A copper rod \( 10 \mathrm{cm} \) long rotates 1800
times per minute about an axis passing through one end at a right angle to the rod. A uniform magnetic field of 1 tesla is applied perpendicular to the plane of rotation. The voltage induced between the ends of the rod is
A . \( 0.235 \mathrm{v} \)
B. \( 0.942 \mathrm{V} \)
c. \( 2.35 v \)
D. zero


The sum of the series \( 10 .^{n} C_{0}+ \)
\( 10^{2} \cdot^{n} C_{1}+10^{3} \cdot^{n} C_{2}+\ldots 10^{n+1} \cdot^{n} C_{n} \) is
A \( \cdot 11^{n} \)
B . \( 10.11^{n} \)
\( \mathbf{c} \cdot 11^{n+1} \)
D. \( 11^{n}-1 \)


Principal quantum number defined
for
A. shell
B. subshell
c. orbital
D. spin


The electronic configuration of
potassium is :
\( \mathbf{A} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3} 4 s^{2} 3 d^{2} \)
B \( \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5} 4 s^{2} \)
\( \mathbf{C} \cdot 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1} \)
D. \( 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1} \)


In the given figure (not drawn to scale),
\( A B C D \) is a parallelogram, \( A D F \) is an
isosceles triangle with \( \boldsymbol{A} \boldsymbol{D}=\boldsymbol{A} \boldsymbol{F} \)
\( F A B \) and \( E D C \) are straight lines. Find
\( \boldsymbol{y} \)
A . 112
в. 102
\( c .132 \)
D. 11


Define demography. What are the reasons for population explosion since
\( 19^{t h} \) century? Describe the environmental impacts caused due to population explosion with the help of diagram.


Which of the following oxo-acid is possible? This question has multiple correct options
A. \( H O C l O_{2} \)
в. НОF Оа
\( \mathrm{c} \cdot \mathrm{HOBrO}_{2} \)
D. НОПО\( _{2} \)


Let \( A=R \times R \) and \( * \) be the binary
operation on A defined by \( (a, b) * \) \( (c, d)=(a+b, b+d) . \) Prove that \( * \) is
commutative and associative find the
identity element for \( * \) on \( \boldsymbol{A} \)


Acquiring an oxygen debt is evidence
that
\( A \cdot O_{2} \) cannot be stored in tissue.
B. Aerobic respiration is more complex than glycolysis.
C. Lactic acid can be converted into glycogen.
D. Anaerobic process are slower than aerobic processes.


When added an impurity into the silicon which one of the following produces \( n \) type of semi-conductors:
A. iron
B. magnesium
c. aluminium
D. phosphorous


Solve \( \boldsymbol{x}+\mathbf{4} \boldsymbol{y}=\mathbf{2 4} \boldsymbol{x} \boldsymbol{y}, \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{2} \mathbf{1} \boldsymbol{x} \boldsymbol{y} \)


Which of the following complexes is used to be as an anticancer agent?
A \( \cdot \) mer \( -\left[\operatorname{Co}\left(N H_{3}\right)_{3} C l\right] \)
B. \( \operatorname{cis}-\left[P t C l_{2} N H_{3}\right)_{2} \)
c. \( \operatorname{cis}-K_{2}\left[P t C l_{2} B r_{2}\right] \)
D. \( N a_{2} \) Co \( C l_{4} \)


Most friable soil is
A. sand
B. clay
c. Loam
D. Parent material


Match the entries in List 1 with
appropriate ones from List 2


Construct a rectangle \( A B C D \) of lengh 6 \( \mathrm{cm} \) and breadth \( 4 \mathrm{cm} . \) Construct angle bisectors of \( \angle A \) and \( \angle B . \) Let them meet
at 0.The distance of 0 from length \( A B \) is:
A . 3
B. 10
c. 2
D. 8


The equation of a simple harmonic progressive wave is given by \( y=A \sin \) \( (100 \pi t-3 x) . \) Find the distance
between 2 particles having a phase difference of \( \frac{\boldsymbol{\pi}}{\mathbf{3}} \)
A \( \cdot \frac{\pi}{9} m \)
в. \( \frac{\pi}{18} m \)
c. \( \frac{\pi}{6} m \)
D. \( \frac{\pi}{3} m \)


Epinephrine (adrenaline) is secreted by
A. Adrenal cortex
B. Adrenal medulla
c. Pancreas
D. Nerve endings


The escape velocity on a planet is \( \boldsymbol{v} . \) If the radius of the planet contracts to \( \frac{1}{4} \) of present value without any change in its mass, the escape velocity will be
A. halved
B. doubled
c. quadrupoled
D. becomes one fourth


Match the following and choose the
correct answer.
\( \begin{array}{lllll}A & \text { String vibration } & 1 & \text { Tabla } \\ B & \begin{array}{l}\text { Membrane } \\ \text { vibration }\end{array} & 2 & \begin{array}{l}\text { Bicycle } \\ \text { bell }\end{array} \\ \text { C } & \text { Vibration of air } & 3 & \text { Sitar } \\ \text { D } & \text { Vibration of plate } & 4 & \text { Flute }\end{array} \)
A . A-1, B-2, C-3, D-4
B. A-2, B-1, C-4, D-3
c. A-3, B-1, C-4, D-2
D. A-4, B-3, C-2, D-1 -


What is digestion? Why do only animals require a digestive system?


Identify \( (A),(B) \) and \( (C) \)
\( \mathrm{Na}_{2} \mathrm{SO}_{4}+ \) carbon \( \longrightarrow(A) \frac{\mathrm{Na}_{2}\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NO}\right]}{\longrightarrow}(B) \) (purple)
\[
\mid \mathrm{CdCO}_{3}
\]
\( \mathbf{A} \cdot(A): N a_{2} S \)
(B) \( : N a_{2}\left[F e(N C)_{5} N O S\right] \)
\( (\mathrm{C}): \mathrm{CdO} \)
B. (A): \( N a O_{2} \)
(B): \( N a_{2}\left[F e(C N)_{5} N O S\right] \)
\( (\mathrm{C}): C d S \)
\( \mathbf{C} \cdot(A): N a_{2} S \)
(B): \( N a_{2}\left[F e(C N)_{5} N O S\right] \)
\( (\mathrm{C}): \mathrm{Cd} S \)
\( \mathbf{D} \cdot(\mathrm{A}): N a_{2} O \)
(В) : \( N a_{2}\left[F e(N C)_{5} N O S\right] \)
\( (\mathrm{C}): P b S \)


Evaluate \( \Delta=\mid \begin{array}{cc}\cos 2 \alpha & \sin 2 \alpha \\ -\sin 3 \alpha & \cos 3 \alpha\end{array} \)


Emergency contraceptives are effective
if used within
A. 72 hrs of coitus
B. 72 hrs of ovulation
c. 72 hrs of menstruation
D. 72 hrs of implantation.


The sum of the infinite series \( \cot ^{-1} 2+ \)
\( \cot ^{-1} 8+\cot ^{-1} 18+\cot ^{-1} 32+\ldots . . \) is
equal to
A . \( \pi / 3 \)
в. \( \pi / 4 \)
c. \( \pi / 6 \)
D. \( \pi / 8 \)


Which of the following has the highest
first ionization energy?
A. Lithium
B. Beryllium
c. Boron
D. carbon


Cathode rays have:
A. mass only
B. charge only
c. no mass and no charge
D. mass and charge both


Which of the following is/are properties of chemisorption?
This question has multiple correct options
A. Easily liquefied gases are more adsorbed
B. Weak van der Waals forces cause the adsorption process
c. Unimolecular layer formation
D. Adsorbtion increases with rise in temperature


A standard hydrogen electrode has zero electrode potential because:
A. hydrogen is easiest to oxidise
B. this electrode potential is assumed to be zero
c. hydrogen atom has only one electron
D. hydrogen is the lightest element


Find the square root of the following number by division method: 5329


If \( \tan \theta=\frac{\sin \alpha-\cos \alpha}{\sin \alpha+\cos \alpha}, \) then
\( A \cdot \sin \alpha-\cos \alpha=\pm \sqrt{2} \sin \theta \)
B. \( \sin \alpha+\cos \alpha=\pm \sqrt{2} \cos \theta \)
\( \mathbf{c} \cdot \cos 2 \theta=\sin 2 \alpha \)
\( D \cdot \sin 2 \alpha+\cos 2 \alpha=0 \)


A farmer wishes to start a 100 square
metres rectangular vegetable garden. since he has only 30 metres barbed wire, he fences three sides of the
rectangular garden. The \( 4^{t h} \) side of the garden is surrounded by the compound wall of his house. The dimensions of the
garden is
\( \mathbf{A} \cdot 25 \mathrm{m} \times 4 \mathrm{m} \)
B . \( 25 \mathrm{m} \times 5 \mathrm{m} \)
c. \( 20 \mathrm{m} \times 5 \mathrm{m} \)
D. \( 20 \mathrm{m} \times 4 \mathrm{m} \)


During photorespiration which compounds are formed having \( 2 C \) and
\( 3 \mathrm{C} \) respectively in peroxisome?
A. Phosphoglycerate, glycolate
B. Glycine, glycerate
c. serine, glycine
D. Glycolate, glycine


An enzyme which catalyses the
conversion of aldose sugar to ketose would be classified as
A. Transferases
B. Isomerases
c. Hydrolases
D. Ligases


a) Assign the position of the element having outer electronic configuration in the periodic table
(i) \( n s^{2} n p^{4} \) for \( n=3 \)
\( (n-1) d^{2} n s^{2} \) for \( n=4 \)
b) The size of \( N a^{+} \) cation is smaller
than \( N a . \) Explain


In the process of vulcanization:
A. natural rubber is heated with sulphur
B. natural rubber is heated with carbon
C. natural rubber is heated with phosphorous
D. natural rubber is heated with sodium


The capacity of a parallel plate condenser is \( 10 \mu F, \) when the distance
between its plates is \( 8 \mathrm{cm} \). If the
distance between the plates is reduced
to \( 4 \mathrm{cm}, \) then the capacity of this parallel plate condenser will be :
A \( .5 \mu F \)
B. \( 10 \mu F \)
c. \( 20 \mu F \)
D. \( 40 \mu F \)


