
dissociation of weak electrolyte. If true enter 1 , if false enter 0 .


In the figure given below, measure of
\( \angle A B C \) is
A . \( 60^{\circ} \)
B. 70
\( c .80 \)
D. 50


Non-metals have properties similar to
that of metals.
A. True
B. False


Among the oxyacids of chlorine, the strongest oxidising agent is:
A. \( \mathrm{HClO}_{4} \)
в. \( \mathrm{HClO}_{3} \)
c. \( \mathrm{HClO}_{2} \)
D. HClO


Find two rational and two irrational
number between 2 and 5


No of line of symmetry of \( n \) sided regular polygon is
\( A \)
B. \( n+1 \)
\( c \cdot n-1 \)
D. 2n


If the radius of the circle is increased by
\( 100 \% \) then the area is increased by
A. \( 100 \% \)
B . 200\%
c. 300\%
D. 400\%


What is true for acidic aqueous
solution?
A \( \cdot\left[H_{3} O^{+}\right]=10^{-7} \mathrm{M} \)
в. \( \left[H_{3} O^{+}\right]<10^{-7} \mathrm{M} \)
c. \( \left[H_{3} O^{+}\right]>10^{-7} \) М
D \( \cdot\left[H_{3} O^{+}\right]<\left[O H^{-}\right] \)


A wire has a mass \( (0.3 \pm 0.003) g \) radius \( (0.5 \pm 0.005) \mathrm{mm} \) and length (6 土 \( 0.06) \mathrm{cm} . \) The maximum percentage error in the measurement of its density is -
\( A \)
B. 2
\( c \cdot 3 \)
D. 4


A particle is dropped from the top of a tower. During its motion it covers \( \frac{\mathbf{9}}{\mathbf{2 5}} \) part of height of tower the last 1
seconds. Then find the height of tower


Give examples and explain what is meant by external fertilisation?


Visually impaired and challenged persons can read and write using:
A. Vedic system
B. Metric System
c. Binary System
D. Braille System


Classify the result as rational or irrationals. \( (3+\sqrt{23})-\sqrt{23} \)
A. Rational number
B. Irrational number
c. Data Insufficient
D. None of the above


Water gas is a mixture of:
A. carbon dioxide and hydrogen
B. carbon monoxide and hydrogen
c. carbon and hydrogen
D. ammonia and hydrogen


Which of the following is renewable source of energy?
A. Nuclear fuels
B. Natural gas
c. Fossil fuels
D. Geothermal energy


A rod of length of \( 1 \mathrm{m} \) is attached to the
string at its mid point. A 6 kg mass is attached to end of the rod and another
mass \( \mathrm{M} \) is hung at a distance of \( 30 \mathrm{cm} \)
from the center of the rod as shown in
the figure. Assume mass of rod is negligible. Find out the value of \( \mathrm{M} \).
\( A \cdot 3 \mathrm{kg} \)
B. \( 5 \mathrm{kg} \)
\( c \cdot 6 \mathrm{kg} \)
D. \( 10 \mathrm{kg} \)
E. 30 kg


During a nuclear fission reaction
A. a heavy nucleus breaks into two fragments by itself
B. a light nucleus bombared by thermal neutrons breaks \( u p \)
C . a heavy nucleus bombared by thermal neutrons breaks up
D. two light nuclei combine to give a heavier nucleus and possibly other products


State Snell's law of refraction of light.


The number of significant figures in
0.00052 is :
\( A \cdot 3 \)
B. 2
\( c \cdot 5 \)
\( D \)


A fuse wire is generally made of
A. tin
B. tin-lead alloy
c. copper
D. either (a) or (b) above


Assertion (A): The points \( \boldsymbol{A}(\mathbf{2}, \mathbf{9}, \mathbf{1 2}), \boldsymbol{B}(\mathbf{1}, \mathbf{8}, \mathbf{8}), \boldsymbol{C}(\mathbf{2}, \mathbf{1 1}, \mathbf{8}) \boldsymbol{D}(\mathbf{1}, \mathbf{1 2} \)
are the vertices of a rhombus
Reason \( (\mathrm{R}): A B=B C=C D=D A \)
and \( \boldsymbol{A C}=\boldsymbol{B D} \)
A. Both A and R are individually true and R is the correct explanation of
B. Both A and R individually true but R is not the correct explanation of A
c. \( A \) is true but \( R \) is false
D. Both A and R false


In which of the following substances, ethanol is not used?
A. Tonics
B. cough mixture
c. candle
D. Alcohol


State True or False :
The larger the exposed surface area, lower is the rate of evaporation.
A. True
B. False


Amino acids are:
A. Acidic
B. basic
c. neutral
D. acidic, basic or neutral


Find the sum of the series \( 1 \cdot 2+2 \)
\( \mathbf{3}+\mathbf{3} \cdot \mathbf{4}+\cdots+\boldsymbol{n}(\boldsymbol{n}+\mathbf{1}) \)


Find the centres of the circles passing through (-4,3) and touching the lines \( \boldsymbol{x}+\boldsymbol{y}=\boldsymbol{2} \) and \( \boldsymbol{x}-\boldsymbol{y}=\boldsymbol{2} \)
A \( \cdot((-10 \pm \sqrt{54}), 0) \)
B. \( (10 \pm \sqrt{54}, 0) \)
c. \( (0,-10 \pm \sqrt{54}) \)
D. \( (0,10 \pm \sqrt{54}) \)


In which of the following option could represent the ball increasing its speed?
\( A \)
\[
\text { (A) } . \quad \bullet \quad \bullet \quad \bullet \quad \text { ・ }
\]
B.
\[
\text { (B) } \bullet \bullet \quad \bullet
\]
\( \mathbf{c} \)
(C)
D.
(D)
\[
\bullet
\]
E .
(E)


Mark the incorrect statement.
A. In our homes, we receive supply of electric power through a main supply
B. Red insulation cover, is called live wire
C. The earth wire, has insulation of green colour
D. None


A bicyclist covers 60 miles between
\( 2 p m \) and \( 6 p m . \) What was his average
speed?
A. 15 mph
в. 30 три
c. 45 mph
D. 60 mph
E. Not enough information is given to be able to say


The reason(s) for small radius of Ga
compared to \( A l \) is/are :
This question has multiple correct options
A. poor screening effect of \( d \) and \( f \) orbitals.
B. increase in nuclear charge
c. presence of higher orbital
D. higher atomic number


An \( \alpha \) particle moves in circular path of
radius \( 0.83 \mathrm{cm} . \) In the presence of a
magnetic field of \( 0.25 W b / m^{2} . \) Find the De Broglie wavelength associated with the particle


Scientists identify the elements that are burning in the stars by using which of the following devices?
A. Refractive telescopes
B. Reflective telescopes
c. spectroscopes
D. Polarimeters
E. Photoelectric mircoscopes


An azeotropic mixture of HCl and water
has:
A . \( 84 \% \) of \( \mathrm{HCl} \)
в. 22.2\% НС।
c. 63\% of HCI
D. 20.2\% HCI


If \( z_{1}=2-i, z_{2}=-2+i \),find
\[
\operatorname{Im}\left(\frac{1}{z_{1} \overline{z_{2}}}\right)
\]


Among the following, the number of
compounds that can react with \( P C l_{5} \) to
give \( P O C l_{3} \) is:
\( O_{2}, C O_{2}, S O_{2}, H_{2} O, H_{2} S O_{4}, P_{4} O_{10} \)
\( A \cdot 4 \)
B. 5
\( c \cdot 3 \)
D. 6


For a certain load, the true power is \( 150 W \) and the reactive power is \( 125 W \) The apparent power is
A. \( 19.52 W \)
В. \( 195.2 W \)
\( \mathrm{c} \cdot 275 \mathrm{W} \)
D. 25W


A compass needle whose magnetic
moment is \( 60 A m^{2} \) pointing
geographical north at a certain place where the horizontal component of
earth's magnetic field is \( 40 \times \)
\( 10^{-6} W b m^{-2} \) experiences a torque of
\( 1.2 \times 10^{-3} N m . \) The declination of the
place is
\( \mathbf{A} \cdot 20^{0} \)
B. \( 45^{\circ} \)
\( c \cdot 60^{\circ} \)
D. \( 30^{\circ} \)


If \( A \) and \( B \) are two mutually exclusive
events then \( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})= \)
A. \( P(A) . P(B) \)
в. \( P(A) \)
c. 0
D.


Which one of the following shows bilateral symmetry?
A. Virus
B. Bacteria
c. Amoeba
D. Planaria
E. sponge


A sensory neuron of the peripheral nervous system takes new impulse from sensory receptors to the
A. Motor neurons
B. Interneurons
c. Autonomic nervous system
D. Central nervous system


The products formed when chloral
hydrate is dissolved in \( N a O H \)
solution and then distilled?
A \( \cdot C H_{2} C l_{2} \) and \( N a C l \)
в. \( C H_{3} C l \) and \( C H_{3} C O O N a \)
c. \( C H C l_{3}, H C O O N a \) and \( H_{2} O \)
D. \( C_{2} H_{5} C l \) and \( C H_{3} C O O N a \)


\( \sqrt{7} \) is a
A. an integer
B. an irrational number
c. a rational number
D. none of these


The electromagnetic radiations are:
a) Visible light
b) IR light
c) UV light
d) Microwaves
The correct order of increasing energy from lowest to highest is:
A. \( d<c<b<a \)
в. \( a<b<c<d \)
c. \( d<b<a<c \)
D. \( b<c<d<a \)


The outermost configuration of the least reactive element is:
A \( \cdot n s^{2} n p^{3} \)
B . \( n s^{2} n p^{4} \)
\( \mathbf{c} \cdot n s^{2} n p^{5} \)
D. \( n s^{2} n p^{6} \)


\( \boldsymbol{p} \boldsymbol{H} \) of a \( \boldsymbol{0 . 0 1} \boldsymbol{M} \) solution \( \left(\boldsymbol{K}_{\boldsymbol{a}}=\boldsymbol{6 . 6} \times\right. \)
\( \left.10^{-4}\right) \) is:
A . 7.6
B. 8
c. 2.6
D.


The ratio of the value of \( G \) in \( S \) l units to
CGS units is
\( \mathbf{A} \cdot 10^{3}: 1 \)
B \( \cdot 10^{2}: 1 \)
\( \mathbf{c} \cdot 10^{-2}: 1 \)
D. \( 10^{-3}: 1 \)


A cyclic compound 'X' has molecular
formula \( C_{6} H_{6} . \) It is an unsaturated
compound and burns with a sooty flame. Identify 'X' and write it's the structural formula.


A ball of mass m strikes a rigid wall
with speed u and rebounds with the
same speed. The impulse imparted to
the ball by the wall is:
A. 2mu
в. mu
c. zero
D. -2mu


Which of the following plant is used for the purification of water?
A. Biggiata
B. Chlorella
c. spirogyra
D. Eichhornia


Identify the series.
\( \mathbf{A} \cdot\{1,2,3,4,5\} \)
B . \( 1+2+3+4+5 \)
c. \( 1 \times 2 \times 3 \times 4 \)
D. \( 2-4 \times 3+1-23 \)


What is the difference between
oil/water (O/W) type and water/oil (W/O) type emulsions? Give an example of each type.


Which metal is extracted by electrolytic reduction method?
A. cu
в. А।
c. \( \mathrm{Fe} \)
D. Agg


In a Zener regulated power supply of a
Zener diode with \( V_{2}=6 V \) is used for
regulation. The load current is to be \( 4 m A \) and the unregulated input is \( 10 V \)
The value of series resistor \( \boldsymbol{R}_{\boldsymbol{S}} \) is
(Assume \( \left.\boldsymbol{I}_{z}=\mathbf{5} \boldsymbol{I}_{L}\right) \)
A. less than \( 5 \Omega \)
B. Infinite
c. greater than \( 100 \Omega \)
D. zero


Find the whole quantity if:
\( 8 \% \) of it is 40 litres


Which of the following is the \( 3^{\circ} \) amine?
A \( \cdot\left(C H_{3}\right)_{3} N \)
в. \( \left(C H_{3}\right)_{2} N H \)
c. \( \left(C H_{3}\right) N H_{2} \)
D. \( N H_{3} \)


About buffer solution which is correct?
This question has multiple correct options
A. It contains a weak acid and its conjugate base
B. It contains a weak base and its conjugate acid
C. It shows change in \( \mathrm{pH} \) on adding small amount of acid or base
D. All of the above


If the sum of first \( n \) term of A.P is \( \frac{1}{2}\left(3 n^{2}+7 n\right) \) then its \( n^{t} h \) term. hence
\( 20^{t} h \) term


Assertion
In ECG graph of heart, pulse 'R' is the peak point
Reason
It shows the atrial depolarisation which takes 0.2 seconds.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


The T-wave in an ECG represents
A . Electrical excitation of atria
B. Return of the ventricles from excited state
C. Depolarisation of ventricles
D. Beginning of systole


The real angle of dip, if a magnet is
suspended at an angle of \( 30^{0} \) to the
magnetic meridian and the dip needle
makes an angle of \( 45^{0} \) with horizontal is :
\( ^{A} \cdot \tan ^{-1}\left(\frac{\sqrt{3}}{2}\right) \)
B \( \cdot \tan ^{-1}(\sqrt{3}) \)
\( ^{\mathbf{c}} \cdot \tan ^{-1}\left(\frac{1}{2}\right) \)
D \( \cdot \tan ^{-1}\left(\frac{2}{\sqrt{3}}\right) \)


Monochromatic light is incident on a pair of narrow slits a distance of \( 0.1 \mathrm{mm} \)
apart. A series of
bright and dark fringes are observed on a screen a distance of \( 2.0 \mathrm{m} \) away. The
distance between
adjacent bright fringes is \( 8.0 \mathrm{mm} \) What is the path difference between the
light waves from the two slits that meet
at the second
order dark fringe?
A \( \cdot 2.0 \times 10^{-7} \mathrm{m} \)
В. \( 4.0 \times 10^{-7} \mathrm{m} \)
\( \mathbf{c} \cdot 6.0 \times 10^{-7} m \)
7


Simplify: \( (3 m+5 n)^{2}-(2 n)^{2} \)


A circular park of radius \( 20 m \) is
situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.
A \( .5 \sqrt{3} \mathrm{cm} \)
B. \( 2 \sqrt{3} \mathrm{cm} \)
c. \( \sqrt{3} \mathrm{cm} \)
D. \( 20 \sqrt{3} \mathrm{cm} \)


"The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the
same ratio as the odd numbers
beginning with unity [namely \( 1 ; 3 ; 5 ; 7 \) \( \ldots . .] " \) prove it.


If \( \Delta P Q R \sim \Delta X Y Z, \angle Q=50^{\circ} \) and
\( \angle R=70^{\circ}, \) then the angle \( \angle X+\angle Y \) is
equal to:
A \( .70^{\circ} \)
B. 50
\( c \cdot 120 \)
D. \( 110^{\circ} \)


A dynamo is used to supply electric current to a small electric bulb, If the
number of turns in the coil of
this dynamo is doubled, then the voltage in the bulb.
A. will decrease
B. Remains unchanged
c. will be doubled
D. Will increase by a factor between 1 and 2


The area in square units bounded by the
curves \( \boldsymbol{y}=\boldsymbol{x}^{3}, \boldsymbol{y}=\boldsymbol{x}^{2} \) and the
ordinates \( \boldsymbol{x}=\mathbf{1}, \boldsymbol{x}=\mathbf{2} \) is
A \( \cdot \frac{17}{12} \)
B. \( \frac{12}{13} \)
\( c \cdot \frac{2}{7} \)
\( D \cdot \frac{7}{2} \)


Assertion
Mass or bulk flow is the movement of
substances in bulk from source to sink
as a result of pressure differences.
Reason
Water, minerals and food are generally moved by mass flow.
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


Deforestation has an alarming effect on
A. Increase in grazing area
B. Weed control
c. Soil erosion
D. Sunlight


A maxima or minima obtained in the
temperature, composition curve of a mixture of two liquid indicates:
A. an azeotropic mixture
B. an eutectic formation
c. that the liquids are immiscible with one another
D. that the liquids are partially miscible at the maximumm or minimum


The most powerful oxidant among the
following is:
A . \( H O C l \)
в. \( H C l O_{2} \)
c. \( H C l O_{3} \)
D. \( H C l O_{4} \)


The Scientist related with the theory of biogenesis and who has done experiment with the swan-necked flask is
A. Haeckel
B. Louis Pasteur
c. van Helmont
D. Milter


External and internal diameters of a
hollow cylinder are measured to be \( (4.23 \pm 0.01) \mathrm{cm} \) and \( (3.89 \pm 0.01) \mathrm{cm} \)
The thickness of the wall of the cylinder is
A . \( (0.34 \pm 0.03) \mathrm{cm} \)
B. \( (0.17 \pm 0.04) \mathrm{cm} \)
c. \( (0.17 \pm 0.01) \mathrm{cm} \)
D. \( (0.34 \pm 0.02) \mathrm{cm} \)


In the environment, ozone is known for
its
A . Harmful effects
B. Useful effects
c. Both A and B
D. Inert nature


The contractile protein of skeletal muscle involving ATPase activity is
A. \( \alpha \) - Actinin
B. Tro ponin
c. Tropomyosin
D. Myosin


Among the complex numbers \( z \) which
satisfy the condition \( |z-25 i| \leq 15 \)
find the number having the least positive and greatest positive
argument.


What are the advantages of sexual
reproduction over asexual
reproduction?


Which of the following is/are correct?
This question has multiple correct options
A. If centre of mass of three particles is at rest and it is known that two of them are moving along different lines, then the third particle must be moving.
B. If centre of mass remains at rest, then net work done
by the forces acting on the system must be zero.
C. If centre of mass remains at rest, then the net external force must be zero.
D. If speed of centre of mass is changing, then there must be some net work being done on the system from outside.


Calculate the moment of inertia of a
uniform disc of mass M and radius R
about a diameter.


The number of moles of sulphuric acid
present in 24.5 g of \( H_{2} S O_{4} \) is:
A . 2.5
B. 0.5
\( c \cdot 4 \)
D. 0.25


When photons of energy h fall on an
aluminium plate (of work function \( \mathrm{E}_{0} \) ), photoelectrons of maximum kinetic energy K are ejected. If the frequency of the radiation is doubled, then
the maximum kinetic energy of the
ejected photoelectrons will be:
\( A \cdot K+E_{0} \)
в. 2k
\( c \cdot k \)
\( D \cdot K+h \)


If a \( 3 c m \) tall object placed
perpendicular to principal axis of a convex lens of focal length \( 15 \mathrm{cm} \)
produces a real invented image of height \( 15 c m, \) then its object distance
\( (u) \) is and image distance \( (v) \) is
A. \( u=-18 m, v=+90 m \)
в. \( u=+18 \mathrm{cm}, v=-90 \mathrm{cm} \)
c. \( u=-18 \mathrm{cm}, V=+90 \mathrm{cm} \)
D. \( y=+18 c m, v=+90 \mathrm{cm} \)


Lightning is observed earlier than the
sound is heard because
A. Light travels faster than sound
B. Thunder is produced later
c. Thunder is produced simultaneously but it travels after light has reached the observer's eyes
D. Man's sense of vision is sharper than his sense of hearing
E. None of the above


A battery of emf \( 10 \mathrm{v} \) and internal resistance of 0.5 ohms is connected
across \( A \) variable resistance R.The
maximum value of \( \mathrm{R} \) is given by:
A . \( 0.5 \Omega \)
B. \( 1.00 \Omega \)
c. \( 2.0 \Omega \)
D. \( 0.25 \Omega \)


Determine the number of moles of \( \boldsymbol{A} \boldsymbol{g} \boldsymbol{I} \)
which may be dissolved in 1 litre of \( 1 M \)
of \( C N^{-} \) solution \( K_{s p} \) for \( A g I \) and \( K_{c} \) for
\( A g(C N)_{2}^{-} 1.2 \times 10^{-17} M^{2} \) and \( 7.1 \times \)
\( 10^{-19} M^{-2} \) respectively.


Which among the following oxides of nitrogen is called nitrogen sesquioxide?
A \( \cdot N O_{2} \)
B. \( N_{2} O_{3} \)
c. \( N_{2} O_{4} \)
D. \( N_{2} O_{5} \)


Sex chromosomes of a female bird are
represented by
A. xo
в. \( x x \)
c. \( x y \)
D. zz
E. zw


Which of the following is an example of soft and fine wool?
A. Merino
B. cotswold
c. Both A and B
D. None of them


A beam of cathode rays is subjected to crossed electric (E) and magnetic fields
(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by :
\( ^{\mathbf{A}} \cdot \frac{B^{2}}{2 v E^{2}} \)
B. \( \frac{2 v B^{2}}{E^{2}} \)
c. \( \frac{2 v E^{2}}{B^{2}} \)
D. \( \frac{E^{2}}{2 v B^{2}} \)


If \( \boldsymbol{A}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\boldsymbol{6} \boldsymbol{x}-\boldsymbol{7}<\mathbf{0}\right\} \) and
\( \boldsymbol{B}=\left\{\boldsymbol{x} \in \boldsymbol{R}: \boldsymbol{x}^{2}+\boldsymbol{9} \boldsymbol{x}+\mathbf{1 4}<\mathbf{0}\right\}, \) then
which of the following is/are correct?
1. \( (\boldsymbol{A} \cap \boldsymbol{B})=(-\mathbf{2}, \mathbf{1}) \)
2. \( (\boldsymbol{A} \backslash \boldsymbol{B})=(-\mathbf{7},-\mathbf{2}) \)
Select the correct answer using the code given below:
A. 1 only
B. 2 only
c. Both 1 and 2
D. Neither 1 nor 2


Classification of elements are done on
the basis of
A. atomic number
B. atomic weight
c. valency
D. none of these


Which of the following is a compound?
A. Carbon dioxide
B. Iron
c. oxygen
D. Air


What is the specific latent heat of the metal?
A. \( 50 J g^{-1} \)
В. \( 2500 J g^{-1} \)
C. \( 5000 J g^{-1} \)
D. \( 500 J g^{-1} \)


In a YDSE, if the incident light consists
of two wavelengths \( \lambda_{1} \) and \( \lambda_{2} \), the slit separation is \( d \), and the distance
between the slit and the screen is \( D \)
the maxima due to each wavelength will coincide at a distance from the central
maxima, given by
A \( \frac{\lambda_{1}+\lambda_{2}}{2 D d} \)
в. \( _{\text {LCM of }} \frac{\lambda_{1} D}{d} \) and \( \frac{\lambda_{2} D}{d} \)
c. \( _{\left(\lambda_{1}+\lambda_{2}\right)} \frac{2 D}{D} \)
D. \( _{\text {HCF of }} \frac{\lambda_{1} D}{d} \) and \( \frac{\lambda_{2} D}{d} \)


Assertion
A mixture of sodium acetate and
sodium propionate forms a buffer
solution.
Reason
A buffer solution reacts with small
quantities of hydrogen or hydroxyl ions and keeps the pH almost same.
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


Which of the following defines the term
opiates?
A. Narcotic analgesics obtained from the opium poppy.
B. Non-narcotic analgesics which reduce fever.
C. Narcotic drugs that inhibit pathogenic microbes.
D. Tranquilizers used to induce sleep.


An ellipse passing through origin has its foci at (5,12) and \( (24,7), \) then its eccentricity is
A \( \cdot \frac{\sqrt{386}}{38} \)
B. \( \frac{\sqrt{386}}{39} \)
c. \( \frac{\sqrt{386}}{47} \)
D. \( \frac{\sqrt{386}}{51} \)


Community dynamics is related to
A. Population growth in an ecosystem
B. Recycling of nutrients in an ecosystem
C. Flow of energy in an ecosystem
D. Ecological succession


In a surface tension experiment with a capillary tube, water rises upto \( 0.1 \mathrm{m} \). If the same experiment is repeated in an artificial satellite revolving around the earth, then the water will rise in the capillary upto a height of
A. \( 0.1 \mathrm{m} \)
B. 9.8 \( m \)
\( c .0 .98 \mathrm{m} \)
D. full length of capillary tube


What is the role of \( M n O_{2} \) in the
preparation of \( O_{2} \) from \( K C l O_{3} ? \)


\( 8 g \) of divalent metal produces \( 9.8 g \) of its nitride. The approx atomic weight of metal is:
A . 9.8
B. 42
\( c .35 \)
D.


Find the value of \( \lim _{x \rightarrow \infty} \frac{\sqrt{x}}{\sqrt{x}+3} \)


Find the determinant of given matrix \( \left[\begin{array}{ccc}\boldsymbol{a}-\boldsymbol{b}-\boldsymbol{c} & \boldsymbol{2} \boldsymbol{a} & \boldsymbol{2} \boldsymbol{a} \\ \boldsymbol{2} \boldsymbol{b} & \boldsymbol{b}-\boldsymbol{c}-\boldsymbol{a} & \boldsymbol{2} \boldsymbol{b} \\ \boldsymbol{2} \boldsymbol{c} & \boldsymbol{2} \boldsymbol{c} & \boldsymbol{c}-\boldsymbol{a}-\boldsymbol{b}\end{array}\right] \)
A \( \cdot 2(a+b+c)^{3} \)
В. \( (a-b-c)^{3} \)
\( \mathbf{D} \cdot(a+b+c)^{3} \)


On heating ammonium dichromate, the gas evolved is:
A . oxygen
B. ammonia.
c. nitrous oxide
D. nitrogen.


An element with atomic number 117 is
known as:
A. nihonium
B. flerovium
c. tennessine
D. roentgenium


White phosphorous reacts with limited chlorine and the product is hydrolyzed in the presence of water. What would be the mass of HCl obtained by the
hydrolysis of the product formed by the reaction of 62 g of white phosphorus with chlorine in the presence of water?
A. 200 g
B. 400 g
c. \( 219 \mathrm{g} \)
D. 100 g


Identify the correct statement(s) about
orthoboric acid.
This question has multiple correct options
A. It has a layer structure in which planar \( B O_{3} \) units are joined by hydrogen bonds
B. Orthoboric acid \( \left(H_{3} B O_{3}\right) \) is a weak monobasic Lewis acid
c. on heating ortho-boric acid form meta-boric acid and on further heating to red hot,forms boric oxide anhdride
D. None of the above


Q Type your question
LISC - 1
A: The coordinates of the
mid point of the line joining
1) (-2,1,1)
\[
(-1,-1,1) \text { and }(-1,1,-1)
\]
B: The coordinates of the
point which divides the line segment joining
2) (-1,0,0)
(2,3,1) and (5,0,4) in the ratio1:2
C: The points and \( P(2,1,-3) \) are three vertices of a
3) \( \left(\frac{13}{3}, \frac{-11}{3}, 6\right) \)
parallelogram PQRS, the fourth vertex
D: The vertices of a triangle \( \operatorname{are}(7,-4,7),(1,-6,10) \)
4) (3,2,2) and (5,-1,1) . centroid of the triangle
\( \mathbf{A} \cdot A-2, B-4, C-1, D-3 \)
B. \( A-1, B-2, C-3, D-4 \)
\( \mathbf{c} \cdot A-2, B-3, C-1, D-4 \)
D. \( A-1, B-4, C-3, D-2 \)


If \( z=x+i y \) and \( w=\frac{1-i z}{z-i}, \) show that
\( |\boldsymbol{w}|=\mathbf{1} \Longrightarrow \boldsymbol{z} \) is purely real.


Find the additive identity of the
integers.


\( C l^{-} \) ions act as activators for:
A. amylases
B. peptidases
c. glycosidases
D. lipases


The effective resistance in between the
points A and B in the circuit given is?


Vital capacity of lungs is
\( \mathbf{A} \cdot \mid R V+E R V \)
B. IRV + ERV + TV - RV
c. \( \operatorname{lRV}+\operatorname{ERV}+\operatorname{TV}+\operatorname{RV} \)
D. IRV + ERV + TV.