The work of \( 146 k J \) is performed in
order to compress 1 kilo mole of a gas adiabatically and in the process the temperature of the gas increases by
\( \mathbf{7}^{\circ} \mathbf{C} . \) The gas is:
\( \left(\boldsymbol{R}=\mathbf{8 . 3} \boldsymbol{J} \boldsymbol{m o l}^{-1} \boldsymbol{K}^{-1}\right) \)
A. Diatomic
B. A mixture of monoatomic and diatomic
c. Monoatomic
D. Triatomic


A rectangular loop carrying current lis located near an infinite long straight
conductor carrying current l as shown
in the figure. The loop,
A. remain stationary
B. is attracted towards the wire
C. is repelled away from the wire
D. will rotate about an axis parallel to the wire


Express the given linear equation in the form \( a x+b y+c=0 \) and indicate the
values of \( a, b \) and \( c \) in given case:
\( \boldsymbol{x}-\frac{\boldsymbol{y}}{\mathbf{2}}-\mathbf{5}=\mathbf{0} \)


On increasing the external pressure, the boiling point of liquid
A. is raised
B. is lowered
c. remain unaffected
D. uncertain


The two elements, with same number of
electrons but different mass number,
are known as
A. isotopes
B. isomers
c. isotones
D. isobars


If \( 2^{2 x-y}=32 \) and \( 2^{x+y}=16 \) then \( x^{2}+ \)
\( y^{2} \) is equal to
A . 9
B. 10
\( c \cdot 11 \)
D. 13


Which one of the following molecular hybrides acts as a Lewis acid?
A \( \cdot C H_{4} \)
в. \( N H_{3} \)
\( \mathrm{c} \cdot \mathrm{H}_{2} \mathrm{O} \)
D. \( B H_{3} \)
E. All of these


Find variance for following data:
\( \begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30 \\ & 10 & 20 & 30 & 40\end{array} \)
frequency ey 6 8
A. 14.75
в. 15.75
c. 17.75
D. 16.75


It takes 15 minutes for an electrical
kettle to heat a certain quantity of
water in grams from \( 0^{\circ} \mathrm{C} \) to boiling
point \( 100^{\circ} \mathrm{C} . \) If it takes 81 minutes to boil water into steam, the latent heat of steam is :
A. 80 cal \( l \),
в. 540 cal \( / g \)
c. 100 cal \( / g \)
D. 336 cal \( / g \)


The coefficient of mean deviation from
median of observations
40,62,54,90,68,76 is
A .2 .16
B. 0.2
\( c .5 \)
D. None of these


Two ends of an inductor of inductance \( L \)
are connected to two parallel
conducting wires. A rod of length \( l \) and
mass \( m \) is given velocity \( v_{0} \) as shown.
The whole system is placed in
perpendicular magnetic field \( B \). Find the maximum current in the inductor.
\( ^{A} \cdot \frac{m v_{0}}{L} \)
в. \( \sqrt{\frac{m}{L}} v_{0} \)
c. \( \frac{m v_{0}^{2}}{L} \)
D. None of these


Which one of the following arrangements of molecules is correct on the basis of their dipole moments?
A. \( B F_{3}>N F_{3}>N H_{3} \)
B. \( N F_{3}>B F_{3}>N H_{3} \)
c. \( N H_{3}>B F_{3}>N F_{3} \)
D. \( N H_{3}>N F_{3}>B F_{3} \)


For two triangles, if sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar. This is called
similarity.
\( \mathbf{A} \cdot A A A \)
в. \( S S S \)
\( c . S A S \)
D. none of these


If the capacity of a spherical conductor is 1 picofarad, then its diameter would
be
A \( \cdot 1.8 \times 10^{-3} \mathrm{m} \)
B . \( 18 \times 10^{-3} m \)
c. \( 1.8 \times 10^{-5} m \)
D. \( 18 \times 10^{-5} m \)


Compound/s which give/s alcohol on
reduction by \( L i A l H_{4} \) is/are:
This question has multiple correct options
\( A \)
B.
c.
D.


The IUPAC name for the complex
\( \left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{O}_{2}\right)\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{5}\right] \boldsymbol{C l} 2 ? \)
A. nitrito-N-pentamminecobalt
(III) chloride
(II) chlorid
B. nitrito-N-pentamminecobalt
c. pentammienenitrito-N-cobalt (II) chloride
D. none


The function \( x^{x} \) decreases in the
interval-
A \( \cdot(0, e) \)
в. (0,1)
\( ^{\mathbf{c}} \cdot\left(0, \frac{1}{e}\right) \)
D. None of the above.


\( \alpha \) -Hydroxypropanoic acid can be prepared from ethanal by following the steps given in the sequence.
A. Treat with \( H C N \) followed by acidic hydrolysis
B. Treat with \( N a H S O_{4} \) followed by reaction with \( N a_{2} C O_{3} \)
c. Treat with \( H_{2} S O_{4} \) followed by hydrolysis
D. Treat with \( K_{2} C r_{2} O_{7} \) in presence of sulphuric acid


A cube of ice melts without changing its shape at the uniform rate of
\( 4 \mathrm{cm}^{3} / \) min. The rate of change of the surface area of the cube, in \( c m^{2} / \)min
when the volume of the cube is \( 125 \mathrm{cm}^{3} \)
is
A. -4
в. \( -\frac{16}{5} \)
c. \( -\frac{16}{6} \)
D. \( -\frac{8}{15} \)


In a cylinder, 2.0 moles of an ideal
monatomic gas initially at \( 1.0 \times \)
\( 10^{6} P a \) and \( 300 K \) expands until its
volume doubles. Compute the work done if the expansion is isothermal, adiabatic and isobaric.


A thin spherical insulating shell of radius R carries a uniformly distributed
charge such that the potential at its
surface is \( V_{0} . \) A hole with small area
\( \alpha 4 \pi R^{2}(\alpha<<1) \) is made on the shell
without affecting the rest of the shell. Which one of the following statement is
correct?
A. The ratio of the potential at the centre of the shell to that of the point at \( \frac{1}{2} R \) from center towards the hole
will be \( \frac{1-\alpha}{1-2 \alpha} \)
B. The potential at the centre of shell is reduced by \( 2 \alpha v_{0} \)
C. The magnitude of electric field at the centre of the shell is reduced by \( \frac{\alpha v_{0}}{2 R} \)
D. The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance \( 2 R \) from the center of the spherical shell will
be reduced by \( \frac{\alpha v_{0}}{2 R} \)


The storage battery generally used in electric power station is:
A. Nickel-Cadmium battery
B. zinc-Carbon battery
c. Lead-Acid battery
D. None of the above


Which of the following species have
same magnetic moment?
This question has multiple correct options
A \( \cdot C r^{+} \)
B. \( F e^{+3} \)
c. \( C o^{+2} \)
D. \( N i^{+2} \)


The structure of \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) is:
A. planar
B. non-planar
c. spherical
D. linear


A student is using a convex lens of focal
length \( 18 \mathrm{cm} \) to study the
image formation by it for the various positions of the object. He observes thatwhen he places the object at \( 27 \mathrm{cm} \) the location of the image is at 54 cmon the other side of the lens. Identify from
the following diagram the three rays that are obeying the laws of refraction
and may be used to draw the
corresponding ray diagram.
A. 1,2 and 4
B. 1,3 and 5
\( c \cdot 2,4 \) and 5
D. 2,3 and 4


Assertion
\( D-2- \) Deoxyglucose reacts with 3
\( \operatorname{mol} P h N H N H_{2} \) and forms an
osazone.
Reason
\( D-2- \) Deoxyglucose has no \( (C- \)
\( O H) \) group \( \alpha \) - to the \( (C=O) \) group
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 place value of 5 in the number
\( \mathbf{2 5 . 3 6 9} \) is
A \( \cdot \frac{5}{10} \)
в. \( \frac{5}{100} \)
\( c .5 \)
D. 50


Alternating current is converted to direct current by
A . rectifier
B. dynamo
c. transformer
D. motor


for two materials \( P \) and \( Q \), a student by
mistake puts strain on the y-axis and
stress on the \( x \) -axis as shown in the
figure. Then the correct statement(s) is
(are)
This question has multiple correct options
A. P has more tensile strength than \( Q \)
B. P is more ductile than \( Q \)
\( c . \) P is more brittle than \( Q \)
Deng's modulus of than that of


Among the cell structures and
materials of bacteria listed below,
which one would be innermost if
arranged in proper order?
A. Glycocalyx
B. Plasma membrane
c. Primary cell wall
D. secondary cell wall


\( H_{3} P O_{4} \) is a tribasic acid with
\( \boldsymbol{p} \boldsymbol{K}_{a_{1}}, \boldsymbol{p} \boldsymbol{K}_{a_{2}} \) and \( \boldsymbol{p} \boldsymbol{K}_{a_{3}} \boldsymbol{2} .12, \boldsymbol{7} .21 \) and
\( 12.32, \) respectively. It is used in fertiliser productions and its various salts are used in food, detergent, toothpaste, and in metal treatment.
Small quantities of \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) are used in imparting the sour or tart taste to soft drinkes, such as Coca Cola, and beers
in which \( H_{3} P O_{4} \) is present \( 0.05 \% \) by weight (density \( \left.=1.0 g m L^{-1}\right) \) \( \mathbf{1 0}^{-3} \boldsymbol{M} \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4}(\boldsymbol{p} \boldsymbol{H}=\mathbf{7}) \) is used in
fertilisers as an aqueous soil digesting. Plants can absorb zinc in water soluble
form only. Zinc phosphate is the source of zinc and \( P O_{2}^{3-} \) ions in the soil. \( K_{s p} \) of zonic phosphate \( =9.1 \times 10^{-33}\left[Z n^{2+}\right] \) ion in the soil is:
A \( .2 .9 \times 10^{-11} \mathrm{M} \)
В. \( 4.0 \times 10^{-10} M \)
c. \( 3.0 \times 10^{-6} M \)
D. \( 9.1 \times 10^{-5} M \)


Differentiate the following w.r.t.x:
\( \sin ^{-1} x+\cos ^{-1} x \)


Find the maximum number of angle,
which are less than \( 90^{\circ} \) in \( I F_{5} \)
\( \mathbf{A} \cdot \mathbf{0} \)
B. 4
\( c \cdot 8 \)
D. 12


When \( n-p-n \) transistor is used as an
amplifier:
A. electrons move from base to collector
B. holes moves from emitter to base
C. holes move from collector to base
D. holes move from base to emitter