A ray of light is incident at an angle of
\( 35^{0} \) on a plane mirror. What is angle \( \theta ? \)


If \( f(x)=\frac{x^{2}+6 x}{\sin x}, \) then \( \lim _{x \rightarrow 0^{-}} f(x)= \)
A . 2
B. 4
\( c \cdot 6 \)
\( D \)


The \( N O_{3}^{-} \) ion can be confirmed by?
A. Addition of conc. \( H_{2} S O_{4} \) in the presence of copper turnings
B. Addition of conc. NaOH + Devarda's alloy
C. The brown ring test only
D. All of these


Varun is climbing steps to the top of a
monument. After climbing 15 steps, Varun stops to tie his shoe laces. If there
are 75 steps in the monument, what percent of the total number of steps has Varun climbed when he stops to tie
his shoe laces?
A . \( 90 \% \)
B. \( 60 \% \)
\( c \cdot 20 \% \)
D. \( 5 \% \)


Resolve into partial fractions
\( \boldsymbol{x}^{\mathbf{3}} \)
\( (x-1)^{4}\left(x^{2}-x+1\right) \)
A \( \cdot \frac{1}{(x-1)^{4}}+\frac{2}{(x-1)^{2}}+\frac{x}{x^{2}-x+1} \)
B. \( \frac{1}{(x-1)^{4}}-\frac{1}{(x-1)^{2}}-\frac{1}{(x-1)}+\frac{x}{x^{2}-x+1} \)
C \( \frac{1}{(x-1)^{4}}+\frac{2}{(x-1)^{2}}-\frac{1}{(x-1)}+\frac{x}{x^{2}-x+1} \)
D \( \frac{-1}{(x-1)^{4}}+\frac{2}{(x-1)^{2}}-\frac{1}{(x-1)}+\frac{x}{x^{2}+x+1} \)


The most highly advanced character in crocodile (reptilia) is the presence of
A. Powerful jaws
B. Shelled eggs
c. Thecodont dentition
D. Four chambered heart


What is wrong with the Lewis dot
structure for \( I O^{-} ? \)
\[
[\because \dot{I}: \dot{O}:]^{-}
\]
A. The bond between \( I \) and \( O \) should be represented with single line
B. The negative symbol should be on the inside of the brackets
c. oxygen is not satisfied according to the octet rule
D. There are not enough electrons


A student scores the following marks in five test: \( 45,54,41,57,43 . \) His score is not known for the sixth test. If the mean
score is 48 in the six tests, then the standard deviation of the marks in six
test is
A \( \cdot \frac{10}{\sqrt{3}} \)
в. \( \frac{100}{\sqrt{3}} \)
c. \( \frac{130}{3} \)
D. \( \frac{10}{3} \)


A chemical reaction was carried out at
\( 300 \mathrm{K} \) and \( 280 \mathrm{K} \). The rate constants
were found to be \( K_{1} \) and \( K_{2} \) at \( 300 \mathrm{K} \)
and \( 280 \mathrm{K} \) respectively. Then which of the following is true?
A. \( K_{1}=4 K_{1} \)
B . \( K_{2}=2 K_{1} \)
c. \( K_{2}=0.25 K_{1} \)
D. \( K_{2}=0.5 K_{1} \)


Assertion
All enzymes found in cells are invariably
proteins which catalyse biological reactions.
Reason
Enzymes act efficiently at a moderate
temperature and \( p H \)
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


In a one-dimensional collision between
two identical particles \( \boldsymbol{A} \) and \( \boldsymbol{B} . \boldsymbol{B} \) is
stationary and \( A \) has momentum \( p \)
before impact. During impact, \( B \) gives
an impulse \( J \) to \( A \). Find the coefficient
of restitution between \( A \) and \( B ? \)


\( \lim _{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{x^{2}} \) is equal to
A \( \cdot \frac{3}{2} \)
B. \( \frac{1}{2} \)
\( c \cdot \frac{2}{3} \)
D. none of these


When a glass rod is rubbed against silk.
A. Glass rod loses electrons and becomes positively charged
B. Silk loses electrons and becomes positively charged
C. Glass rod losses electrons and becomes negatively charged
D. silk loses electrons and becomes negatively charged


An element \( Z \) has atomic number 16 .
Answer the following questions on \( Z \)
State the period and group to which \( Z \)
belongs:


External ear is found in
A. Reptiles
B. Mammals
c. Amphibians
D. Fishes


What would be thw minimum
uncertainty in de-Broglie wavelenght of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is \( \frac{7}{22} n m ? \)
A. \( 6.25 \AA \)
в. \( 6 \dot{A} \)
c. \( 0.625 \hat{A} \)
D. \( 0.3125 \dot{A} \)


A simple pendulum is released from \( \boldsymbol{A} \)
as shown in figure. If \( m \) and \( l \) represent
the mass of the bob and the length of
the pendulum respectively, the gain in
kinetic energy at \( B \) is then
A \( \cdot \frac{m g}{2} \)
B. \( \frac{m g}{\sqrt{2}} \)
\( c \)
D. \( \frac{2}{\sqrt{3}} m g l \)


For \( \left(\boldsymbol{\theta}_{1}, \boldsymbol{\theta}_{2}, \boldsymbol{\theta}_{3}, \ldots \ldots \boldsymbol{\theta}_{n}\right) \boldsymbol{\epsilon}(\mathbf{0}, \boldsymbol{\pi} / 2) \) if
\( \ln \left(\sec \theta_{1}-\tan \theta_{1}\right)+\ln \left(\sec \theta_{2}-\right. \)
\( \left.\tan \theta_{2}\right)+\ldots . \ln \left(\sec \theta-\tan \theta_{n}\right)+\ln \pi= \)
0 then find the value of \( \cos \left[\left(\sec \theta_{1}+\right.\right. \)
\( \left.\tan \theta_{1}\right)\left(\sec \theta_{2}+\tan \theta_{2}\right) \dots . .\left(\sec \theta_{n}+\right. \)
\( \left.\tan \theta_{n}\right) \)


Find the 12 th term of a G.P whose 8 th
term is 192 and the common ratio is 2


A RC circuit has an emf of \( 300 \cos (2 t) \)
volts, a resistance of 150 ohms, a
capacitance of \( \frac{1}{600} \) farad, and an initial
charge on the capacitor of 5 coulombs.
Find the charge on the capacitor at any
time \( t \)
A \( \cdot \frac{2}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
B \( \cdot \frac{1}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
c. \( \frac{3}{5}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)
D \( \cdot \frac{1}{6}\left(23 e^{-4 t}+\sin (2 t)+2 \cos (2 t)\right) \)


\( \frac{1}{88} \)
48
86
6.8


Acetylene on treatment with alkaline
\( \boldsymbol{K} \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{4} \) yields :
A . oxalic acid
B. ethanol
c. glyoxal
D. 1,2 - Ethanediol


Peroxodisulphate salts (e.g., \( N a_{2} S_{2} O_{8} \) ) are
strong oxidizing agents used as bleaching agents for fats, oils, etc. Given :
\( O_{2}(g)+4 H^{\oplus}(a q)+4 e^{-} \rightarrow 2 H_{2} O(l) \)
\( E^{\ominus}=1.23 V \)
\( S_{2} O_{8}^{2-}(a q)+2 e^{-} \rightarrow S O_{4}^{2-}(a q) \)
\( E^{\ominus}=2.01 V \)
Which of the following statements is (are) correct?
This question has multiple correct options
A. Oxygen gas can oxidize sulphate ion to per-oxo disulphate ion \( \left(S_{2} O_{8}^{2-}\right) \) in acidic solution
в. \( O_{2}(g) \) is reduced to water
c. water is oxidized to \( O_{2} \)
D. \( S_{2} O_{8}^{2-} \) ions are reduced to \( S O_{4}^{2-} \) ions


What length of the bottom \( A B \) the man
can see?


If \( \boldsymbol{f}(\boldsymbol{x})=\boldsymbol{p}|\sin \boldsymbol{x}|+\boldsymbol{q} e^{|\boldsymbol{x}|}+\boldsymbol{r}|\boldsymbol{x}|^{3} \) and if
\( f(x) \) is differentiable at \( x=0, \) then
A \( \cdot p=q=r=0 \)
B. \( p+q=0 ; r \) is any real number
c. \( q+r=0 ; p \) is any real number
D. \( r=0 ; p=0, q \) is any real number


Which of the following hydrides is most
acidic?
A. \( H_{2} \) Te
в. \( H_{2} S e \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( H_{2} S_{S} \)


How is the functioning of Lac operon different from that of trp
operon?


State the number of lines of symmetry for the following figures
(a) An equilateral triangle
(b) Isosceles
triangle (c) Scalene triangle
(d) A square
(e) A rectangle
(f) \( A \) rhombus
(g) A parallelogram
(h) A
quadrilateral
(i) A regular hexagon (j) A circle.


Which one of the following is used in the extraction of aluminium by electrolytic process?
A. \( A l_{2} O_{3} \)
\( \mathbf{B} \cdot A l(O H)_{3} \)
c. \( A l C l_{3} \)
D. \( A l_{2}\left(S O_{4}\right)_{3} \)


A particle oscillates as per the equation \( \boldsymbol{x}=\mathbf{7} \cos (\mathbf{0 . 5} \boldsymbol{\pi} \boldsymbol{t}) \mathrm{m}, \) the time taken by
the particle to move from the mean position to a point \( 3.5 \mathrm{m} \) away is:
A \( \cdot \frac{1}{3} s \)
в. \( \frac{1}{2} s \)
c. \( 1 s \)
D. \( \frac{2}{3} s \)


In an electron transition inside a
hydrogen atom, orbital angular momentum may change by ( \( h= \) Planck
constant)
This question has multiple correct options
\( A \cdot h \)
в. \( \frac{h}{\pi} \)
c. \( \frac{h}{2 \pi} \)
D. \( \frac{h}{4 \pi} \)


Angular velocity of rod about \( \boldsymbol{O} \) is
\( \frac{3 \sqrt{5}<F>(\Delta t)}{M L} \)
B. \( \frac{2 \sqrt{5}<F>(\Delta t)}{M L} \)
c. \( \frac{2 \sqrt{3}<F>(\Delta t)}{M L} \)
D. \( \frac{3 \sqrt{3}<F>(\Delta t)}{M L} \)


A cell of constant \( e m f \) first connected
of a resistance \( R_{1} \) and then connected
to a resistance \( \boldsymbol{R}_{2} \). If power delivered in
both cases is same then the internal
resistance of the cell is:
A \( \cdot \sqrt{R_{1} R_{2}} \)
в. \( \sqrt{\frac{R_{1}}{R_{2}}} \)
c. \( \frac{R_{1}-R_{2}}{2} \)
D. \( \frac{R_{1}+R_{2}}{2} \)


Write the first three terms of the AP
when a and d are as given below:
\( \boldsymbol{a}=\mathbf{5}, \boldsymbol{d}=\mathbf{3}, \) then first three terms are
\( \mathbf{5}, \mathbf{8}, \mathbf{1 1} \)
If true then enter 1 and if false then
enter 0


The distance between the lines \( 5 x- \)
\( 12 y+2=0 \) and \( 5 x-12 y-3=0, \) is
A . 5
B.
c. \( \frac{5}{13} \)
D. \( \frac{1}{13} \)


The value of current \( i \) for the given
circuit is :-
\( \mathbf{A} \cdot 10 A \)
B. \( 5 A \)
c. \( 2.5 A \)
D. \( 20 A \)


The solution of a salt of a weak acid and
weak base will have \( \mathrm{pH}:\left(K_{b}=1 \times 10^{-6}\right. \)
and \( \boldsymbol{K}_{\boldsymbol{a}}=\mathbf{1} \times \mathbf{1 0}^{-\mathbf{4}} \mathbf{)} \)
A . 7.0
B. 8.0
\( c \cdot 6 \)
D. 4.0


Solve: \( \frac{\mathbf{3}}{\boldsymbol{x}+\mathbf{3}}=\frac{\mathbf{5}}{\boldsymbol{x}+\mathbf{2}} \)


The Tyndall's effect associate colloidal
particles is due to:
A. presence of charge
B. scattering of light
c. absorption of light
D. reflection of light


An advantage of detergents over soaps
¡s:
A. detergents always contain heads
B. detergents are biodegradable
C. detergents are cheaper to make
D. detergents do not precipitate in hard water


The law of conservation of mass is in
agreement with Dalton's atomic theory.
A. True
B. False


On what sum will the compound
interest at \( 5 \% \) per annually for 2 years compounded annually be \( R s .164 ? \)


\( f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^{2} & 2 x \\ \tan x & x & 1\end{array}\right| . \) The value of
\( \lim _{x \rightarrow 0} \frac{f(x)}{x} \) is equal to
A . 1
B. -
\( c \cdot 0 \)
D. None of these


In the nuclear reaction presented above, the "other particles" might be
A. an alpha particle, which consists of two protons and neutrons
B. two protons
c. one protons and one neutron
D. two neutrons


A block of mass ' \( m^{\prime} \) is kept on the ground as shown in figure. The normal force points :
A . \( u p \)
B. down
c. right
D. left


Let \( \boldsymbol{f}:\{\mathbf{1}, \mathbf{3}, \mathbf{4}\} \rightarrow\{\mathbf{1}, \mathbf{2}, \mathbf{5}\} \) and \( \boldsymbol{g} \)
\{1,2,5\}\( \rightarrow\{1,3\} \)
given by \( \boldsymbol{f}=\{(\mathbf{1}, \mathbf{2}),(\mathbf{3}, \mathbf{5}),(\mathbf{4}, \mathbf{1})\} \) and
\( \boldsymbol{g}=\{(1, \mathbf{3}),(\mathbf{2}, \mathbf{3}),(\mathbf{5}, \mathbf{1})\} \) write down
gof


The diagram shows the displacement-
time graph for a vibrating body. Give an
example of a body producing such
vibrations :


A ball thrown by your friend towards you, undergoes:
A. curvilinear motion
B. linear motion
c. rotational motion
D. projectile motion


The most abundant metal in earth's
crust is:
A . iron
B. magnesium
c. calcium
D. aluminium


Which is/are the correct IUPAC name(s)
of the corresponding structures? This question has multiple correct options
A. 3-(N-Ethylamino)-2-methylcyclohexan-1-ol
B. 3- (2-Aminoethyl)-2-methylcyclohexan-1-ol
c. Methyl 4-chlorocarbonyl-3-cyanobutanoate
D. Cyclohexanal


Write differences between low and high density polymers.


State whether given statement is True or False

Woollen yard is a bad conductor of heat.
A. True
B. False


Which one is not equal to zero for an
ideal solution?
A. \( \Delta V_{\operatorname{mix}} \)
B. \( \Delta P=P_{\text {observed }}-P_{\text {Rooult}} \)
c. \( \Delta H_{\operatorname{mix}} \)
D. \( \Delta S_{\text {mix }} \)


0.4037 g of an organic compound containing \( S \) was treated with conc.
\( H N O_{3} \) in a Carius tube. On
precipitation with \( B a C l_{2} 0.1936 \) g of \( B a S O_{4} \) was 0.35 g. Find the percentage of sulphur.
A . 6.58
B. 7.12
\( c .8 .33 \)
D. 1.67


Carbon monoxide is posionous because
it?
A. Dries up
B. Reduces the organic matter of tissues
c. combines with haemoglobin and causes
deficiency of oxygen in bloodd
D. combines with the
\( O_{2} \) present in blood to form
\( C O_{2} \)


Which will react faster with NBS?
A. \( C_{6} H_{6} \)
в. \( C H_{4} \)
c. Toluene
D. Cyclopropane


\( K_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \) and
\( \left(N H_{4}\right)_{2} S O_{4} \cdot A l_{2}\left(S O_{4}\right)_{3} \cdot 24 H_{2} O \) are:
A. isotopes
B. allotropes
c. isomorphous
D. isomers


In a rectangle \( A B C D(B C=2 A B) \)
the moment of inertia along axis will be
minimum through:
\( A . B C \)
B. \( B D \)
\( c . H F \)
D. \( E G \)


Fill in the blanks with approprite words. A thick-strand of underground hyphae resembling a root is known as....


The standard heat of combustion of
solid boron is equal to:
A. \( \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
(2)
B \( \cdot \frac{1}{2} \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathbf{c} \cdot 2 \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)
\( \mathbf{D} \cdot-\frac{1}{2} \Delta_{f} H^{\circ}\left(B_{2} O_{3}\right) \)


\( \frac{-}{\sigma} \)
of
0
0


Match the column


lonization potential of \( N a \) would be
numerically the same as:
A. electron affiniy of \( N a^{+} \)
B. electronegativity of \( N a^{+} \)
c. electron affiniy of \( H e \)
D. ionization potential of \( M g \)


A brick is kept in three different ways on
a table as shown in Figure. The pressure exerted by the brick on the table will be
A. maximum in position A
B. maximum in position B
c. maximum in position c
D. equal in all cases.


The addition of concentrated \( H N O_{3} \) to
unknown metal produced an brown gas. Identity the gas?
A \( \cdot C l_{2} \)
в. \( H_{2} \)
\( c \cdot O_{2} \)
D. \( C O_{2} \)
E. \( N O_{2} \)


The presence of nematocysts and radially symmetrical body is shown by
A. Porifera
B. Coelenterates
c. Mollusca
D. Amphibians
E. Polychaetes


A chemist while studying the properties
of gaseous \( C_{2} C l_{2} F_{2}, \) a chlorofluorocarbon refrigerant cooled a \( 125 \mathrm{g} \) sample at constant atmospheric pressure of 1.0 atm from 320 to 293 K.
During cooling, the sample volume decreased from 274 to 284 mL.
Calculate \( \Delta H \) and \( \Delta U \) for the
chloroflurocarbon for this process. For
\( \boldsymbol{C a C l}_{2} \boldsymbol{F}_{2}, \boldsymbol{C}_{\boldsymbol{p}}=-\mathbf{8 0 . 7} \boldsymbol{J} / \boldsymbol{m o l} \boldsymbol{K} \)


Copper metal is used in making:
A. electric wires
B. fuse wires
c. filling cavity in teeth
D. preparation of hydrogen


current induced in the loop when arm
PQ is moved with velocity \( 20 \mathrm{m} / \mathrm{s} \)
\begin{tabular}{c|ccccc|cc}
\( \times \mathrm{N} \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \mathrm{P} \times \) & \( \times \) & \\
\hline\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & 0 \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \\
\( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \) & \\
\( \times \mathrm{M} \times \) & \( \times \) & \( \times \) & \( \times \) & \( \times \mathrm{Q} \times \) & \( \times \) &
\end{tabular}


The compound molecular in nature in gas phase but ionic in solid state is :
A. \( P C l_{5} \)
в. \( C C l_{4} \)
c. \( P C l_{3} \)
D. \( P O C l_{3} \)
E. None of the above


Use the principle of mathematical induction to prove that \( \boldsymbol{a}+(\boldsymbol{a}+\boldsymbol{d})+ \)
\( (\boldsymbol{a}+\mathbf{2 d})+\ldots .+[\boldsymbol{a}+(\boldsymbol{n}-\mathbf{1}) \boldsymbol{d}]= \)
\( \boldsymbol{n} / 2[2 \boldsymbol{a}+(\boldsymbol{n}-1) \boldsymbol{d}] \)


The major organic compound formed by the reaction of \( 1,1,1- \) trichloroethane with silver powder is:
A. 2-butyne
B. 2-butene
c. acetylene
D. ethene


Explain, why white light is dispersed when passing through a prism.


Light energy is not used directly or indirectly in which of the following option?
A. Splitting of \( H_{2} O \)
B. To develop proton gradient during photophosphorylation
c. \( C O_{2} \) reduction in dark reaction
D. To develop proton gradient during oxidative photophosphorylation


Which of the following property does not support anamolous behaviour of boron?
A. Small size
B. High electronegativity
c. High ionization energy
D. Formation of trinalides


Prove that
(4,0),(-2,-3),(3,2),(-3,-1)
coordinates are not the vertices of
parallelogram.


The shapes \( \boldsymbol{P C l}_{4}^{+}, \boldsymbol{P C l}_{4}^{-} \) and \( \boldsymbol{A} \boldsymbol{s} \boldsymbol{C l}_{5} \)
are respectively:
A. square planar, tetrahedral and see-saw
B. tetrahedral, see-saw and trigonal bipyramidal
c. tetrahedral, square planar and pentagonal bipyramidal
D. trigonal bipyramidal, tetrahedral and square pyramidal


The plot of \( \frac{1}{X_{A}} \) vs \( \frac{1}{Y_{A}} \) (where \( X_{A} \) and
\( \boldsymbol{Y}_{A} \) are the mole fractions of liquid \( \mathrm{A} \) in liquid and vapour phase, respectively) is linear. The slope and intercept of this plot are respectively:
\( ^{\mathrm{A}} \cdot \frac{P_{d}^{0}}{P_{B}^{0}} \) and \( \frac{P_{A}^{0}-P_{B}^{0}}{P_{B}^{0}} \)
в. \( \frac{P_{d}^{0}}{P_{B}^{0}} \) and \( \frac{P_{B}^{0}-P_{A}^{0}}{P_{B}^{0}} \)
c. \( \frac{P_{B}^{0}}{P_{A}^{0}} \) and \( \frac{P_{A}^{0}-P_{B}^{0}}{P_{B}^{0}} \)
D. \( \frac{P_{B}^{0}}{P_{A}^{0}} \) and \( \frac{P_{B}^{0}-P_{A}^{0}}{P_{B}^{0}} \)


Four cells each of emf \( 1.9 \mathrm{V} \) and the
internal resistance \( 1 \Omega \) are connected to
an external resistance of 18 Omega as shown in the figure. Find the terminal potential difference of this combination


\( \frac{1}{0} \)
\( \frac{\partial}{t} \)


A particle having mass \( 5 \mathrm{kg} \) is moving on a straight line \( y=2 x+4 \) with velocity \( 3 \sqrt{5} \mathrm{m} / \mathrm{s} . \) Find its angular momentum about origin.


Which of the following is not true solidliquid equilibrium?
A. It can be established in any given temperature.
B. The mass of solid does not change in time.
C. The mass of liquid does not change with time.
D. There is no exchange of heat between the system and surrounding.


Frictional force always opposes motion
of a body.
A . True
B. False


Two vectors \( a \) and \( b \) are said to be equal
if
।. \( |\boldsymbol{a}|=|\boldsymbol{b}| \)
Il. they have same or parallel support.
III. the same sense.
Which of the following is true?
A. Onlyı
c. Both I and III
D. All three


A body is hanging from a rigid support by an extensible string of length \( L \). It is struck inelastically by an identical body of mass \( m \) with horizontal velocity \( v= \)
\( \sqrt{2 g l}, \) the tension in the string
increases just after striking by:
A . \( m g \)
в. \( 3 m g \)
c. \( 2 m g \)
D. None of these


Complete the following reactions and
identify the products of above reactions
\( (a) \)


The value of the series \( \frac{1}{3 !}+\frac{2}{5 !}+\frac{3}{7 !}+ \)
to \( \infty \) is equal to
A \( \cdot \frac{1}{2} e \)
в. \( \frac{1}{2 e} \)
\( c \cdot \frac{3}{2 e} \)
D. \( \frac{4}{5 e} \)


Jabu is building a new flower bed and is using a bucket to carry soil from another part of the garden to the new bed. He knows his bucket has a
capacity of 10 litres. If he has 300 litres of soil, and for each trip he fills the bucket to the top, how many trips will Jabu have to make with bucket?
A . 10
B . 20
c. 30
D. 40


A weak mono acidic base is \( 5 \% \) ionized
in \( 0.01 M \) solution. The hydroxide ion
concentration in the solution is:
A. \( 5 \times 10^{-2} \)
В. \( 5 \times 10^{-4} \)
c. \( 5 \times 10^{-10} \)
D. \( 2 \times 10^{-11} \)


Electrolysis of sea-water produces
\( C l_{2}(g) \) at the anode by the oxidation of
Cl (aq) ions. What volume of the gas will be produced at STP by current of \( 1.50 \mathrm{A} \) applied for 90.0 minutes?
B. 0.548 L
c. \( 0.94 \mathrm{L} \)
D. 0.470 L


Assertion: Dipole oscillations produce electromagentic waves, Reason: Accelerated charge produces electromagnetic waves
A. If both assertion and reason are true but the reason is the correct explanation of assertion.
B. If both assertion and reason are true but the reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both the assertion and reason are false
E. If reason is true but assertion is false


What would be the product for the
following reaction?
\( A \cdot P h-C \)
в. \( P h-N_{2} \)
\( c \)
\( D \)


One mole of gas of specific heat ratio 1.5 being initially at temperature \( 290 K \) is adiabatically compressed to increase
its pressure 8 times. The temperature of the gas after compression will be
\( \mathbf{A} \cdot 580 K \)
B. \( 870 K \)
c. \( 290 \sqrt{2} K \)
D. \( 1160 K \)


Assertion
In Rutherford's gold foil experiment, very
few \( \alpha \) -particles are deflected back.
Reason

Nucleus present inside the atom is heavy.
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


Which acts both an oxidizing as well as reducing agent?
A. \( H N O_{3} \)
в. \( H N O_{2} \)
c. \( H_{2} S O_{4} \)
D. \( H C l \)


In an atom, an electron is moving with a
speed of \( 600 m / s \) with an accuracy of \( 0.005 \% . \) Certainty with which the position of the electron can be located
is:
\( \left(h=6.6 \times 10^{-34} k g m^{2} s^{-1} \) mass of \right.
elecrtron \( \left.\boldsymbol{m}_{e}=\mathbf{9 . 1} \times \mathbf{1 0}^{-\mathbf{3 1}} \mathbf{k g}\right) \)
A \( .5 .10 \times 10^{-3} \mathrm{m} \)
В. \( 1.92 \times 10^{-3} \mathrm{m} \)
c. \( 3.84 \times 10^{-3} \mathrm{m} \)
D. \( 1.52 \times 10^{-3} \mathrm{m} \)


The above diagrams show the electric field lines of charged particles. Identify which of the following drawing represents field lines between two
parallel plates?
A. Drawing
B. Drawing II
c. Drawing III
D. Drawing IV
E. Drawing V


\( \operatorname{Let} \phi(\boldsymbol{x})=\frac{\boldsymbol{b}(\boldsymbol{x}-\boldsymbol{a})}{\boldsymbol{b}-\boldsymbol{a}}+\frac{\boldsymbol{a}(\boldsymbol{x}-\boldsymbol{b})}{\boldsymbol{a}-\boldsymbol{b}}, \) where
\( x \in R \) and \( a \) and \( b \) are fixed real numbers
with \( a \neq b . \) Then \( \phi(a+b) \) is equal to:
A. \( \phi(a b) \)
(i)
в. \( \phi(-a b) \)
\( \mathbf{c} \cdot \phi(a) \mid \phi(b) \)
D. \( \phi(a-b) \)
E \( . \phi(0) \)


\( \left|\begin{array}{ccc}\mathbf{0} & \boldsymbol{p}-\boldsymbol{q} & \boldsymbol{p}-\boldsymbol{r} \\ \boldsymbol{q}-\boldsymbol{p} & \boldsymbol{0} & \boldsymbol{q}-\boldsymbol{r} \\ \boldsymbol{r}-\boldsymbol{p} & \boldsymbol{r}-\boldsymbol{q} & \boldsymbol{0}\end{array}\right| \) is equal to
A. \( p+q+r \)
B.
c. \( p-q-r \)
\( \mathbf{D} \cdot-p+q+r \)


A flooring tile has the shape of a parallelogram whose base is \( 24 \mathrm{cm} \) and
the corresponding height is \( 10 \mathrm{cm} . \) How many such tiles are required to cover a
floor of area \( 1080 m^{2} ? \)
A . 45,000
B. 75,000
c. 40,000
D. 45,00


Which of the following phosphorus is the most reactive?
A. Red phosphorus
B. White phosphorus
c. Scarlet phosphorus
D. Violet phosphorus


A sphere of constant radius \( 2 k \) passes
through the origin and meets the axes in \( A, B, C . \) The locus of the centroid of
the tetrahedron \( \boldsymbol{O} \boldsymbol{A} \boldsymbol{B} \boldsymbol{C} \) is
A \( \cdot x^{2}+y^{2}+z^{2}=4 k^{2} \)
B \cdot \( 9\left(x^{2}+y^{2}+z^{2}\right)=4 k^{2} \)
C . \( x^{2}+y^{2}+z^{2}=k^{2} \)
D. None of these