Benzene hexachloride is used as a:
A \( \cdot \) dye
B. antimalarial drug
c. antibiotic
D. insecticide


Choose the correct statement(s) for
froth flotation process, which is used for
the concentration of sulphide ore.
a) It is based on the difference in the
ability of different minerals to become
wet.
b) It uses sodium ethyl xanthate,
\( C_{2} H_{5} O C S_{2} N a \) as collector.
c) It uses \( N a C N \) as a depressant in the
mixture of \( Z n S \) and \( P b S, \) where \( Z n S \)
forms soluble complex and \( P b S \) forms
froth.
(a) and (b) are correct
A. only
B. Only (b) and (c) are correct
c. only (a) and (c) are correct
D. All statements are correct


Two complex numbers are represented
by ordered pairs \( z_{1}:(a, 0) \& z_{2}:(c, d) \)
which of the following is correct
simplification for \( z_{1} \times z_{2}=? \)
\( \mathbf{A} \cdot(a c,-a d) \)
B. \( (a d, a c) \)
\( \mathbf{c} \cdot(a c, a d) \)
D. None of these


Why do insulators take larger time to
heat up?
A. They need more heat per every degree Celsius rise in temperature
B. They need more energy per every degree Celsius rise in temperature
C. They need more to perform more work per every degree Celsius rise in temperature.
D. They need more heat per every degree Farenheit rise in temperature


If \( \lim _{x \rightarrow a}\left\{\frac{f(x)}{g(x)}\right\} \) exists, then
\( \mathbf{A} \cdot \operatorname{both} \lim _{x \rightarrow a} f(x) \) and \( \lim _{x \rightarrow a} g(x) \) must exist
B. \( \lim _{x \rightarrow a} f(x) \) need not exist but \( \lim _{x \rightarrow a} g(x) \) exists
C. neither \( \lim _{x \rightarrow a} f(x) \) nor \( \lim _{x \rightarrow a} g(x) \) may exist
D. \( \lim _{x \rightarrow a} f(x) \) exists but \( \lim _{x \rightarrow a} g(x) \) need not exist


Prove that the points (3,0)(6,4) and (-1,3) are the vertices of a right angled isosceles triangle.


How many structural isomers possible for monobromodichloro benzene?


Give two differences between
macromolecular colloids and
associated colloids.


If we assume only gravitational attraction between proton and electron in hydrogen atom and Bohr's quantization rule to be followed, then the expression for the ground state energy of the atom will be the mass of proton is \( \mathrm{M} \) and that of the electron is
\( m): \)
\( ^{\mathrm{A}} \cdot \frac{G^{2} M^{2} m^{2}}{h^{2}} \)
\( ^{\text {В }} \cdot \frac{2 \pi^{2} G^{2} M^{2} m^{3}}{h^{2}} \)
c. \( \frac{2 \pi^{2} G M^{2} m^{3}}{h^{2}} \)
D. None of these


While leakage in L.P.G. gas cylinders, gas which gives fowl smell is:
A. butane
B. propane
c. methane
D. ethyl mercaptan


Which type of isomerism is shown by but-1-yne and but-1,3-diene?
A. Functional isomerism
B. Chain isomerism
c. Ring chain isomerism
D. Position isomerism


If \( \boldsymbol{f}(\mathbf{0})=\mathbf{0} \) and \( \boldsymbol{f}^{\prime \prime}(\boldsymbol{x})>\mathbf{0} \) for all \( \boldsymbol{x}>\mathbf{0} \)
then \( \frac{\boldsymbol{f}(\boldsymbol{x})}{\boldsymbol{x}} \)
A \( \cdot \) decreases on \( (0, \infty) \)
B . increases on \( (0, \infty) \)
c. decreases on \( (1, \infty) \)
D. neither increases nor decreases on \( (0, \infty) \)


State whether given statement is True or False.

Silver is a good conductor of electricity.
A. True
B. False


Cells are able to live and perform its functions due to the presence of
A. organelles
B. Lysosomes
c. Cell wall
D. Ribosomes


The apparatus in which electrical energy is converted into chemical
energy is known as:
A. voltameter
B. coulometer
\( c \cdot \operatorname{both}(A) \) and \( (B) \)
D. none of these


During protein synthesis, amino acid gets attached to tRNA with the help of?
\( A . \) mRNA
B. Aminoacyl synthetase
c. Ribosome
D. rRNA


The \( p H \) of a saturated solution of
\( M g(O H)_{2} \) in water will be :
\( \left(K_{s p}=4 \times 10^{-12}\right) \)
A. \( 4-\log 2 \)
B. \( 10-\log 2 \)
c. \( 4+\log 2 \)
D. \( 10+\log 2 \)


Use the figure below to answer the question that follows. Which of the four molecular structures,
I-IV, exhibits trigonal planar molecular geometry?
0
\( 0=x \)
\( 0= \)
\( A \)
B.
\( c \)
\( D \cdot \mid V \)


Electronegativity of carbon atoms
depends upon their state of hybridisation. In which of the following compounds, the carbon marked with asterisk is most electronegative?
\( \mathbf{A} \cdot C H_{3}-C H_{2}-C^{*} H_{2}-C H_{3} \)
в. \( C H_{3}-C H=C H-C H_{3} \)
c. \( C H_{3}-C H_{2}-C \stackrel{*}{C} \equiv H \)
D. \( C H_{3}-C H_{2}-C H=C^{*} H_{2} \)


Compare the bond length \( x \) and \( y \) of the
above given compound.
\( 4 \cdot x=y \)
\( 3 \cdot x>y \)
\( c \cdot x<y \)
D. x >>


Which one among the following can be classified as amphoteric?
A. \( N a_{3} P O_{4} \)
в. нс
c. маОН
D. \( H S O_{4}^{-} \)
E \( \cdot C_{2} O_{4}^{2} \)


Two Mark Questions:
Differentiate between ZZ and XY type of sex determination mechanism.


What is the structural formula of
lithium tetrahydrido aluminate?
\( \mathbf{A} \cdot A l\left[L I H_{4}\right] \)
B. \( A l_{2}\left[L i H_{4}\right]_{3} \)
c. \( L i\left[A l H_{4}\right] \)
D. \( L i\left[A l H_{4}\right]_{2} \)


Which pair of atomic numbers represents s-block elements?
A . 7, 15
B. 6, 12
c. 9,17
D. 3, 12


Elements with low electronegativity are usually non-metallic.
A. True
B. False


\( f(a, b, c \text { are in } A P \) then Prove that \( \left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{2} & \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\mathbf{2} \boldsymbol{a} \\ \boldsymbol{x}+\mathbf{3} & \boldsymbol{x}+\mathbf{4} & \boldsymbol{x}+\mathbf{2} \boldsymbol{b} \\ \boldsymbol{x}+\mathbf{4} & \boldsymbol{x}+\mathbf{5} & \boldsymbol{x}+\mathbf{2} \boldsymbol{c}\end{array}\right|=\mathbf{0} \)


Consider the following Lewis
Dot structure:
\( [: \ddot{O}=N=\ddot{O}:]^{+} \)
The sum of formal charges on \( N \) and \( O \)
is:


Check the commutative property of multiplication for \( \frac{\mathbf{2 2}}{\mathbf{4}}, \frac{\mathbf{3}}{\mathbf{4}} \)


Find the value of \( (47)^{3} \) using the shortcut or column method


\( H_{2} O_{2} \) oxidises \( M n O_{2} \) to \( M n O_{4}^{-} \) in
basic medium. \( \boldsymbol{H}_{2} \boldsymbol{O}_{2} \) and \( \boldsymbol{M} \boldsymbol{n} \boldsymbol{O}_{2} \) react
in the molar ratio of \( x: y . \) What is the
value of \( \boldsymbol{x}+\boldsymbol{y} ? \)


If \( \frac{\cos \left(\theta_{1}-\theta_{2}\right)}{\cos \left(\theta_{1}+\theta_{2}\right)}+\frac{\cos \left(\theta_{3}+\theta_{4}\right)}{\cos \left(\theta_{3}-\theta_{4}\right)}=0 \)
then \( \tan \theta_{1} \tan \theta_{2} \tan \theta_{3} \tan \theta_{4} \) is equal
to
A . -1
B.
\( c \cdot 2 \)
\( D \)


Membrane separating air in pulmonary alveoli from blood capillaries.
A. Alveolar epithelium
B. Cardiac epithelium
c. Endothelium of blood capillaries
D. Both'1' and '3'


Charges \( Q, 2 Q \) and \( 4 Q \) are uniformly distributed in three dielectric solid
spheres 1,2 and 3 of radii \( \mathrm{R} / 2, \mathrm{R} \) and \( 2 \mathrm{R} \) respectively. If magnitudes of the electric fields at point \( P \) at a distance \( R \) from the centre of spheres 1,2 and 3 are
\( E_{1}, E_{2}, \) and \( E_{3} \) respectively, then:
A. \( E_{1}>E_{2}>E_{3} \)
в. \( E_{3}>E_{1}>E_{2} \)
c. \( E_{2}>E_{1}>E_{3} \)
D. \( E_{3}>E_{2}>E_{1} \)


Write physical methods of food preservation.


Which one from the following is associated with occupational hazard?
A. Auorosis
B. Pneumoconiosis
c. silicosis
D. Both B and C


Magnetic lines of force always cross
each other. Is the given statement true or false? Justify.


Fill in the blanks.
At least
must interact for a force to come into
play.
\( A \cdot 1 \)
B. 2
\( c \cdot 3 \)
D. 4


Diabetes insipidus results from low levels of
\( \mathbf{A} \cdot \) АСТН
B. TSH
c. АDH
D. Aldosterone


When the forward bias voltage of a diode is changed froth \( 0.6 ~ V \) to \( 0.7 ~ V \)
the current changes from \( 5 m A \) to
15 m \( A \). Then its forward bias resistance
is:
\( \mathbf{A} \cdot 0.01 \Omega \)
в. \( 0.1 \Omega \)
c. \( 10 \Omega \)
D. \( 100 \Omega \)


When a man moves down the inclined
plane with a constant speed \( 5 m s^{-1} \)
which makes an angle of \( 37^{\circ} \) with the horizontal, he finds that the rain is
falling vertically downward. When he moves up the same inclined plane with
the same speed, he finds that the rain makes an angle \( \theta=\tan ^{-1}\left(\frac{7}{8}\right) \) with the horizontal. The speed of the rain is
A \( \cdot \sqrt{116} \mathrm{ms}^{-1} \)
B. \( \sqrt{32} \mathrm{ms}^{-1} \)
c. \( 5 m s^{-1} \)
D. \( \sqrt{73} \mathrm{ms}^{-1} \)


Fill in the blanks:
The distance between pole and focus is


Is it a closed curve?


Which of the following has weakest \( \boldsymbol{H}- \)
bond?
A \( . H-F \)
в. \( O-H \)
c. \( N-H \)
D. \( C-H \)


State the rule to determine the
direction of current induced in a coil
due to its rotation in a magnetic field.


Which is a quadratic equation?
A \( \cdot x+\frac{1}{x}=2 \)
B . \( x^{2}+1=(x+3)^{2} \)
c. \( x(x+2) \)
D. \( _{x+\frac{1}{x}} \)


Three identical dipoles with charges \( q \)
and -q and separation between the
charges are placed at the corners of an equilateral triangle of side d as shown in
Fig. \( 3.123 . \) Find the interaction energy of
the system \( (a< \)


Stat whether the following pairs of sets
are equal or not
(I) \( A=\{x: x \text { is a letter of the world 'paper' }\} \) and \( A=\operatorname{set} \) of digits in the number 59672
(ii) \( A=\{x: x \text { is a letter of the world 'pepar' }\} \) and \( \mathrm{B}=\operatorname{set} \) of digits in the number 756889


The equivalent conductance of \( B a^{2+} \)
and \( C l^{-} \) are respectively 127 and 76
\( \operatorname{oh} m^{-1} c m^{2} e q^{-1} \) at infinite dilution.
What will be the equivalent
conductance of \( B a C l_{2} \) at infinite
dilution?
A . 139.5 ohm \( ^{-1} \mathrm{cm}^{2} \) eq \( ^{-1} \)
B . 203 ohm \( ^{-1} \mathrm{cm}^{2} \) eq\( ^{-1} \)
c. 279 ohm \( ^{-1} \mathrm{cm}^{2} \) eq \( ^{-1} \)
D. 101.5 ohm \( ^{-1} \mathrm{cm}^{2} \) eq \( ^{-1} \)


If \( ^{n} C_{3}=^{n} C_{9}, \) then \( ^{n} C_{2}= \)
A . 66
B. 132
c. 72
D. 98


Which option is correct?
\[
\mathrm{HC} \equiv^{2}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}
\]
\( A \)
\[
\stackrel{1}{\mathrm{C}} \Rightarrow \text { sp hybridised }
\]
в.
\[
\stackrel{5}{\mathrm{C}} \Rightarrow \mathrm{sp}^{2} \text { hybridised }
\]
\( c \)
\( \stackrel{3}{\mathrm{C}} \Rightarrow \) sp \( ^{3} \) hybridised
D. A


\( 1 m A= \)


Half life of a certain radioactive
substance is 6 hours. If you had \( 3.2 k g \) of this substance in the beginning, how much of it will disintegrate in one day?


Effective collisions are those in which
molecules must:
A. have energy equal to or greater than the threshold energy
B. have proper orientation
c. acquire the energy of activation
D. all of the above


Which of the following statement is true regarding growth regulators in plants?
A. Plant growth regulators are produced only in the shoot system
B. Plant growth regulators are produced only in the root system
c. There is no specialised tissue producing plant growth regulators
D. None of the above


Verify whether the following are zeros of the polynomial indicated against them:
\( \boldsymbol{g}(\boldsymbol{x})=\mathbf{5} \boldsymbol{x}^{2}+\mathbf{7} \boldsymbol{x}, \boldsymbol{x}=\mathbf{0},-\frac{\mathbf{7}}{\mathbf{5}} \)
A. True
B. False


The reflex arc which is made of two
neurons is known as
A. Monosynaptic reflex arcc
B. Disynaptic arc
c. Polysynaptic reflex arc
D. Asynaptic reflex arcçç


Diamond is a non conductor of
electricity because?
A. There are no free electron
B. Giant polymer structure
c. High refractive index
D. Its IP value is highh


If the sum of the diagonals of a
rhombus is \( 12 \mathrm{cm} \) and its perimeter is \( 8 \sqrt{5} \mathrm{cm} \) then the lengths of the diagonals are:
\( \mathbf{A} \cdot 6 \mathrm{cm} \) and \( 6 \mathrm{cm} \)
B. \( 7 \mathrm{cm} \) and \( 5 \mathrm{cm} \)
c. \( 8 \mathrm{cm} \) and \( 14 \mathrm{cm} \)
D. \( 9 \mathrm{cm} \) and \( 3 \mathrm{cm} \)


In the given figure, how many people
study only 2 subjects?
Mathematics
A . 11
\( B .23 \)
\( c \cdot 12 \)
D. 40


The diagonals of a parallelogram are represented by \( R_{1}=3 \hat{i}+2 \hat{j}-7 \hat{k} \) and \( \boldsymbol{R}_{2}=\mathbf{5} \hat{\boldsymbol{i}}+\boldsymbol{6} \hat{\boldsymbol{j}}-\boldsymbol{3} \hat{k} . \) Find the area of the
parallelogram.


\( B r F_{3} \) has \( T \) -shaped structure.
Answer whether the above statement is
true or false.
If true enter 1 , else enter 0 .


The spin-only magnetic moments of \( \left[M n(C N)_{6}\right]^{4-} \) and \( \left[M n B r_{4}\right]^{2-} \) in Bohr Magnetons, respectively, are:
A .5 .92 and 5.92
B. 4.89 and 1.73
c. 1.73 and 5.92
D. 1.73 and 1.73


If the radius of curvature of a spherical
mirror is \( 20 \mathrm{cm}, \) then its focal length is
\( \mathrm{cm} \)
A . 20
B. 40
c. 10
D. None of these


If \( y=\left(\tan ^{-1} x\right)^{2}, \) show that \( \left(x^{2}+\right. \)
1) \( ^{2} y_{2}+2 x\left(x^{2}+1\right) y_{1}=2 \)


Which of the following is proton
acceptor?
A. Bronsted-Lowery acid
B. Arrhenius acid
c. Lewis acid
D. Bronsted-Lowery base
E. Lewis base


Integumentary nephridia are also called
A. Enteronephric
B. Exonephric
C. Sometimes enteronephic and sometimes exoneph
D. Both (a) and (b)


\( O \) is the centre of the circle. \( A B \) and
\( C D \) are two chords of the circle. \( O M \perp \)
\( A B \) and \( O N \perp C D . \) If \( O M=O N=3 \)
\( \operatorname{cmand} A M=B M=4.5 \mathrm{cm}, \) then \( C D \)
is equal to
\( A \cdot 8 \mathrm{cm} \)
B. 9 cm
\( c .10 \mathrm{cm} \)
D. None of these


Find \( A \) if \( \tan 49^{\circ}=\cot A \)


How many parallel lines can be drawn to a given line
\( \mathbf{A} \cdot \mathbf{0} \)
B.
\( c \cdot 2 \)
D. Infinite


There are three points with position vectors \( -2 a+3 b+5 c, a+2 b+3 c \) and
\( 7 a-c . \) What is the relation between the
three points?
A. Collinear
B. Forms a triangle
c. In different plane
D. None of the above


Find the value of
(a) \( ^{14} C_{5} \)
(b) \( ^{90} C_{2} \)


The point at which a satellite launched from earth into lunar orbit is nearest to
the surface of the moon is called.
A. Pericynthion
B. Perithelion
c. Aphelion
D. Apocynthion


Binomial system of nomenclature
means that every organism
has
A. Two names, one scientific and the other popular
B. One name given by two scientists
C. One scientific name consisting of a generic and specific name
D. A number in an international catalogue by which it can be identified


Why does bluish colour predominate in a clear sky?


If \( 0 \leq x \leq \frac{\pi}{2}, \) then which one of the
following is always correct? This question has multiple correct options
A \( \quad \sin ^{2} x<\frac{1}{2} \) and \( \cos ^{2} x>\frac{1}{2} \)
B. \( \quad \sin ^{2} x>\frac{1}{2} \) and \( \cos ^{2} x<\frac{1}{2} \)
c. \( \quad \sin ^{2} x<\frac{1}{2} \) and \( \cos ^{2} x<\frac{1}{2} \)
D. Atleast one of the sin \( ^{2} x, \cos ^{2} x \) is less than 1


Which one of the following statements is not true about the effect of an
increase in temperature on the distribution of molecular speeds in
a gas?
A. The area under the distribution curve remains same as under the lower temperature
B. The distribution becomes broader.
c. The fraction of the molecules increases with the most probable speed.
D. The most probable speed increases.


The velocity vector of a sphere after it hits a vertical wall which is parallel to \( \hat{j} \) is \( (-\hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}) \) on a smooth horizontal
surface. The coefficient of restitution
between ball and wall is (1/2). Find the
velocity vector of sphere immediately before collision:
\( \mathbf{A} \cdot \hat{i}+3 \hat{j} \)
В. \( -2 \hat{i}+3 \hat{j} \)
c. \( -\hat{i}+3 \hat{j} \)
D. \( 2 \hat{i}+3 \hat{j} \)


f \( x, y, z \) are three real numbers of the
same sign, then the value of \( \left(\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\right) \) lies in the interval
A. \( [2, \infty) \)
(n)
B. \( [3, \infty) \)
\( c \cdot(3, \infty) \)
D. \( (-\infty, 3) \)


If \( \boldsymbol{A}=\operatorname{diag}[\mathbf{2},-\mathbf{3},-\mathbf{5}], \boldsymbol{B}= \)
\( \operatorname{diag}[4,-6,-3] \) and \( C=\operatorname{diag}[-3,4,1] \)
then find
\( \mathbf{2 A}+\boldsymbol{B}-\mathbf{5} \boldsymbol{C} \)


Rain water harvesting is a method employed to:
A. stop soil erosion in a place
B. raise the water table of a place
c. increase afforestation around a place
D. decrease floods and droughts in a place


How many teachers are more than 35
years old?
\( A \ldots \)
B. 5
\( c \cdot 10 \)
D. 2


An animal with same generic, specific and subspecific name is
A. Man
B. Rabbitt
c. Gorilla
D. Elephant