A rectangular loop of resistance \( \mathrm{R} \) and sides I and \( x \) is pulled out of a uniform magnetic field B with a steady velocity
v. The necessary force F required for maintaining uniform velocity of withdrawal is
A. \( B x l^{2} v / R \)
B \( \cdot B^{2} l^{2} v / R \)
c \( \cdot B^{2} l^{2} v^{2} / R \)
D. zero


When does an electric dipole placed in a uniform electric field experience
a. Maximum Torque
b. Minimum Torque


A body moves through a distance of \( ^{\prime} \boldsymbol{m}^{\prime} \)
in the following different ways. In which case is the maximum work done?
A. when pushed over an inclined plane
B. when lifted vertically upward
c. when pushed over smooth rollers
D. when pushed on a plane horizontal surface


The time period of oscillation of a particle, that executes SHM, is \( 1.2 s \). The time, starting from mean position, at which its velocity will be half of its velocity at mean position is?
A . \( 0.1 s \)
B. \( 0.2 s \)
\( c .0 .4 s \)
D. \( 0.6 s \)


The colour of sky is due to:
A. transmission of light
B. wavelength of scattered light
C. absorption of light by atmospheric gases
D. all of these


Evaluate \( \int \frac{1}{a^{x} b^{x}} d x \)


Match the following
List - I 1 \( t-1 \) The in
a) Relative velocity
and separation are approach e) Interaction
between bodies sity of app
are same
b) Bodies stick together
f) Newton's ॥I 1 law
\( c \)
Force g) Coefficient
of restitution \( = \)
1 1
d) Recoil of the gun h) Coefficient
of restitution \( = \)
0
¡) Binding
energy A er
\( A \cdot a-g ; b-h ; c-e ; d-f \)
B. \( a-h ; b-g ; c-f ; d-e \)
\( C \cdot a-g ; b-e ; c-f ; d-h \)
D. \( a-e ; b-f ; c-g ; d-i \)


Which oxide has three dimensional
strucutre?
A \( \cdot C O_{2} \)
в. \( S O_{2} \)
\( c \cdot c o \)
D. \( \operatorname{si} 0_{2} \)


Assertion
The complex ion \( \left[C o(e n)_{2} B r_{2}\right]^{-} \) has
three stereoisomers.
Reason
The complex ion \( \left[C o(e n)_{2} B r_{2}\right]^{-} \) has an
octahedral geometry.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A passenger in a train moving at an acceleration 'a', drops a stone from the
window. A person, standing on the ground, by the sides of the rails, observes the ball following:
A. Vertically with acceleration \( \sqrt{g^{2}+a^{2}} \)
B. Horizontally with an acceleration \( \sqrt{g^{2}+a^{2}} \)
C. Along a parabola with acceleration \( \sqrt{g^{2}+a^{2}} \)
D. Along a parabola with acceleration 'g"


If the angle \( \alpha \) lies in the first quadrant
and \( \tan \alpha+\cot \alpha=2, \) then the value
of \( \sqrt{\tan \alpha}+\sqrt{\cot \alpha} \) is
A . -4
B. - -
\( c \cdot 2 \)
D. 4


Which one of the following is s-butyl
phenyl vinyl methane?
\( A \)
B.
\( c \)
\( D \)


A short bar Magnet with its north pole facing North forms a neutral point P in the horizontal plane. If the magnet is rotated by \( 90^{0} \) in the horizontal plane, the net magnetic induction at \( \mathrm{P} \) is:
(Horizontal component of earths
magnetic field is \( B_{H} \) )
A. 0
в. \( 2 B_{H} \)
c. \( \frac{\sqrt{5}}{2} B_{H} \)
D. \( \sqrt{5} B_{H} \)


If \( \frac{(p+i)^{2}}{2 p-i}=\mu+i \lambda, \) then \( \mu^{2}+\lambda^{2} \) is
equal to
\( ^{A \cdot} \cdot \frac{\left(p^{2}+1\right)^{2}}{4 p^{2}-1} \)
B. \( \frac{\left(p^{2}-1\right)^{2}}{4 p^{2}-1} \)
c. \( \frac{\left(p^{2}-1\right)^{2}}{4 p^{2}+1} \)
D. \( \frac{\left(p^{2}+1\right)^{2}}{4 p^{2}+1} \)


One half of a convex lens of focal length \( 10 \mathrm{cm} \) is covered with a black paper.can such a lens produce an image of a complete object placed at a distance of \( 30 \mathrm{cm} \) from the lens? Draw a ray
diagram to justify your answer. A \( 4 \mathrm{cm} \) tall object is placed perpendicular to its principal axis of a convex lens of focal length \( 20 \mathrm{cm} . \) The distance of the object from the lens is \( 15 \mathrm{cm} \). Find the nature, position and the size of the
image.


You are sitting in a room in which a strong magnetic field is directed from your left towards right. A beam of electrons is directed from front towards
you. What would be the direction of
magnetic force on this beam?
A. downwards
B. upwards.
c. towards right
D. towards left


Give one example each of the following types of motion:
(a) Linear
(b) Translation
(c) Circular (d)
Periodic


Give two uses of Infrared Rays.


Sum of molecular mass of gas:
A . 23
B. 56
c. 48
D. none of these


Two absolute scales \( A \) and \( B \) have triple points of water defined to be \( 200 \mathrm{A} \) and
350 B. What is the relation between \( \boldsymbol{T}_{\boldsymbol{A}} \)
and \( T_{B} ? \)


Heating of pyrites to remove sulphur is called as
A. roasting
B. calcination
c. smelting
D. froth-floatation


Cobalt chloride acts as a calalyst, in the decomposition of bleaching powder.
A. True
B. False


Evaluate: \( \int_{0}^{\pi / 4} \log (1+\tan \theta) d \theta \)


Nickel (atomic number \( =28 \) amu)
combines with a uninegative
monodentate ligand \( X^{-} \) to form a
paramagnetic complex \( \left[N i X_{4}\right]^{2-} . \) The number of unpaired electron(s) in nickel and the geometry of this complex ion are respectively:
A. two, square planar
B. one, tetrahedral
c. two, tetrahedral
D. one, square planar


\( B i C l_{3} \) on hydrolysis forms a white
precipitate of :
A. bismuth acid
B. bismuth oxychloride
c. bismuth pentachloride
D. bismuth hydride


Without using distance formula, show that points (-2,-1),(4,0),(3,3) and (-3,2) are the vertices of a parallelogram


The most basic rule of dimensional
analysis is that of dimensional homogeneity. Only commensurable quantities may be
A. compared
B. equated
c. added or subtracted
D. all of the above


The \( p H \) of \( 0.1 M \) solution of the
following salts increases in the order:
A \( \cdot \operatorname{NaCl}<N H_{4}^{+}<N a C N<H C l \)
в. \( H C l<N H_{4}^{+}<N a C l<N a C N \)
c. \( \operatorname{NaCN}<N H_{4}^{+}<N a C l<H C l \)
D. \( H C l<N a C l<N a C N<N H_{4} \)


An AC source is connected in parallel
with an L-C-R circuit as shown. Let
\( I_{S}, I_{L}, I_{C} \) and \( I_{R} \) denote the currents
through and \( V_{S}, V_{L}, V_{C} \) and \( V_{R} \)
voltages across the corresponding
components. Then:
A \( \cdot I_{S}=I_{L}+I_{C}+I_{R} \)
В. \( V_{S}=V_{L}+V_{C}+V_{R} \)
\( \mathbf{c} \cdot\left(I_{L}, I_{C}, I_{R}\right)<I_{S} \)
D. \( I_{L}, I_{C} \) may be greater than \( I_{S} \)


In which of the following situations will a fuse possibly melt? This question has multiple correct options
A. The earth wire is broken
B. There is a short circuit in the electrical circuit
c. The fuse is fixed along the neutral wire instead of the live wire
D. The fuse wire is connected to earth wire


What will come in place of the question mark (?) in the following question? \( 65 \% \) of \( 240+x \% \) of \( 150=210 \)
\( \mathbf{A} \cdot 45 \)
B. 46
c. 32
D. 36
E. None of these


The characteristic properties of an acid is due to the presence of
A. hydride ions
B. hydroxyl ions
c. hydronium ions
D. oxide ions


Which of the following is the correct description of \( C ? \)
A. It is ethanolic acid
B. It is 2-hydroxy ethanal
c. It is 2 -hydroxy oxirane
D. It can be either \( B \) or \( C \)


An electric heater has resistance 150
ohms and can bear a maximum current
of 1 ampere. If the heater is to be used
on 220 volt mains, the least resistance
required in the circuit will be
A. 70 ohms
B. 5 ohms
c. 2.5 ohms
D. 1.4 ohms


Solid \( P C l_{5} \) exists as:
A \( \cdot P C l_{5} \)
B \( \cdot P C l_{4}^{+} \)
c. \( P C l_{6} \)
D. \( P C l_{4}^{+} \) and \( P C l_{6}^{-} \)


In a meter bridge experiment the null deflection is obtained at a length of 25cm. When a standard resistance of 5
ohm is employed. The value of resistance in the left gap is
A . \( 2 \Omega \)
B. \( 1.66 \Omega \)
\( c \cdot 4 \Omega \)
D. \( 1.2 \Omega \)


Solve : \( \int \frac{x^{2}+1}{(x+1)^{2}} d x \)


A step-up transformer of turns ratio 2
1 has \( 50 H z A C \) voltage applied to
primary. The frequency of \( A C \) output
voltage across secondary is
A. zero
B. \( 25 H z \)
\( \mathbf{c} .50 H z \)
D. \( 100 H z \)


If \( (x, y)=(3,5) ; \) then values of \( x \) and \( y \)
are
A. 3 and
B. 4 and 7
c. -1 and 17
D. 2 and 4


The reaction of slaked lime with \( C l_{2} \) gas
gives:
A. only \( C a O C l_{2} \)
B. only \( C a C l_{2} \)
C. a mixture of \( C a(O C l)_{2}, C a(O H)_{2}, C a C l_{2} \) and \( H_{2} O \)
D. quick lime


The probability of finding the electron in
\( p_{x} \) -orbital is:
This question has multiple correct options
A. maximum on two opposite sides of the nucleus along x-axis
B. zero at the nucleus
c. same on all the sides around the nucleus
D. zero on the z-axis


Which one of the following is the unit of compressibility
A \( \cdot m^{3} / N \)
B . \( m^{2} / N \)
\( \mathrm{c} \cdot m^{2}-N \)
D. \( m / N \)


Which one of the following shows highest magnetic moment?
A \( \cdot F e^{2} \)
в. \( C o^{2} \)
\( c \cdot C r^{3} \)
D. \( N i^{2} \)


\( \angle A \) and \( \angle B \) are liner pair of angles. If
\( 4 \angle A=5 \angle B . \) then find \( \angle A \) and \( \angle B \)


Three equal cubes are placed in a row touching each other Find the ratio of the
total surface area of the resulting cuboid to that of the sum of surface
areas of the three cubes
A . 5: 7
B. 7:9
c. 9: 7
D. None of these


When the velocity of a body is doubled
A. kinetic energy is doubled
B. acceleration is doubled
c. momentum is doubled.
D. potential energy is doubled


Equal mass which of the following substance of occupy maximum volume
at room temperature?
A . Sugar
B. water
c. oxygen
D. Graphite


Which of the following organisms reproduces by budding?
A. Plasmodium
B. Planaria
c. Paramecium
D. Hydra


In a fuel cell \( H_{2} \) and \( O_{2} \) react to produce
electricity. In the process \( H_{2} \) gas is
oxidised at the anode and \( O_{2} \) is reduced
at the cathode. If 67.2 litre of \( H_{2} \) at
NTP reacts in 15 minute, what is the
average current produced? If the entire current is used for electro-deposition of \( C u \) from \( C u^{2+}, \) how many \( g \) of \( C u \) are deposited?


Which of the following method is used
for separation of different components of petroleum?
A. Fractional distillation
B. Sublimation
c. chromatography
D. simple distillation


In an experiment starting with 1 mole of ethyl of alcohol, 1 mole of acetic acid
and 1 mole of water at \( 100^{\circ} \mathrm{C} \), the
equilibrium mixture on analysis shows that \( 54.3 \% \) of the acid is esterified.
Calculate the equilibrium constant of this reaction.


A bag contains \( (2 n+1) \) coins. It is
known that \( n \) of these coins have a head
on both sides, whereas the remaining \( n+1 \) coins are fair. A coin is picked up
at random from the bag and tossed. If the probability that the toss results in a head is \( \frac{31}{42}, \) then \( n \) is equal to
A . 10
B. 11
c. 12
D. 13


Find the value of \( \operatorname{cosec}^{2} 60^{\circ}-\tan ^{2} 30^{\circ} \)


\( 0^{2} \)
\( \sigma \)
\( \sigma \)
\( \sigma \)
\( \sigma^{c} \)


If \( \vec{a} \) be the position vector whose tip is \( (5,-3), \) find the coordinates of a point \( B \) such that \( \overrightarrow{A B}=\vec{a}, \) the coordinates of \( A \)
being (4,-1)
A. (9,-4)
B. (-9,-4)
\( c \cdot(9,4) \)
D. none of these


Which of the following carboxylic acids is a tricarboxylic acid?
A . Oxalic acid
B. Citric acid
c. succinic acid
D. Adipic acid


The ratio of mass percent of \( C \) and \( H \) of
an organic compound \( \left(C_{X} H_{Y} O_{Z}\right) \) is
\( \mathbf{6}: 1 . \) If one molecule of the above
compound \( \left(C_{X} H_{Y} O_{Z}\right) \) contain half as much oxygen as required to burn one
molecule of compound \( C_{X} H_{Y} \)
completely to \( C O_{2} \) and \( H_{2} O . \) The
empirical formula of compound
\( C_{X} H_{Y} O_{Z} \) is :
A \( \cdot C_{3} H_{4} O_{2} \)
в. \( C_{2} \) Н \( _{4} \) О \( _{3} \).
\( \mathrm{c} \cdot C_{3} H_{6} O_{3} \)
D. \( C_{2} H_{4} O \)


Complete the following:
\[
N a_{2} S+N a_{2} F e(C N)_{5} N O \rightarrow
\]


Any vector in an arbitrary direction can always be replaced by two (or three)
A. parallel vectors which have the original vector as their resultant
B. mutually perpendicular vectors which have the original vector as their resultant.
c. arbitrary vectors which have the original vector as their resultant
D. it is not possible to resolve a vector.