Let \( [x] \) be the greatest integer function
\( f(x)=\frac{\sin \frac{1}{4} \pi[x]}{[x]} \) is-
This question has multiple correct options
A. not continuous at any point
B. continuous at \( \frac{3}{2} \)
c. discontinuous at 2
D. differentiable at \( \frac{4}{3} \)


At a certain university, \( 4 \% \) of men are
over 6 feet tall and \( 1 \% \) of women are over
6 feet tall. The total student population
is divided in the ratio 3: 2 in favour of
women. If a student is selected at
random from among all those over six feet tall, what is the probability that the
student is a woman?
\( A \cdot \frac{3}{11} \)
В. \( \frac{5}{11} \)
\( c \cdot \frac{7}{11} \)
D. none of these


In the above problem, acceleration of
the system is
A \( \cdot 4.9 m / s^{2} \)
B . \( 2.94 m / s^{2} \)
c. \( 1.4 m / s^{2} \)
D. \( 9.8 m / s^{2} \)


Respiratory disorder due to excessive pollution resulting in collapse and alveolar breakdown is
A. Emphysema
B. Hydrothorax
c. cyanosis
D. All of the above


A circular coil of radius \( 25 \mathrm{cm} \), carries a
current of \( 50 A \). If it has 35 turns, the
flux density at the centre of the coil is \( W b / m^{2} \)
A \( \cdot \pi \times 10^{-3} \)
В. \( 1.4 \pi \times 10^{-3} \)
c. \( 14 \pi \times 10^{-3} \)
D \( .2 \pi \times 10^{-3} \)


Which molecule has a plane of symmetry?
\( A \)
B. I
c. ॥॥
D. None of these


In which following events is a pushing
force involved?
This question has multiple correct options
A. Badminton
B. Javelin
c. Archery
D. Bowling


Magnetic field through a coil having
200 turns and cross - sectional area
\( 0.04 m^{2} \) changes from \( 0.1 W b m^{-2} \) to
\( 0.04 W b m^{-2} \) in 0.02 sec. Find the
induced emf


Common source of energy used for cooking in rural parts of India is:
A. sun
B. coal
c. wood and animal dung
D. None of the above


Which of the following is/are bad conductors of heat?

This question has multiple correct options
A. Glass
B. Aluminium
c. Iron
D. woodd


If a mass of \( 20 g \) having charge \( 3.0 m C \) moving with velocity 20 ms\( ^{-1} \) enters a
region of electric field of \( 80 N C^{-1} \) in
the same direction as the velocity of
mass, then the velocity of mass after \( 3 s \)
in the region will be
A \( \cdot 40 \mathrm{ms}^{-1} \)
B. \( 44 \mathrm{ms}^{-1} \)
\( \mathrm{c} \cdot 56 \mathrm{ms}^{-1} \)
D. \( 80 m s^{-1} \)


The s-block element used as a catalyst in the manufacture of Buna-S rubber is
\( \mathbf{A} \cdot M g \)
в. \( C a \)
\( c . B a \)
D. Na


For a chemical reaction, \( \boldsymbol{A} \rightarrow \boldsymbol{B} \), it is
observed that the rate of reaction
doubles when the concentration of \( A \) is
increased four times. The order of
reactions in \( A \) is :
A. Two
B. One
c. Half
D. zero


Classify the following proteins on the basis of their molecular shapes.
(a) Collagen
(b) Albumin (c)
Haemoglobin
(d) Myosin


Phototropism of stem and geotropism
of root are due to
A. Epinasty and hyponasty
B. Effect of light
c. Differential hormonal effect
D. Graviception


During the formation of the ionic bond, electron transfer takes place from one
atom to the others.
A. True
B. False


Two nuclei have mass number in the
ratio \( 1: 2, \) what is the ratio of their
nuclear densities?


When ammonia is added to the
solution, \( p H \) is raised to \( 11 . \) Which half-
cell reaction is affected by \( p H \) and by
how much?
\( \mathbf{A} \cdot \mathrm{E}_{\mathrm{oxd}} \) will increase by a factor of 0.65 from \( \mathrm{E}_{\text {oxd }}^{\circ} \) are
B. \( \mathrm{E}_{\text {oxd }} \) will decrease by a factor of 0.65 from \( \mathrm{E}_{\text {oxd }}^{\circ} \)
C \( \cdot \mathrm{E}_{\text {red }} \) will increase by a factor of 0.65 from \( \mathrm{E}_{\text {red }}^{\circ} \)
D. \( \mathrm{E}_{\text {red }} \) will decrease by a factor of 0.65 from \( \mathrm{E}^{\circ} \) red


Which of the following is a non-point sources of water pollution?
A. Roads runoff
B. Oil wells
c. Thermal power plants
D. Underground coal mines


In how many ways 11 players can be
selected from 15 players, if only 6 of
these players can bowl and the 11 players must include atleast 4 bowlers?


The tissue is defined as a group of
A. Cells which are dissimilar in origin, but are similar in form and function
B. Cells which are similar in origin, but dissimilar in form and function
C. Cells which are dissimilar in origin, form and function
D. Cells which are similar in origin, form and function


The oxidation states of central iodine
\( \operatorname{atom} \operatorname{in} I_{2} O_{4} \) and \( I_{4} O_{9} \) are
respectively:
\( \mathbf{A} \cdot+4,+5 \)
B. +3,+3
\( \mathrm{c} \cdot+2,+3 \)
D. +1,+3


Benzylamine reacts with nitrous acid to form mainly?
A. phenol
B. benzyl alcohol
c. benzaldehyde
D. nitrosbenzene


Match the column.


Structure of \( N_{2} O \) is similar to that of
\( \boldsymbol{C O}_{2} \)
A. True
B. False


heated on the flame directly. It crumbled to give white powder of calcium oxide. After cooling, when water is added to it a hissing sound is heard and water started boiling. If it is allowed to stay over night, a clear solution (top layer) is taken and for this experiment
below as lime water.

When carbon dioxide is bubbled into
testtube a clear solution of lime water,
turbidity appears first and later a white precipitate of calcium carbonate is formed. Carbon dioxide is continued to
passed into the same solution and the solution again became clear because of formation of calcium bicarbonate. On
heating the contents of the tube, white precipitate of calcium carbonate
reappears.
On heating limestone, the following are formed.
A. Calcium hydroxide, carbon dioxide
B. Calcium bicarbonate
c. calcium oxide and carbon dioxide
D. Calcium oxide and water


How far must a particle be on the line joining earth to sun, in order that the gravitational pull on it due to sun is
counterbalanced by that due to earth.
Given orbital radius of earth is \( 10^{8} \mathrm{Km} \)
and \( M_{S}=3.24 \times 10^{5} M_{E} \)
A \( \cdot 6.4 \times 10^{5} \mathrm{Km} \)
В. \( 1.75 \times 10^{2} \mathrm{Km} \)
\( \mathbf{c} \cdot 1.75 \times 10^{9} \mathrm{Km} \)
D. \( 6400 \mathrm{Km} \)


The normal boiling point of a liquid \( A \) is
\( 350 \mathrm{K} . \Delta \boldsymbol{H}_{\boldsymbol{v a p}} \) at normal boiling point
is \( 35 \mathrm{KJ} / \mathrm{mole} \). Pick out the correct
statement(s). (Assume \( \Delta H_{v a p} \) to be independent of pressure)
A. \( \Delta S_{\text {vaporisation}}>100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 0.5 \mathrm{atm} \)
B. \( \Delta S_{\text {vapprisation}}<100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 0.5 \mathrm{atm} \)
C. \( \Delta S_{\text {vaporisation}}<100 \) J/K mole at \( 350 \mathrm{K} \) and 2 atm
D. \( \Delta S_{\text {vaporisation}}=100 \mathrm{J} / \mathrm{K} \) mole at \( 350 \mathrm{K} \) and \( 2 \mathrm{atm} \)


Which type of energy sources are fossil
fuels? Write down any two names of fossil fuels.


If under the action of fore \( \boldsymbol{F}=-(\boldsymbol{y} \hat{\boldsymbol{i}}+ \)
\( x \hat{i} \) ) a particle moves form (0,0) to \( (a, 0) \)
then to \( (a, a) \) then find work done by force


Calculate the frequency of light emitted
for an electron transition from the sixth
to second orbit of the hydrogen atom. In
what region of the spectrum does this
light occur?


Example 3. in the following \( A P_{S} \) find
teh ,missing terms in the boxes:
A. \( 2,, 26 \)
B . \( 5, \quad,, 9 \frac{1}{2} \)
\( \mathrm{c} \ldots, 13,, 3 \)
D. Do all the above options


Human nails are good insulators
A . True
B. False


The area (in square units) bounded by the curves \( \boldsymbol{y}=\sqrt{\boldsymbol{x}} \)
\( 2 y-x+3=0, \) and lying in the first
quadrant is


What is the coordination entity formed
when excess of aqueous \( K C N \) is added
to an aqueous solution of copper
sulphate? Why is it that no precipitate of copper sulphide is obtained when
\( \boldsymbol{H}_{2} \boldsymbol{S}(\boldsymbol{g}) \) is passed through this
solution?


The length of the sides of a triangle are \( \mathbf{2} \boldsymbol{x}+\frac{\boldsymbol{y}}{\mathbf{2}}, \boldsymbol{5} \frac{\boldsymbol{x}}{\mathbf{3}}+\boldsymbol{y}+\frac{\mathbf{1}}{\mathbf{2}}, \boldsymbol{2} \frac{\boldsymbol{x}}{\mathbf{3}}+\mathbf{2} \boldsymbol{y}+\frac{\mathbf{5}}{\mathbf{2}} \)
the triangle is equilateral. Then its
perimeter is \( \frac{m}{2} . \) Find \( m \)


Two liters air formed \( 1915 \mathrm{ml} \) of ozonized
air when passed through Brodio's apparatus. The volume of ozone formed
is :
\( A \cdot 85 \mathrm{m} \)
B. 170 m1
c. 225 \( \mathrm{ml} \)
D. 42.5 m


A mass of \( 20 \mathrm{kg} \) moving with a speed of \( 10 m / s \) collides with another stationary mass of 5 kg. As a result of the collision,
the two masses stick together. The kinetic energy of the composite mass
will be
\( \mathbf{A} \cdot 600 J \)
в. \( 1000 J \)
c. \( 800 J \)
D. \( 1200 J \)


The maximum number of H-bonds
formed by a water molecule is:
A . 2
B. 8
c. 1
\( D \)


An example of curvilinear motion is -
A. an apple falling from a tree
B. a spinning wheel
c. the motion of a pendulum
D. throwing of a javelin


Solubility of Potassium nitrate:
A. increases with temperature
B. decreases with temperature
C. remains constant with temperature
D. is not related to the temperature fluctuations


In the figure below, AL is perpendicular
to BC and CM is perpendicular to AB. If
\( C L=A L=2 B L, \) find \( \$ \$ \backslash \) dfrac \( \{\text { MC }\} \)
\( [\mathrm{AM}\} \)
\( A \)
B.
\( c \)
'. cannot be determine


Determine the characteristic
impedance of a transmission line which has a capacitance of 35 pF \( / \) ft and an inductance of \( 0.25 \mu H / f t \)
A . 84.5
B. 95
\( c \cdot 65 \)
D. 66


What is the value of \( (1+i)\left(1+i^{2}\right)(1+ \)
\( \left.\boldsymbol{i}^{3}\right)\left(\mathbf{1}+\boldsymbol{i}^{4}\right) ? \)


Define the term standard unit.


Two balls are projected making an angle of 30 and 45 respectively with the horizontal. If both have the same
velocity at the highest points of their paths, then the ratio of their velocities of projection is
A. \( \sqrt{3}: \sqrt{2} \)
B. \( \sqrt{2}: 1 \)
c. \( \sqrt{2}: \sqrt{3} \)
D. \( \sqrt{3}: 2 \)


The area between the curves \( x^{2}=4 y \)
and line \( \boldsymbol{x}+\mathbf{2}=\mathbf{4} \boldsymbol{y} \) is
A \( \cdot \frac{9}{8} \)
в. \( \frac{9}{4} \)
\( c \cdot \frac{9}{2} \)
D.


If \( A \) and \( B \) are two events, then, \( 1+ \)
\( \boldsymbol{P}(\boldsymbol{A} \cap \boldsymbol{B})-\boldsymbol{P}(\boldsymbol{B})-\boldsymbol{P}(\boldsymbol{A}) \) is equal to
\( \mathbf{A} \cdot P(\bar{A} \cup \bar{B}) \)
B \( \cdot P(A \cap \bar{B}) \)
\( \mathbf{c} \cdot P(\bar{A} \cap B) \)
D \( \cdot P(A \cup B) \)
E \( \cdot P(\bar{A} \cap \bar{B}) \)


What happens when lactic acid is
treated with \( P C l_{5} \) ? Write the equation.


A mixture of carbon monoxide and
carbon dioxide is found to have a
density of 1.7 g/lit at S.T.P. The mole fraction of carbon monoxide is:
A . 0.37
B. 0.40
\( c \cdot 0.30 \)
D. 0.50


Assertion
Lower parts of the ship or bridge is
coated with coal tar
Reason
It is to increase rusting
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


Find the mode of the following:
\( \mathbf{1 8}, \mathbf{1 4}, \mathbf{2 2}, \mathbf{2 3}, \mathbf{1 4}, \mathbf{1 8}, \mathbf{1 7}, \mathbf{2 8}, \mathbf{2 8}, \mathbf{1 4}, \mathbf{2 5}, \mathbf{1} \)
A . 12
B. 13
c. 14
D. 15


Solve the following differential equation \( \frac{d y}{d x}+1=\sin x \)


Nitrogen dioxide \( \left(N O_{2}\right) \) dissociates
into nitric oxide \( (N O) \) and oxygen \( \left(O_{2}\right) \)
as follows:
\( 2 N O_{2} \rightarrow 2 N O+O_{2} \)
If the rate of decrease of concentration
of \( N O_{2} \) is \( 6.0 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)
What will be the rate of increase of
concentration of \( O_{2} ? \)
В. \( 6 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)
D. \( 1.5 \times 10^{-12} \) mol \( L^{-1} s^{-1} \)


Arrange the following compound in the
correct increasing rate of aromatic
electrophilic substitution.
A \( . A<B<C<D \)
B . \( D<A<B<C \)
c. \( B<C<D<A \)
\( . C<A<B<D \)
\( D \)


If the sum of \( n \) terms of an A.P. is \( n A+ \)
\( n^{2} B, \) where \( A, B \) are constants, then its
common difference will be
A. \( A-B \)
в. \( A+B \)
\( c .2 A \)
D. 2 \( B \)


A particle is moving with velocity \( 5 \mathrm{m} / \mathrm{s} \) towards the east and its velocity changes to \( 5 \mathrm{m} / \mathrm{s} \) north in 10 sec. Find the acceleration.
A \( \cdot \sqrt{2} m / s^{2} \mathrm{N}-\mathrm{w} \)
B. \( \frac{1}{\sqrt{2}} m / s^{2} \) N-w
\( ^{\mathrm{c}} \cdot \frac{1}{\sqrt{2}} m / s^{2} \mathrm{N}-\mathrm{E} \)
D. \( \sqrt{2} m / s^{2} \) N-E


Assertion
In a series \( L C R \) circuit, at resonance
condition power consumed by circuit is
maximum.
Reason
At resonance condition, the effective
resistance of circuit is maximum.
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 value of \( \int \frac{\sin x+\cos x}{\sqrt{1+\sin 2 x}} d x \)
\( \mathbf{A} \cdot \sin x+c \)
B. \( x+c \)
c. \( \cos x+c \)
D \( \cdot \frac{1}{2}(\sin x+\cos x) \)


Which of the following terms in the
Arrhenius equation, \( \boldsymbol{k}=\boldsymbol{A} \boldsymbol{e}^{-\boldsymbol{E}_{a} /(\boldsymbol{R} \boldsymbol{T})}, \) is
not labeled correctly?
\( \mathbf{A} \cdot E_{A} \) is the activation energy of the reaction
B. T refers to temperature
C. \( k \) refers to the rate constant of the reaction
D. R refers to electrical resistance of the reaction mixture
E. e is Euler's number, the natural base of the exponential function with a value of approximately 2.718281828


\( H_{2} O_{2} \) is always stored in black bottles
because:
A . It is highly unstable
B. Its enthalpy of decomposition is highh
c. It undergoes autooxidation on prolonged standing
D. None of these


\( A \) and \( B \) are two sets such that \( n(A \cup \)
\( B)=25, n\left(A^{\prime} \cap B\right)=8 \) and \( n(A \cap \)
\( \left.\boldsymbol{B}^{\prime}\right)=\mathbf{9} \)
Use venn -diagram to find \( n(B-A) \)


A cell of emf \( E \) and internal resistance \( r \)
is connected in series with an external
resistance \( n r . \) Then, the ratio fo the
terminal potential difference to E.M.F is
\( \mathbf{A} \cdot 1 / n \)
в. \( \frac{1}{n+1} \)
c. \( \frac{n}{n+1} \)
D. \( \frac{n+1}{n} \)


Figure shows a charge \( q \) placed at the centre of a hemisphere. A second
charge \( Q \) is placed at one of the positions \( A, B, C \) and \( D . \) In which position(s) of this second charge, the flux of the electric field through the
hemisphere remains unchanged?
his question has multiple correct options
\( A \)
3.
\( c \)
\( D \)


The diagram given show the variation of
voltage and current in an AC circuit. The circuit contains
A. Only a resistor
B. Only a pure inductor
c. Only a capcacitor
D. A capacitor and and inductor


If \( a, b, c \) are non-zero, unequal rational
numbers, then the roots of the equation \( a b c^{2} x^{2}+\left(3 a^{2}+b^{2}\right) c x-6 a^{2}-a b+ \)
\( 2 b^{2}=0 \) are
A . rational
B. imaginary
C. irrational
D. none of these


State whether given statement is True or False.
A motion is said to be in uniform
motion if a body undergoes equal displacements in equal intervals of
time.
A. True
B. False


toppr
Q Type your question
top of the object that will help us located the image? The light rays are solid blue. The dashed blue lines help
show direction
\( A \)
B.
\( c \)
\( D \)
\( E \)


Find the next term of the sequence:
\( \mathbf{0 . 5}, \mathbf{2}, \mathbf{3 . 5}, \mathbf{5}, \dots \dots \dots \)
A . 5.5
B. 6
\( c .6 .5 \)
\( D \)


Let \( r \) be the distance from the origin to
a point \( \boldsymbol{P} \) with coordinates \( \boldsymbol{x} \) and \( \boldsymbol{y} \) Designate the ratio \( \frac{y}{r} \) by \( s \) and the ratio \( \frac{x}{r} \) by \( c . \) Then the values of \( s^{2}-c^{2} \) are limited to the numbers:
A. less than -1 and greater than +1 , both excluded
B. less than -1 and greater than +1 , both included
c. between -1 and \( +! \), both excluded
D. between -1 and \( +1, \) both included
E. -1 and +1 only


In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are \( 70 m s^{-1} \) and \( 63 m s^{-1} \)
respectively. What is the lift on the wing
if its area is \( 2.5 \mathrm{m}^{2} \) ? Take the density of
air to be \( 1.3 \mathrm{kgm}^{-3} \)


Stainless steel contains:
A. \( F e, N i, C r \)
B. \( F e, N i, S n \)
c. \( F e, C, s \)
D. \( F e, P, C r \)


Which of the following statement is not
true?
\( \mathbf{A} \cdot C H_{3} C H_{2} N H_{2} \) is ethanamine
B. \( C H_{2} C H_{2} O H \) is an ether
C . Cyclopentane and 2-pentene have a molecular formula of \( C_{5} H_{10} \)
D. Alkenes an alkynes are unsaturated


Which is the wrong statement from the
following?
A. When tripalmitin is used as a substrate in respiration, the R.Q. is 0.7
B. The intermediate compound which links glycolysis with Kreb's cycle is malic acid.
C. One glucose molecule yields a net gain of 36 ATP molecules during aerobic respiration.
D. One glucose molecule yields a net gain of 2 ATP molecules during fermentation.
E. The scheme of glycolysis was given by Embden, Meyerhof and Parnas.


Development involves
A. Growth
B. Differentiation
C. Dedifferentiation
D. Both A and B


The number of complexes that can
be can be made with varying \( \boldsymbol{N} \boldsymbol{H}_{3} \) ligands to satisfy primary and secondary valencies of platinum are:
Complex; \( \left[P t C l_{4} \cdot x N H_{3}\right] \)
A. 5
B. 3
\( c \cdot 4 \)
D.