An electron is moving in \( 2^{n d} \) excited orbit of H-atom Radius of orbit in terms
of de-Broglie wavelength \( \lambda \) of electron can be given as
\( A \cdot \frac{\lambda}{\pi} \)
в. \( \frac{2 \lambda}{\pi} \)
c. \( \frac{3 \lambda}{2 \pi} \)
D. \( \frac{\lambda}{2 \pi} \)


If the second term of the expansion \( \left[\boldsymbol{a}^{1 / 13}+\frac{\boldsymbol{a}}{\sqrt{\boldsymbol{a}^{-1}}}\right]^{n} \quad \boldsymbol{i s} 14 \boldsymbol{a}^{5 / 2}, \) then the
value of \( \frac{n_{\mathbf{S}}}{n_{\mathbf{C}_{2}}} \) is
A .4
B. 3
c. 12
D. 6


Ozone is a
A. mild oxidizing agent
B. powerful oxidizing agent
C . powerful reducing agent
D. mild reducing agent


If \( \tan A=\frac{1}{2} \) and \( \tan B=\frac{1}{3}, \) then the
value of \( \boldsymbol{A}+\boldsymbol{B} \) is
A \( \cdot \frac{\pi}{6} \)
в. \( \pi \)
c. zero
D.


Select the correct statement.
A. The charge to mass ratio of the particles in anode rays depend on the gas present in the tube
B. Behavior of cathode rays particle and anode rays particle are same in presence of magnetic field (in terms of extent of deviations)
C. Cathode and anode rays start from cathode and anode respectively
D. The charge to mass ratio of the particle in cathode rays depends on the voltage applied across the terminal


If \( x=\frac{1}{x-5}, \) find
\( x^{2}+\frac{1}{x^{2}} \)
A . 34
B. 65
\( c \cdot 13 \)
D. 27


Which of the following is a non-metallic conductor:
A . cs
B. coke
c. diamond
D. graphite


If \( |\boldsymbol{A}|=\mathbf{3} \) and \( \boldsymbol{A}^{-1}=\left[\begin{array}{cc}\mathbf{3} & -\mathbf{1} \\ -\mathbf{5} & \mathbf{2} \\ \hline \mathbf{3} & \mathbf{3}\end{array}\right] \) then
\( \boldsymbol{a} \boldsymbol{d} \boldsymbol{j} \boldsymbol{A}=? \)
\( \mathbf{A} \cdot\left[\begin{array}{cc}9 & 3 \\ -5 & -2\end{array}\right] \)
В. \( \left[\begin{array}{cc}9 & -3 \\ -5 & 2\end{array}\right] \)
\begin{tabular}{lll}
C. \( \left[\begin{array}{cc}-9 & 3 \\
5 & -2\end{array}\right] \) \\
\hline
\end{tabular}
D. \( \left[\begin{array}{cc}9 & -3 \\ 5 & -2\end{array}\right] \)


Two tangent galvanometers A and B are identical except in their number of turns. They are connected in series. On passing a current through them,
deflections of \( 60^{\circ} \) and \( 30^{\circ} \) are produced.
The ratio of the number of turns in \( A \)
and B is
A . 1: 3
B. 3: 1
c. 1: 2
D. 2: 1


If \( z=\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}, \) then
A \( \cdot|z|=1, \arg z=\frac{\pi}{4} \)
в \( \cdot|z|=1, \arg z=\frac{\pi}{6} \)
с. \( \quad|z|=\frac{\sqrt{3}}{2}, \arg z=\frac{5 \pi}{24} \)
D. \( \quad|z|=\frac{\sqrt{3}}{2}, \arg z=\tan ^{-1} \frac{1}{\sqrt{2}} \)


Physiologically functional part of wood
is?
A. Heart wood only
B. Sap wood only
c. only primary woodd
D. Both of heart wood and sap woodd


At a place, the angle of dip is \( 30^{0} . \) If the horizontal component of earth's field is
\( B_{H}, \) then the net field intensity at the place will be :
A \( \cdot \frac{B_{H}}{2} \)
в. \( \frac{2 B_{H}}{\sqrt{3}} \)
c. \( B_{H} \sqrt{2} \)
D. \( B_{H} \sqrt{3} \)


Identify to which type does the following complex reaction belong to:
isomeristaion of cyclopropane


The number of lines of symmetry in a regular pentagon is
A . 3
B. 4
\( c .5 \)
\( D \)


A series battery of six lead accumulators, each of emf \( 2.0 \mathrm{V} \) and
internal resistance \( 0.50 \Omega \) is charged by
a \( 100 \mathrm{V} \) dc supply. The series resistance should be used in the charging circuit in order to limit the current to
8.0A is
A . \( 4 \Omega \)
B. \( 6 \Omega \)
\( c .8 \Omega \)
D. \( 10 \Omega \)


One of the following did not work on
gases:
A. Avogadro
B. Boyle
c. charles
D. Faraday


Fig. shows a water heater in which water is heated by a gas burner from below. A and B are two pipes.(i) Name the pipe used as inlet for cold water. (ii) Name the pipe used as outlet for hot
water
(iii) Show the direction of
convection currents in the diagram so as to obtain hot water continuously.


What is a hole? Which type of doping
creats a hole?


Which of the following compounds is an example of homologous series of alcohols?
A. \( C H_{3} O H \)
в. \( C H_{3} C H_{2} \) ОН
c. \( C H_{3} C H_{2} C H_{2} O H \)
D. All of the above


Identify the statement which best describe transfer of electrical energy through a conductor.
A. It happens at nearly the speed of light
B. It happens slower than a leisurely walking pace
c. It is slower than the movement of the electrons in the conductor
D. It happens when marbles enter the conductor
E. It happens when marbles exit the conductor


A cell of emf \( 6 V \) is being charged by \( 1 A \) current. If the internal resistance of the
cell is 1 ohm, the potential difference across the terminals of the cell is
A . \( 5 V \)
в. \( 7 V \)
\( c .6 V \)
D. 8V


An LC circuit contains a \( 40 \mathrm{mH} \) inductor
and a \( 25 \mu \) F capacitor. The resistance of the circuit is negligible. The time is measured from the instant the circuit
is closed. The energy stored in the circuit is completely magnetic at times (in milliseconds)
A . 0,3.14,6.28
B. 0, 1.57, 4.71
c. 1.57,4.71,7.85
D. 1.57, 3.14, 4.71


Solve: \( \lim _{x \rightarrow 2} \frac{e^{x^{2}}-\cos x}{x^{2}} \)


ff \( y=e^{4 x}+2 e^{-x} \) satisfies the equation
\( \boldsymbol{y}_{3}+\boldsymbol{A} \boldsymbol{y}_{1}+\boldsymbol{B} \boldsymbol{y}=\mathbf{0} \) then the value of
\( A B \) is


\( \frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}= \)
\( \mathbf{A} \cdot \frac{\cos \theta}{1+\sin \theta} \)
B. \( \frac{1+\cos \theta}{\sin \theta} \)
\( \mathbf{C} \cdot \frac{1+\sin \theta}{\cos \theta} \)
D. \( \frac{1-\sin \theta}{\cos \theta} \)


A smooth sphere (mass \( 10 \mathrm{kg} \)
negligible radius) moves on a smooth
curved surface from the point with a
speed of \( 10 \mathrm{m} / \mathrm{s} \) as shown in figure. The
sphere reaches the point D passing
through point B. If the ground is taken
as reference, Then \( \left[\boldsymbol{g}=\mathbf{1 0 m} / \boldsymbol{s}^{2}\right] \)
This question has multiple correct options
A. The total mechanical energy of the sphere at point A is zero
B. The total mechanical energy of the sphere at the point A is 2500 J
C. The kinetic energy at point B is 2500 J
D. The notential energy at point B is 0 J


Marine algae flourished well during which of the following period?
A. Triassic
B. Devonian
c. Permian
D. Ordovician


Hill reaction occurs in
A. High altitude plants
B. Total darkness
C. Absence of water
D. Presence of ferricyanide


Two identical wires \( A \) and \( B \), each of
length \( l \), carry the same current \( l \). Wire
\( A \) is bent into a circle of radius \( R \) and
wire \( B \) is bent to form a square of side \( a \)
If \( B_{A} \) and \( B_{B} \) are the values of
magnetic field at the centres of the circle and square respectively, then the ratio \( \frac{B_{A}}{B_{B}} \) is:
A \( \cdot \frac{\pi^{2}}{16 \sqrt{2}} \)
в. \( \frac{\pi^{2}}{16} \)
c. \( \frac{\pi^{2}}{8 \sqrt{2}} \)
D. \( \frac{\pi^{2}}{8} \)


Use factor theorem to find if \( x+\sqrt{2} \) is a
factor of \( 2 \sqrt{2} x^{2}+5 x+\sqrt{2} \)


Which of the following is a good conductor of heat?
A. Plastic
B. Mercury
c. water
D. Alcohol


The physical quantity which has the dimensional formula as that of
\( \frac{\text {energy}}{\text {mass} \times \text {length}} \) is:
A. Force
B. Power
c. Pressure
D. Acceleration


AD bisects angle \( A \) of triangle \( A B C \) where D lies on BC and angle \( \mathrm{C} \) is greater than angle B. then angle ADB is greater than angle ADC.
A . True
B. False


Mendel studied the inheritance
patterns of 12 different pairs of
characters of the pea plant. He could
ascertain the independent assortment
for only 7 of these 12 pairs of characters
by repeated experiments. What can be
deduced from this?
A. The pea plant could have atleast seven pairs of chromosomes.
B. The pea plant can have a maximum of seven pairs of chromosomes.
C. The pea plant has exactly seven pairs of chromosomes.
D. The pea plant can have haploid chromosome number between 7 and 12 only.


The two acids present in Chlorine water
are:
A \( \cdot \) нс।, \( H_{2} S O_{4} \)
в. нс।, \( H N O_{3} \)
c. нС।, нос।
D. нсI, \( H C l O_{4} \)


When the nucleus of an atom is
smashed it releases energy. This energy is commonly called:
A. heat energy
B. light energy
c. chemical energy
D. nuclear energy


Observe the following compound and
answer questions given below
Degree of unsaturation in above
compound is:
\( A \)
\( B \)
\( c \)
D. 10


Find \( \boldsymbol{A} \) or \( \boldsymbol{B} \)


Explain emission and absorption
spectra


Natesh borrowed some money at rate \( 6 \% \) p.a.for the first 3 years, \( 9 \% \) p.a.for the next five years and 13 p.a. beyond 8 years. The above are all simple interest
rates. If Natesh pays a total of Rs. 8160
as an interest after 11 years, how much money did he borrow?
A . Rs. 8000
B. Rs. 10000
c. Rs. 12000
D. Rs. 14000


Cork is used for insulation and acts as
shock absorber because
A. It is porous
B. It is very hard
c. It is light and does not catch fire easily
D. The cells of cork are living


Evaluate : \( \int_{-1}^{1} \frac{1}{x^{2}+2 x+5} d x \)


What are fossils?


A physicist works in a laboratory where
the magnetic field is 2 T. She wears a
silver necklace enclosing an area 100
\( c m^{2} \) of field and having a resistance of
\( 0.1 \Omega . \) Because of power failure, the
field decays to \( 1 T \) in millisecond. The
electric charge circulated in the
necklace assuming that the magnetic field is perpendicular to area covered by the necklace is
\( \mathbf{A} \cdot 0.01 C \)
в. \( 0.001 C \)
c. \( 0.1 C \)
D. \( 1.0 C \)


The solution of the differential equation
\( \boldsymbol{y}^{\prime}=\frac{\mathbf{1}}{e^{-\boldsymbol{y}}-\boldsymbol{x}}, \) is
\( \mathbf{A} \cdot x=e^{-y}(y+c) \)
B . \( y+e^{-y}=x+c \)
C \( . x=e^{y}(y+c) \)
D. \( x+y=e^{-y}+c \)


The simple interest of a certain sum of money \( R s .61 \) at rate of \( 5 \% \) p.a.for 3 years is


Papillary muscles are found in mammalian
A. Auricles
B. Ventricles
c. Pinna
D. Eyes


\( f\left(\alpha, \beta \text { are the roots of } x^{2}+x+1=0\right. \)
\( \operatorname{then}\left|\begin{array}{ccc}\boldsymbol{y}+\mathbf{1} & \boldsymbol{\beta} & \boldsymbol{\alpha} \\ \boldsymbol{\beta} & \boldsymbol{y}+\boldsymbol{\alpha} & \mathbf{1} \\ \boldsymbol{\alpha} & \mathbf{1} & \boldsymbol{y}+\boldsymbol{\beta}\end{array}\right|=? \)
A \( \cdot y^{2}-1 \)
В . \( y\left(y^{2}-1\right) \)
c. \( y^{2}-y \)
D. \( y^{3} \)


Let us consider emission of \( \alpha \) -particle
from uranium nucleus:
\( \mathbf{9}_{2} \boldsymbol{U}^{2 \mathbf{3 5}} \rightarrow_{\mathbf{2}} \boldsymbol{H} \boldsymbol{e}^{\mathbf{4}} \rightarrow \mathbf{9 0} \boldsymbol{T} \boldsymbol{h}^{\mathbf{2 3 1}} \)
\( \boldsymbol{e}=\mathbf{9 2} \quad \boldsymbol{e}=\mathbf{0} \quad \boldsymbol{e}=\mathbf{9 0} \)
\( \boldsymbol{p}=\mathbf{9 2} \quad \boldsymbol{p}=\mathbf{2} \quad \boldsymbol{p}=\mathbf{9 0} \)
\( \boldsymbol{n}=\mathbf{1 4 3} \quad \boldsymbol{n}=\mathbf{2} \quad \boldsymbol{n}=\mathbf{1 4 1} \)
Shortage of two electrons in thorium is
due to:
This question has multiple correct options
A. conversion of electron to positron
B. combination with positron to evolve energy
c. annihilation
D. absorption in the nucleus


Describe the fluid mosaic model of
plasma membrane.