The solubility product of aluminium sulphate is given by the expression:
A \( \cdot 4 s^{3} \)
B. \( 6912 s^{7} \)
\( c \cdot s^{2} \)
D. \( 108 S^{5} \)


It is desired to make a long cylindrical
conductor whose temperature
coefficient of resistivity at \( 20^{\circ} C \) will be close to zero. If such a conductor is
made by assembling alternate disks of iron and carbon, Find the ratio of the
thickness of a carbon disk to that an
iron disk. (For carbon, \( \boldsymbol{\rho}=\mathbf{3 5 0 0} \times \)
\( 10^{-8} \Omega m \) and \( \alpha=-0.50 \times 10^{-3}^{\circ} C^{-1} \)
for iron, \( \rho=9.68 \times 10^{-8} \Omega \) and \( \alpha= \)
\( \left.\mathbf{6 . 5} \times \mathbf{1 0}^{-\mathbf{3} \circ} \mathbf{C}^{-\mathbf{1}}\right) \)
A . 0.36
B. 0.036
\( c .1 . \)
D . 2.0


Name the procedure used in the working of artificial kidney.


Simplify and round to the appropriate number of significant digits
\( (a) 16.235 \times 0.217 \times 5 \)
(b) \( 0.00435 \times 4.6 \)


The range of the function \( \boldsymbol{f}(\boldsymbol{x})= \) \( \frac{\sin (\pi[x])}{x^{2}+1} \) (where [.] denotes greatest
integer function) is
\( A \cdot\{0\} \)
в. \( R \)
c. (0,1)
() 5
\( D \cdot(0, \infty) \)


Alcoholic fermentation is carried out by
A. Saccharomyces.
B. Lactobacillus.
c. clostridium.
D. Aspergillus


State whether true or false:
Atoms normally have equal number of
protons and electrons
A. True
B. False


\( \boldsymbol{C H}_{3}-\boldsymbol{C H}_{2}-\boldsymbol{C}\left(\boldsymbol{C H}_{3}\right)(\boldsymbol{C l})-\boldsymbol{C H}_{3} \) is
\( \mathbf{a} \)
alkyl chloride.
A. primary
B. secondary
c. tertiary
D. none of these


If two balls each of mass \( 0.6 \mathrm{kg} \) moving in opposite directions with speed of \( 4 \mathrm{m} \)
\( \mathrm{s}^{-1} \) collide and rebound with same
speed, then the impulse imparted to each ball due to other is:
A. \( 0.48 k g m s^{-1} \)
B. \( 0.53 k g m s^{-1} \)
c. \( 0.81 k g m s^{-1} \)
D. \( 0.92 k g m s^{-1} \)


Western India has
A. winter
B. Rain
c. Hot summers
D. Humid climate


A particle executes SHM with time period \( \boldsymbol{T} \) and amplitude \( \boldsymbol{A} \). The
maximum possible average velocity in time \( \boldsymbol{T} / \boldsymbol{4} \) is:
\( ^{\mathrm{A}} \cdot \frac{2 A}{T} \)
в. \( \frac{4 A}{T} \)
c. \( \frac{8 A}{T} \)
D. \( \frac{4 \sqrt{2} A}{T} \)


coordinates as \( \boldsymbol{v}=\left(\boldsymbol{x}^{2}-\boldsymbol{y}^{2}\right) \)
Corresponding electric field lines in \( x-y \)
plane as shown in the figure are
\( A \)
B.
\( \mathbf{c} \)
D.


Platinum is used as a catalyst in:
A. oxidation of ammonia to form nitric acid
B. hydrogenation of oils
C. production of synthetic rubber
D. synthesis of methanol


In addition to Bombyx mori, there are several other organisms, which produce commercial silk. Match the name of the
species with the correct commercial name of their produce by selecting appropriate answers from the given codes.
\( \begin{array}{llll} & \text { List I } & & \text { List II } \\ \text { A } & \text { Antheraea pernyi } & 1 & \text { Eri silk } \\ \text { B } & \text { Attacus atlas } & 2 & \text { Oak tasar } \\ \text { C } & \text { Ailanthus } & 3 & \text { Fagara silk } \\ \text { D } & \text { Pinna squamosa } & 4 & \text { Mussel silk }\end{array} \)
A . A- 2, B- 3, C-1, D- 4
B. A- 4, B- 3, C- 2, D-1
c. \( A-1, B-2, C-4, D-3 \)
D. A- 3, B- 2, C-1, D-4


The A.M. of the observations
\( \mathbf{1} . \mathbf{3 . 5}, \mathbf{3 . 5 . 7}, \mathbf{5 . 7 . 9}, \ldots,(\mathbf{2 n}-\mathbf{1})(\mathbf{2 n}+ \)
1) \( (2 n+3) \) is \( (\forall n \in N) \)
A \( \cdot 2 n^{3}+6 n^{2}+7 n-2 \)
В \( \cdot n^{3}+8 n^{2}+7 n-2 \)
c. \( 2 n^{3}+5 n^{2}+6 n-1 \)
D. \( 2 n^{3}+8 n^{2}+7 n-2 \)


What is the distance of geo-stationary satellites from the Earth?
\( \mathbf{A} \cdot 37,956 \mathrm{km} \)
B. \( 35,786 \mathrm{km} \)
c. \( 43,000 \mathrm{km} \)
D. \( 23,123 \mathrm{km} \)


Which surfaces will reflects most of the
light falling on them?
A. Flat surface
B. Shiny surface
c. smooth surface
D. Opaque surface


\( (1+x)^{m}(1-x)^{n} x^{2}-6 \)
Find absolute value at \( \boldsymbol{x}=\mathbf{0} \)
\( A \cdot 6 \)
B. -6
c. 12
D. 24


The distance between an object and the screen is \( 100 \mathrm{cm} . \) A lens produces an image on the screen when the lens is
placed at either of the positions \( 40 \mathrm{cm} \) apart. The power of the lens is nearly
A. 3diopter
B. 5 diopter
c. 2 diopter
D. 9 diopter


Which of the following statements are
true?
This question has multiple correct options
A. In lung capillaries \( C O_{2} \) combines with water to give carbonic acid
B. In tissue capillaries, carbonic acid breaks down to
\( C O_{2} \) to water
C. In lung capillaries, the carbonic acid breaks down to \( C O_{2} \) and \( H_{2} O \)
D. It tissue capillaries, the carbonic acid combines with hydrogen ions to form the bicarbonate ions


Which of the following aromatic compound gives sulphonation reaction very easily?
A. Chlorobenzene
B. Nitrobenzene
c. Toluene
D. Benzene


On vigorous oxidation by permanganate solution \( \left(\boldsymbol{C H}_{3}\right)_{2} \boldsymbol{C}=\boldsymbol{C H}-\boldsymbol{C H}_{2} \boldsymbol{C H O} \)
gives:
A \( \cdot\left(C H_{3}\right)_{2} C O \) and \( O H C-C H_{2}-C H O \)
в. \( \left(C H_{3}\right)_{3} C O H \) and \( H C H O O \)
c. \( \left(C H_{3}\right)_{2} C O \) and \( O H C-C H_{2}-C O O H \)
D. \( \left(C H_{3}\right)_{2} C O \) and \( C H_{2}(C O O H)_{2} \)


Find out about the traditional systems of water harvesting/management in your region.
A. tanks
B. Rainwater
c. Sea
D. Holes


Two identical balls are projected, one vertically up and the other at an angle of \( 30^{0} \) to the horizontal, with same
initial speed. The potential energy at the highest point is in the ratio:
A . 4: 3
B. 3:
\( c \cdot 4: \)
D. 1:


How many sides does a Decagon have?
A. 7
B. 8
\( c \cdot 9 \)
D. 10


Thigmotropism is best seen in
\( A . \) Root apex
B. Stem apex
c. Leaf apex
D. Tendrils


The moment of inertia of an uniform
solid cylinder about it's geometrical
axis is 8 units. The moment of inertia
about the axis tangential to one of plane circular faces, i.e., about diameter of the circular base is (length of
cylinder is 3 times it's radius)
A. 52 units
B. 26 units
c. 104 units
D. 49 units


Calculate the formal charge on \( C l \) atom
in \( \boldsymbol{H} \boldsymbol{C l} \boldsymbol{O}_{4} \)


If \( \frac{x}{(x-3)(x-2)}=\frac{3}{x-3}+\frac{A}{x-2} \)
then \( A= \)
A . 1
B . 2
\( c \cdot-1 \)
D. - 2


When a wire of length \( 10 \mathrm{m} \) is subjected
to a force of \( 100 N \) along its length, the
lateral strain produced is \( 0.01 \times 10^{-3} \)
The Poisson's ratio was found to be 0.4
If the area of cross-section of wire is
\( 0.025 m^{2}, \) its Young's modulus is:
A \( \cdot 1.6 \times 10^{8} N / m^{2} \)
B . \( 2.5 \times 10^{10} N / m^{2} \)
c. \( 12.5 \times 10^{11} N / m^{2} \)
D. \( 16 \times 10^{10} N / m^{2} \)


Which of the following Indian scientists was also one of the Presidents of India?
A. A. P. J. Abdul Kalam
B. Homi Jehangir Bhabha
c. Jagadish Chandra Bose
D. Har Gobind Khorana


A current of 9.65 amp flowing for 10 minute deposits \( 3.0 g \) of a metal. The
equivalent wt. of the metal is:
A . 10
B. 30
c. 50
D. 96.5


The marked price of an article is Rs. 900 and the rate of sales-tax on it is \( 6 \% \). If on
selling the article at its marked price, a retailer has to pay \( \mathrm{VAT}=\mathrm{Rs} .4 .80 ; \) find the money paid by him (including salestax) for purchasing this article.
A. \( R s .754 .20 \)
B. \( R s .869 .20 \)
c. \( R s .946 .20 \)
D. Rs.1023.20


A body moves with a velocity of \( 36 \mathrm{km} \)
\( \boldsymbol{h}^{-1} . \) What is the value of the velocity in
\( m s^{-1} ? \)