What is amphimixis?
A. A fusion of pronuclei of male gametes.
B. A fusion of pronuclei from male and female gametes.
C. A fusion of pronuclei of female gametes.
D. The development of a somatic cell into an embryo.


The area bounded by the line \( x=1 \) and the curve \( \sqrt{\frac{\boldsymbol{y}}{\boldsymbol{x}}}+\sqrt{\frac{\boldsymbol{x}}{\boldsymbol{y}}}=\mathbf{4} \) is
A \( .2 \sqrt{3} \)
B. \( \sqrt{3} \)
c. \( 3 \sqrt{2} \)
D. \( 4 \sqrt{3} \)


\( \boldsymbol{H}_{3} \boldsymbol{C}-\boldsymbol{C H}_{2}-\stackrel{\boldsymbol{C}}{\boldsymbol{C}}=\boldsymbol{C} \boldsymbol{H}-\underset{\boldsymbol{C}_{2} \boldsymbol{H}_{5}}{\boldsymbol{C} \boldsymbol{H}} \)
\( C H_{3} \)
\( \boldsymbol{C H}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{2}-\boldsymbol{C H}_{3} \)
The correct IUPAC name of the
compound:
A. 5-Ethyl-3, 6-dimethylnon-3-ene
B. 5-ethyl-4,7-dimethyl non-3-ene
c. 4 -methyl-5, 7-diethyloct-2-ene
D. 2,4-ethyl-5-methyl oct-2-ene


Which of the following options is correct?
(1) Every integer and fraction is a rational number.
(2) A rational number \( \frac{p}{q} \) is positive if \( p \)
and \( q \) are either both positive or both negative.
(3) A rational number \( \frac{p}{q} \) is negative if one of \( p \) and \( q \) is positive and other is
negative.
(4) If there are two rational numbers
with same denominator, then the one
with the larger numerator is larger numerator is larger than the other.
A. Both 1 and 4 are incorrect
B. Both 2 and 3 are incorrect
c. only 1 is correct
D. All are correct


The distinction between conductors,
insulators and semiconductors is
largely concerned with
A. their ability to conduct current
B. the type of crystal lattice
c. binding energy of their electrons
D. relative widths of their energy gaps


When the bob of a simple pendulum swings, the work done by tension in the string is?
\( \mathbf{A} \cdot>0 \)
B . \( <0 \)
c. zero
D. maximum


Match the column
1. Common salt
a. magnetic separation
2. lodine in chloroform
b. alcohol and water
3. Separating funnel \( \quad \) c. evaporation
4. Fractional
d. liquid-liquid distillation
A. \( 1-\mathrm{c}, 2-\mathrm{a}, 3-\mathrm{d}, 4-\mathrm{b} \)
B. 1-c, 2-d, 3-a, 4-b
c. \( 1-d, 2-c, 3-b, 4-a \)
D. \( 1-b, 2-c, 3-d, 4-a \)


Assertion
In the three cases shown in the figure,
force exerted by liquid on three vessels
is the same.
Reason
Pressure at the bottom in each case is
same.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


A man marks his goods at a price that would give him \( 20 \% \) profit. He sells \( \frac{3}{5} \) of the goods at the marked price and sells the remaining at \( 20 \% \) discount. Find his gain percent on the whole transaction
A . \( 10.4 \% \)
В. \( 12.7 \% \)
c. \( 15.6 \% \)
D. \( 14.36 \% \)


Ratio of hydrogen to oxygen in water is:
A .2: 1
B. 1: 2
\( c \cdot 7: 1 \)
D. 8: 1


Ammonia reacts with excess of chlorine
to form :
A \( . N_{2}+N H_{4} C l \)
B. \( N C l_{3} \) and \( H C l \)
c. \( N H_{4} C l \) and \( N C l_{3} \)
D. \( N_{2} \) and \( H C l \)


Enzymes normally have
A. Same pH and temperature optima
B. Same pH but different temperature optima
C. Different pH but same temperature optima
D. Different \( \mathrm{pH} \) and temperature optima


During \( S_{N} 1 \) reactions, the leaving
group leaves the molecule before the
incoming group is attached to the molecule
A. True
B. False


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


\( T i^{3+} \) is more easily reduced than \( C o^{3+} \)
If true enter 1 , else enter 0 .


The number of electrons in an element
\( X \) is 15 and the number of neutrons is
16. The element can be represented as:
A. \( 31_{X} \)
\( 15^{X} \)
в. \( 31_{X} \)
\[
16^{\text {月 }}
\]
D. 15
\( 16^{X} \)


The value of \( \theta \) of mean value theorem for
the function \( f(x)=a x^{2}+b x+c \) in
[1,2] is
\( A \cdot \frac{3}{2} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{4} \)
D.


Tangents are drawn to the ellipse \( \frac{x^{2}}{9}+ \) \( \frac{y^{2}}{5}=1 \) at the ends of both latus
rectum. The area of the quadrilateral so formed is
A. 27 sq.units
B. \( \frac{13}{2} \) sq.units
c. \( \frac{15}{4} \) sq.units
D. 45 sq.units


A force of 50 dynes is acted on a body of mass \( 5 g \) which is at rest for an interval
of \( 3 s, \) then impulse is:
A. \( 0.15 \times 10^{-13} \mathrm{Ns} \)
В. \( 0.98 \times 10^{-3} N s \)
\( \mathrm{c} \cdot 1.5 \times 10^{-3} \mathrm{Ns} \)
D. \( 2.5 \times 10^{-3} N s \)


The length, breadth and thickness of a
rectangular lamina are \( 1.024 m, 0.56 m \)
and 0.0031 m. The volume, in \( m^{3}, \) is:
A \( .1 .8 \times 10^{-3} \)
В. \( 1.80 \times 10^{-3} \)
c. \( 0.180 \times 10^{-4} \)
D. 0.00177


Two balls are dropped from the same
height from places \( A \) and \( B \). The body at
\( B \) takes two seconds less to reach the
ground at \( B \) strikes the ground with a
velocity greater than at \( A \) by \( 10 m / s \) The product of the acceleration due to gravity at the two places \( A \) and \( B \) is:
A . 5
B . 25
c. 125
D. 12.5


A radio-controlled toy car travels along a
straight line for a time of \( 15 s \). The
variation with time \( t \) of the velocity v of the car is shown.

What is the average velocity of the toy
car for the journey shown by the graph?
A. \( -1.5 m s^{-1} \)
B. \( 0.0 m s^{-1} \)
c. \( 4.0 m s^{-1} \)
D. \( 4.5 m s^{-1} \)


If \( 3 \vec{a}+4 \vec{b}-7 \vec{c}=0 \) then the ratio in
which \( C(\vec{c}) \) divides the join of \( \boldsymbol{A}(\overrightarrow{\boldsymbol{a}}) \) and \( B(\vec{b}) \) is
A .1: 2
B. 2: 3
\( c \cdot 3: 2 \)
D. 4: 3


When cells are connected in series
greater emf is obtained in the circuit.
A. True
B. False


If \( \tan ^{2} \alpha=1-p^{2}, \) then \( \sec \alpha+\tan ^{3} \alpha \)
\( \operatorname{cosec} \alpha= \)


A body is accelerated by applying a force of 30 N. The momentum of the
body after 2 sec:
A. \( 7.5 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
B. 40 kg-m/s
c. \( 120 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)
D. \( 60 \mathrm{kg}-\mathrm{m} / \mathrm{s} \)


Find the value of \( x: \)
\[
2 \tan ^{-1}(\sin x)=\tan ^{-1}\left(2 \sec ^{2} x\right), 0<
\]
\( \boldsymbol{x}<\frac{\boldsymbol{\pi}}{2} \)


The fractional change in the value of free-fall acceleration \( g \) for a particle when it is lifted from the surface to an
elevation \( \boldsymbol{h}(\boldsymbol{h}<<\boldsymbol{R}) \) is :
A \( \cdot \frac{h}{R} \)
в. \( \frac{2 h}{R} \)
\( c \cdot-\frac{2 h}{R} \)
D. \( -\frac{h}{R} \)


\( \ln \) a 125 amino acid sequence, if \( 25^{t h} \) amino acid is mutated to UAA, then
A. A polypeptide of 124 amino acids is formed.
B. A polypeptide of 25 amino acids is formed
c. A polypeptide of 24 amino acids is formed.
D. Any of the above can be possible.


Statement: Reducing agents are mostly non-metals while oxidizing agents are
mostly metals.

State whether the given statement is
true or false.
A. True
B. False


The value of \( \left|\begin{array}{lllll}\mathbf{1} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{2} & \mathbf{2} & \mathbf{0} & \mathbf{0} & \mathbf{0} \\ \mathbf{4} & \mathbf{4} & \mathbf{3} & \mathbf{0} & \mathbf{0} \\ \mathbf{5} & \mathbf{5} & \mathbf{5} & \mathbf{4} & \mathbf{0} \\ \mathbf{6} & \mathbf{6} & \mathbf{6} & \mathbf{6} & \mathbf{5}\end{array}\right| \)
\( A \cdot 6 \)
B. 5
c. \( 1.2^{2} .3 .4^{3} .5^{4} .6^{4} \)
D. None of these


\( \operatorname{can} \tan 65^{0}=\tan 25^{0}+\tan 40^{0} ? \)
If Yes answer is \( 1, \) else 0


Answer the following:
What are the rules used for drawing
ray diagrams for the formation of image by spherical mirror?


A dynamo dissipate 25 W when it supplies a current of 5 A through it. If the potential difference is 220
\( v, \) then the emf produced is
A. \( 210 V \)
B. \( 225 V \)
\( \mathbf{c} \cdot 230 V \)
D. \( 235 V \)


The endocrine gland related to the
immune system is
A. Thyroid
B. Thymus
c. Adrenal
D. Pineal


Which pigment is found in phaeophyceae?
A. Chl. a, c and fucoxanthin
B. Chl. a, dand violaxanthin
c. \( \beta \) carotene and phycocyanin
D. None of these


If all measurements in an experiment
are taken up to the same number of
significant figures, then mention two possible reasons for maximum error


Which of the following statements is/are incorrect?
This question has multiple correct options
A. Rust is \( F e_{2} O_{3} \)
B. zn-Cu cell is called Daniell cell.
c. Saline water slows down rusting.
D. Pure metals undergo corrosion faster than impure metals.


Find the \( 7^{t h} \) term from the end in the
expansion of \( \left(2 x^{2}-\frac{3}{2 x}\right)^{8} \)
A . \( 4033 x^{9} \)
В. \( 4023 x^{11} \)
c. \( 4032 x^{10} \)
D. None of these


Find the slope of the tangent to the curve \( y=x^{3}-x \) at \( x=2 \)


If \( \left|z_{1}-z_{2}\right|=\left|z_{1}\right|+\left|z_{2}\right|, \) then
This question has multiple correct options
A \( \cdot \arg \left(\frac{z_{1}}{z_{2}}\right)=\frac{\pi}{2} \)
B \( \cdot \arg \left(\frac{z_{1}}{z_{2}}\right)=(2 n+1) \pi, n \in I \)
\( \mathbf{c} \cdot z_{1} \overline{z_{2}}+\overline{z_{1}} z_{2} \leq 0 \)
D. \( z_{1}=l z_{2}, l \in R \)


Two concentric, thin metallic spherical
shells of radii \( R_{1} \) and \( R_{2}\left(R_{1}>R_{2}\right) \) bear
charges \( Q_{1} \) and \( Q_{2} \) respectively. Then the
potential at radius 'r' between \( R_{1} \) and \( R_{2} \)
will be \( \frac{1}{4 \pi \epsilon_{0}} \) times
A \( \cdot \frac{Q_{1}+Q_{2}}{r} \)
В \( \cdot \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{r} \)
c. \( \frac{Q_{1}}{R_{1}}+\frac{Q_{2}}{R_{2}} \)
D. \( \frac{Q_{1}}{R_{2}}+\frac{Q_{2}}{R_{2}} \)


Due to its great affinity for water
\( H_{2} S O_{4} \) is used as the dehydrating
agent.
A. True
B. False


Identify which of the following
statements is true?
A. Displacement is a scalar and distance is a vector
B. Displacement is a vector and distance is scalar.
c. Both displacement and distance are vectors.
D. Neither displacement nor distance the vectors
E. Displacement and distance are slangs equal


With the help of neat circuit diagram obtain an expression for voltage gain of a transistor amplifier in \( \boldsymbol{C}-\boldsymbol{E} \)
configuration.


Fish die in water bodies polluted by
sewage due to
A. Pathogens
B. clogging of gills by silt
c. Reduction in oxygen
D. Foul smell


If \( \boldsymbol{y}=\cot ^{-1}\left(\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right) \)
then \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}} \) is equal to
A .
B. 1/2
c. \( \frac{1}{1+\sin x} \)
D. \( \frac{1}{\sqrt{1+\sin x}}+\frac{1}{\sqrt{1-\sin x}} \)


\( \frac{2}{\frac{2}{2}} \)


Who defined the term root pressure?
A. Stephan Hales
B. Mendel
c. Griffith
D. Godiewski


The maximum wavelength of photons that can be detected by a photo-diode, which is made of a semiconductor of
band gap \( 2 e V \) is about :
\( \mathbf{A} \cdot 620 n m \)
B. 700 nm
\( c .740 n m \)
D. \( 860 n m \)
E. \( 1240 n m \)


Assertion
The formula connecting \( u, v \) and \( f \) for \( a \) spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason
Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.
A. Statement-1 is True, Statement-2 is True; Statement - is a correct explanation for Statement-
B. Statement-1 is True, Statement-2 is True; Statement - 2 is NOT a correct explanation for Statement-1.
C. Statement- -1 is True, Statement-2 is False
D. Statement-1 is False, Statement-2 is True.


The distance of closest approach of the particle to the nucleus will be
A \( \cdot 6.4 \times 10^{-13} \mathrm{m} \)
B . \( 4.3 \times 10^{-13} \mathrm{m} \)
c. \( 2.1 \times 10^{-13} \mathrm{m} \)
D. \( 3.4 \times 10^{-14} \mathrm{m} \)


The Earth's surface, the ionosphere and
the atmosphere is known as:
A. global atmosphere electrical circuitt
B. local atmosphere electrical circuit
c. electrical circuit
D. none of these


Write about hydrogen bonding in ice
and water.


If \( S=\left[\begin{array}{ll}6 & -8 \\ 2 & 10\end{array}\right]=P+Q, \) where \( P \) is \( a \)
symmetric \& Q is a skew -symmetric matrix, then \( Q= \)
A. \( \left[\begin{array}{cc}0 & 5 \\ -5 & 0\end{array}\right] \)
В. \( \left[\begin{array}{cc}0 & -5 \\ 5 & 0\end{array}\right] \)
C \( \cdot\left[\begin{array}{cc}0 & 8 \\ -8 & 0\end{array}\right] \)
D. \( \left[\begin{array}{cc}0 & 6 \\ -6 & 0\end{array}\right] \)


\( \operatorname{Let} \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{l}\mathbf{1}+|\boldsymbol{x}|, \quad \boldsymbol{x}<-\mathbf{1} \\ {[\boldsymbol{x}], \quad \boldsymbol{x} \geq-\mathbf{1}}\end{array} \) where \right.
denotes the greatest integer function,
Find \( \boldsymbol{f}\{\boldsymbol{f}(-\mathbf{2 . 3})\} \)


An arsenious sulphide sol carries a negative charge. The maximum precipitating power of this sol is possessed by :
A. \( K_{2} S O_{4} \)
в. \( C a C l_{2} \)
\( \mathbf{c} \cdot N a_{3} P O_{4} \)
D. \( A l C l_{3} \)


The ionic bonds \( X^{+} Y^{-} \) are formed
when
(I) electron affinity of \( Y \) is high
(II) ionization energy of \( \boldsymbol{X} \) is low
(III) lattice energy of \( \boldsymbol{X} \boldsymbol{Y} \) is high
(IV) lattice energy of \( \boldsymbol{X} \boldsymbol{Y} \) is low
A . I and II
B. I and III
c. ।, ॥ and III
D. All


is a definite
path in which the electron revolves
round the nucleus
A. Orbit
B. Circular ring
c. orbital
D. both \( A \) and \( B \)


The electronic structure of four
elements a, b, c, d respectively are:
(a) \( 1 s^{2} \)
(b) \( 1 s^{2} 2 s^{2} 2 p^{2} \)
\( (c) 1 s^{2} 2 s^{2} 2 p^{5} \)
(d) \( 1 s^{2} 2 s^{2} 2 p^{6} \)
The tendency to form electrovalent bond will be largest in :
\( A \cdot A \)
B. B
\( c \cdot c \)
D.


A boy held a book of \( 1 \mathrm{kg} \) at a height of 1 metre for 60 seconds. Calculate the
work done.
A . 60 J
B. 30 J
c. 15 J
D.


Find the coordinates of the foci, the
vertices, the length of major axis, the minor axis, the eccentricity and the
length of the latus rectum of the ellipse \( 36 x^{2}+4 y^{2}=144 \)


Of the following, the wrong statement is:
A. the first ionization potential of \( A \) l is less than the first ionization potential of Mg.
B. the second ionization potential of Mg is greater than the second ionization potential of \( \mathrm{Na} \)
C. the first ionization potential of Na is less than the first ionization potential of Mg.
D. the third ionization potential of Mg is greater than the third ionization potential of Mg.


What will be the product, if dilute hydrochloric acid is added to \( F e S ? \)
A. Element
B. Mixture
c. compound
D. None of these


If \( \cot ^{-1} x+\cot ^{-1} y+\cot ^{-1} z=\frac{\pi}{2} \) then
\( \boldsymbol{x}+\boldsymbol{y}+\boldsymbol{z} \) equals
A \( . x y z \)
в. \( x y+y z+z x \)
\( \mathrm{c} \cdot 2 x y z \)
D. None of these


Fill in the blanks:
(i) \( \boldsymbol{C a}_{3} \boldsymbol{P}_{2}+\boldsymbol{6} \boldsymbol{H} \boldsymbol{C l} \rightarrow \boldsymbol{3} \boldsymbol{C a} \boldsymbol{C l}_{2}+ \)
\( p \)
\( - \)
(ii) \( P_{4}+3 N a O H+3 H_{2} O \rightarrow \)
\( q_{--}+3 N a H_{2} P O_{2} \)
(iii) \( P H_{4} I+K O H \rightarrow K I+H_{2} O+ \)
p, \( q \) and \( r \) respectively are:
A. \( P H_{3}, H_{3} P O_{3}, P I_{3} \)
в. \( P H_{3}, P H_{3}, P H_{3} \)
c. \( P C l_{3}, H_{3} P O_{4}, P H_{3} \)
D. \( P C l_{5}, P H_{3}, P_{4} O_{6} \)


Two copper wires, one of length \( 1 \mathrm{m} \) and the other of length \( 9 \mathrm{m}, \) are found to have the same resistance.
Their diameters are in the ratio:
A. 3:
B. 1: 9
\( c \cdot 9: \)
\( D \cdot 1: 3 \)


Write the composition of aqua-regia:
\( \mathbf{A} \cdot 67 \% \) conc. \( H C l \) and \( 33 \% \) conc. \( H N O_{3} \)
B. \( 25 \% \) conc. \( H C l \) and \( 75 \% \) conc. \( H N O_{3} \)
C \( .75 \% \) conc. \( H C l \) and \( 25 \% \) conc. \( H N O_{3} \)
D. \( 50 \% \) conc. \( H C l \) and \( 50 \% \) conc. \( H N O_{3} \)


A common characteristic of all
vertebrates is
A. Presence of skull
B. Division of body into head, neck, trunk and tail
C. Presence of two pairs of functional appendages
D. Body is covered with an exoskeleton


A batsman scores runs in 10 innings as \( \mathbf{3 8}, \mathbf{7 0}, \mathbf{4 8}, \mathbf{3 4}, \mathbf{4 2}, \mathbf{5 5}, \mathbf{6 3}, \mathbf{4 6}, \mathbf{5 4}, \mathbf{4 4 .} \) The
mean deviation about mean is :
A. 8.6
B. 6.4
c. 10.6
D. 7.6


The important function of lymph is to
A. Transport oxygen to the brain
B. Transport carbon dioxide to the lungs
C. Return RBCs to the lymph nodes
D. Return interstitial fluid to the blood


Modern atomic mass scale is based on
the mass of
\( \mathbf{A} \cdot H-1 \)
B. \( C-12 \)
c. \( C-14 \)
D. \( C-16 \)


If \( \cdot \) donotes fractional part of \( x, \) then
\( \lim _{x \rightarrow 3+}\{x\}^{2} \frac{\sin (x-3)}{(x-3)} \) is equal?
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{1}{2} \)
\( c \cdot \frac{1}{3} \)
\( D \)


Find out the resistance:


A die is thrown twice. Each time the
number appearing on it is recorded. Describe the following event:
\( B= \) Both numbers are even


Which of the following cause water pollution?
A. Smoke/fly ash
B. Automobile exhausts
c. silt and pesticides
D. Aeroplanes


Find the moments of time when the
particle is at the distance \( 10.0 \mathrm{cm} \) from the origin.
A. \( 1.1,9, \) and \( 11 s \)
B. \( 1,10, \) and \( 11 s \)
c. \( 1.1,10, \) and \( 11 s \)
D. \( 1.1,9, \) and \( 13 s \)


What is the angle between \( \vec{P} \times \vec{Q} \) and \( \vec{P}+\vec{Q} ? \)
\( \mathbf{A} \cdot \mathbf{0} \)
в. \( \frac{\pi}{2} \)
\( c . \pi \)
D. \( \frac{3 \pi}{2} \)


Two structure of \( H_{2} O_{2} \) are drawn below.
Identify the phase \( (X) \) and \( (Y) \) of \( H_{2} O_{2} \)
\( \mathbf{A} \cdot(X) \) is the structure of \( H_{2} O_{2} \) in gas phase and \( (Y) \) in solid phase
B. \( (X) \) is structure of \( H_{2} O_{2} \) in solid phase and \( (Y) \) in gas phase
c. \( (X) \) and \( (Y) \) are structures of \( H_{2} O_{2} \) in gas phase
D. \( (X) \) and \( (Y) \) are structures of \( H_{2} O_{2} \) in solid phase


is used in gas lamp
material.
A. \( M n O_{2} \)
в. \( C e O_{2} \)
c. \( N_{2} O_{5} \)
D. \( F e_{2} O_{3} \)


Five defective mangoes are accidently
mixed with 15 good ones. Four mangoes
are drawn at random from this lot. Find
the probability distribution of the number of defective mangoes.


4 men or 6 women earn Rs 360 in one
day. Find how much will 6 men and 4
women earn in one day?
A . Rs 780
B. Rs 720
c. Rs 760
D. Rs 740


If \( \lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-x}}{2 x}=\frac{1}{a}, \) then \( a \) is
equal to


The value of \( \frac{1}{x-y}\left|\begin{array}{ccc}1 & 0 & 0 \\ 3 & x^{3} & 1 \\ 5 & y^{3} & 1\end{array}\right| \) is
\( \mathbf{A} \cdot x+y \)
B . \( x^{2}-x y+y^{2} \)
c. \( x^{2}+x y+y^{2} \)
D. \( x^{3}-y^{3} \)


A radio isotope 'X' with a half life \( 1.4 \times \)
\( 10^{9} \) years decays to 'Y' which is stable. A
sample of the rock from a cave was found to contain ' \( X \) ' and ' \( Y \) ' in the ratio
1 : 7. The age of the rock is
A \( \cdot 1.96 \times 10^{9} \)years
В. \( 3.92 \times 10^{9} \) years
c. \( 4.20 \times 10^{9} \) years
D. \( 8.40 \times 10^{9} \) years


The magnetic flux linked with a coil of
\( N \) turns of area of cross-section \( A \) held
with its plane parallel to the field \( B \) is
A. \( \frac{N A B}{2} \)
в. \( N A B \)
c. \( \frac{N A B}{4} \)
D. 0
E . \( 2 N A B \)


Assertion: The most important factor in determining the chemical properties of an element is the number of electrons
in the outermost shell.

Statement 2 : The number of electrons
in the outer shell determines the
bonding characteristics of the element.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is not correct
D. Assertion is not correct but Reason is correct
E. Both the Assertion and Reason are not correct


Through the point (3,4) are drawn two
straight lines each inclined at \( 45^{\circ} \) to
the straight line \( x-y=2 . \) Find their
equations and find also the area included by the three lines.


If \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{S}, \) defined by \( \boldsymbol{f}(\boldsymbol{x})=\sin \boldsymbol{x}- \)
\( \sqrt{3} \cos x+1, \) in onto, then the interval
of \( \boldsymbol{S} \) is
A . [0.1]
B . [-1,1]
\( c \cdot[0,3] \)
D. [-1,3]


Choose the correct statement.
A. Stroma lamella membrane lacks PS II and PS I.
B. When PS I is functional, electron flow in a noncyclic
way.
C. ATPase enzyme consists of \( F_{0} \) and \( F_{1} \) units
D. NADP reductase is a part of PS II.


Heat of combustion of \( \boldsymbol{C H}_{4}, \boldsymbol{C}_{2} \boldsymbol{H}_{6} \) and
\( C_{3} H_{8} \) are respectively -210,-368.4 and
\( -526.8 \mathrm{Kcal} \) mol \( _{1} \) Hence, heat of
combustion of \( C_{8} H_{16} \) is approximately:
A. -1267.2 Kcal / mol
в. -684 Кса\( / \) (тод
c. \( -840 K c a l / m o l \)
D. \( -1000 K \) cal \( / \) mol


Find the equation of the circles passing through the point (2,8) touching the line \( 4 x-3 y-24=0 \) and \( 4 x+3 y- \)
\( 42=0 \) and having \( x \) coordinate of the
centre of the circle less than or equal to
8


Match Column I with Column II:


If the light from a flashlight makes an
angle of \( 30^{\circ} \) with the mirror's
perpendicular, the angle of the reflected
beam will be \( 120^{\circ} \)
A. True
B. False


If the angle between two lines is \( \pi / 4 \)
and slope of one of the line is \( 1 / 2, \) find the slope of the other line.


Sulphur bums in oxygen to form sulphur dioxide. The properties of sulphur dioxide are:
A. totally different from sulphur and oxygen
B. similar to sulphur
c. similar to oxygen
D. more similar to sulphur than oxygen


For the velocity \( (v) \) -time \( (t) \) graphs
shown in figure, the total
distance covered by the particle in the
last two seconds of its motion is what
fraction of the total distance covered by
it in all the seven seconds?
\( A \cdot 1 / 8 \)
B. \( 1 / 6 \)
\( c \cdot 1 / 4 \)
D. \( 1 / 2 \)


Draw, wherever possible, a rough sketch
of:

A triangle with both line and rotational symmetries of order more than 1


In a 500 ml flask, the degree of
dissociation of \( \boldsymbol{P C l}_{5} \) at equilibrium is
\( 40 \% \) and the initial amount is 5 moles.
The value of equilibrium constant in
mol.lit \( ^{-1} \) for the decomposition of
\( \boldsymbol{P C l}_{5} \) is :
A . 2.33
B . 2.66
\( c .5 .32 \)
D. 4.66


Draw the flow chart for obtaining different gases from air


A solution containing \( 4 g \) of a non-
volatile organic solute per \( 100 m L \) was found to have an osmotic pressure
equal to \( 500 \mathrm{cm} \) of mercury at \( 27^{\circ} \mathrm{C} \) The molecular weight of solute is:
A .14 .97
B. 149.7
\( c .1697 \)
D. 1.497


A hockey player receives a corner shot
at a speed of \( 15 \mathrm{m} / \mathrm{s} \) at angle \( 30^{\circ} \) with \( \mathrm{y} \)
axis and then shoots the ball along \( x \)
axis with the speed \( 30 \mathrm{m} / \mathrm{s} \). If the mass
of the ball is 150 g and it remains in contact with the hockey stick for 0.01 s, the force exerted on the ball along \( x \)
axis is :
\( A \cdot 281 \mathrm{N} \)
B. 187.5
c. \( 562.5 \mathrm{N} \)
\( D .3 \)


Write the order of reaction in which unit
of rate and rate constant becomes
equal?