A carbon compound contains \( 12.8 \% \) of carbon; \( 2.1 \% \) of hydrogen and \( 85.1 \% \) of bromine. The molecular mass of
compound is \( 187.9 . \) Calculate the molecular formula of the compound (Atomic mass \( \mathrm{H}=1.008, \mathrm{C}=12, \mathrm{Br}= \)
79.9)
A \( . C H_{3} B r \)
в. \( C H_{2} B r_{2} \)
\( \mathbf{c} \cdot C_{2} H_{4} B r_{2} \)
D. \( C_{2} H_{3} B r_{3} \)


The correct order of ionisation energy of
\( \boldsymbol{C}, \boldsymbol{N}, \boldsymbol{O} \& \boldsymbol{F} \) is:
A. \( F<N<C<O \)
в. \( C<N<O<F \)
c. \( C<O<N<F \)
D. \( F<O<N<C \)


State True or False.
All the molecules in a gas have the same kinetic energy.
A. True
B. False


A polished, silvery surface is a:
A. Good absorber and good reflector of heat
B. Good absorber and bad radiator of heat
C. Poor absorber and good reflector of heat
D. Poor reflector and good radiator of heat


In which plant Calvin experimented by radioactive isotope to discover the
stable product of \( C_{3} \) cycle?
A. Chlorella
B. Cycas
c. Daucus
D. Nicotiana


Use remainder theorem to find
remainder when \( p(x) \) is divided by \( q(x) \) in the following questions:
\( \boldsymbol{p}(\boldsymbol{x})=\mathbf{2} \boldsymbol{x}^{2}-\mathbf{5} \boldsymbol{x}+\mathbf{7}, \boldsymbol{q}(\boldsymbol{x})=\boldsymbol{x}-\mathbf{1} \)


Solve:
\( \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin x+\cos x}{\sqrt{\sin 2 x}} d x \)


Find the number of ligands (s) which are monodentate, neutral as well as a non-classical ligand.
\( \left[\boldsymbol{C O}, \boldsymbol{C N}^{-}, \boldsymbol{S}_{2} \boldsymbol{O}_{3}^{2-}, \boldsymbol{P F}_{3}\right] \)


Short / Long Answer Types:
Are carbohydrates such as glucose the only source of energy for the cell?


If a body is positively charged, then it
has
A. Excess of electrons
B. Excess of protons
c. Deficiency of electrons
D. Deficiency of neutrons


\( \left[\boldsymbol{N} \boldsymbol{H}\left(\boldsymbol{C H}_{2}\right)_{6} \boldsymbol{N H C O}\left(\boldsymbol{C H}_{2}\right)_{4} \boldsymbol{C O}\right]_{n} \)
\( \mathbf{a} \)
A. copolymer
B. addition polymer
c. thermosetting polymer
D. homopolymer


The lanthanoid ion which contains
unpaired electrons is:
A \( \cdot C e^{4} \)
в. \( Y b^{2} \)
c. \( L u^{3} \)
D. \( E u^{2} \)


For \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{3} \) and \( \boldsymbol{H}_{3} \boldsymbol{P} \boldsymbol{O}_{4} \) the correct
choice is :
A \( \cdot H_{3} P O_{3} \) is dibasic and reducing agent
B. \( H_{3} P O_{3} \) is diabasic and non-reducing agent
c. \( H_{3} P O_{4} \) is tribasic and reducing agent.
D. \( H_{3} P O_{3} \) is tribasic and non-reducing agent


Answer in 40 to 80 words:
With reference to ecological succession
define the following terms:
i) Climax community
ii) Sere(s)
iii) Pioneer species.


A boy of mass \( \mathrm{m} \) is standing on a block of mass M kept on a rough surface. When the boy walks from left to right on
the block, the centre of mass(boy \( + \)
block) of the system.
A. Remains stationary
B. Shifts towards left
c. shifts towards right
D. Shifts toward right if \( \mathrm{M}>\mathrm{m} \) and toward left if \( \mathrm{M}<\mathrm{m} \).


Respiration is controlled by
A. Medulla oblongata
B. Cerebellum
c. Hypothalamus
D. Cerebrum


A rigid tank contains \( 35 k g \) of nitrogen
at 6 atm. Sufficient quantity of oxygen is supplied to increase the pressure to 9 atm, while the temperature remains constant. Amount of oxygen supplied to the tank is :
A. \( 5 k g \)
B. \( 10 \mathrm{kg} \)
c. \( 20 k g \)
D. \( 40 \mathrm{kg} \)


A student wrote the relation for one
unified atomic mass unit (u) as \( 1 u= \)
\( 931.5 M e V . \) What is the correct
relation?
A. \( 1 u \times c=931.5 \) MeV
В . \( 1 u \times c^{2}=931.5 \mathrm{MeV} \)
c. \( \frac{1 u}{c^{2}}=931.5 \mathrm{MeV} \)
D. \( (1 u)^{2} \times c=931.5 \mathrm{MeV} \)


A mono-electronic species in energy
level with energy X was provided with
excess of energy so that it jumps to higher energy level with energy Y. If it
can emit 6 wavelengths originated from all possible transition between these groups levels, then which of the
following relation is correct?
(Here \( n \) is the principle quantum of
energy level \( X \) )
A \( . X / Y=(n-1)^{2} \)
B. \( X / Y=1+3 / N \)
c. \( \sqrt{(X / Y)}=1+3 / N \)
D. \( X / Y=N / 6 \)


A body of mass 5 kg undergoes a change in speed from 20 to \( 0.20 \mathrm{m} / \mathrm{s} \)
The momentum of the body would:
A. increase by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
B. decrease by \( 99 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
c. increase by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)
D. decrease by \( 101 \mathrm{kg} \mathrm{m} / \mathrm{s} \)


Synthetic fibers are obtained from which of the following?
A. Plants
B. Sheeps
c. chemicals
D. Jute


An alpha particle moving with an initia velocity \( (u j) \) enters a region of uniform
magnetic field \( B=B k \). the de-Broglie
wavelength of the alpha particle.
A. Increases to a higher constant value
B. Decreases to a lower constant value
c. Increases and decreases periodically
D. Remains constant


Imbibition involves
A . Solute potential
B. Gravity potential
c. Matric potential
D. Pressure potential


The magnetic field in a region is given by \( \vec{B}=B_{0}\left(1+\frac{x}{a}\right) \hat{k} . \) A square loop of edge length \( d \) is placed with its edge
along the \( x \) - and \( y \) -axes. The loop is
moved with a constant velocity \( \overrightarrow{\boldsymbol{v}}=\boldsymbol{v}_{\mathbf{0}} \hat{\boldsymbol{i}} \)
The emf induced in the loop is
A \( \cdot \frac{v_{0} B_{0} d^{2}}{a} \)
B. \( \frac{v_{0} B_{0} d^{3}}{a^{2}} \)
\( \mathbf{c} \cdot v_{0} B_{0} d \)
\( \mathbf{D} \cdot 2 v_{0} B_{0} d \)
E . zero


Which of the following particles will experience maximum magnetic force (magnitude) when projected with the same velocity perpendicular to a magnetic field?
A. Electron
B. Proton
\( \mathrm{c} \cdot \mathrm{He}^{+} \)
D. \( L i^{+} \)


Prove that the product of the lengths of the perpendiculars drawn from the points \( (\sqrt{a^{2}-b^{2}}, 0) \) and
\( (-\sqrt{a^{2}-b^{2}}, 0) \) to the line \( \frac{x}{a} \cos \theta+ \)
\( \frac{y}{b} \sin \theta=1 \) is \( b^{2} \)


Silver metal is recovered industrially by using the chemistry shown below. Which of the following statements is/are not true?
\( \boldsymbol{2} \boldsymbol{K}\left[\boldsymbol{A} \boldsymbol{g}(\boldsymbol{C} \boldsymbol{N})_{2}\right]+\boldsymbol{Z} \boldsymbol{n} \rightarrow \)
\( \mathbf{4} \boldsymbol{K}_{\mathbf{2}}\left[\boldsymbol{Z} \boldsymbol{n}(\boldsymbol{C} \boldsymbol{N})_{4}\right]+\mathbf{2} \boldsymbol{A} \boldsymbol{g} \)
This question has multiple correct options
A. Ag has been oxidised and Zn reduced
B. Ag has been reduced and Zn oxidised
c. Both \( \mathrm{Ag} \) and \( \mathrm{Zn} \) have been oxidised
D. Both Ag and Zn have been reduced


Which of the following units is a unit of
power?
A. Kilowatt hour
B. Watt
c. Erg
D. Calorie


Investigate the behaviour of the
function \( \boldsymbol{y}=\left(\boldsymbol{x}^{3}+\boldsymbol{4}\right)(\boldsymbol{x}+\mathbf{1})^{3} \) and
construct its graph. How many
solutions does the equation \( \left(x^{3}+\right. \)
4)\( (x+1)^{3}=c \) possess?


How many stereocenters are there in
the following molecule?
\( A \)
B.
\( c \cdot 2 \)
\( D \)


The b.p. of a solution of \( 5 g \) of sulphur in
100g of carbon disulphide is \( 0.476^{\circ} \)
above that of pure solvent. Determine
the moles of sulphur in this solvent. The
b.p. of pure carbon disulphide is
\( 46.30^{\circ} \mathrm{C} \) and its heat of vaporation is
84.1 calories per gram.


How will you convert benzene into \( p \) nitrotoluene?


The offspring of a cross between two individuals differing in at least one set of characters is called as
A. Polyploid
B. Mutant
c. Hybrid
D. Variant


\( \int_{100}^{2014} \frac{\sqrt{x}}{\sqrt{2114-x}+\sqrt{x}} d x= \)
A . 1914
в. 957
\( c .1007 \)
D. \( \frac{2015}{2} \)


One factor of \( \Delta= \)
\( \left|\begin{array}{ccc}a^{2}+\lambda & a b & a c \\ a b & b^{2}+\lambda & c b \\ c a & c b & c^{2}+\lambda\end{array}\right| \)
\( A \cdot \lambda^{2} \)
B. \( 1 / \lambda \)
c. \( \left(a^{2}+\lambda\right)\left(b^{2}+\lambda\right)\left(c^{2}+\lambda\right) \)
D. none


A point on the parabola \( y^{2}=18 x \) at
which the ordinate increase at twice the
rate of the abscissa is \( \left(\frac{d x}{d t} \neq 0\right) \)
\( ^{\text {A }} \cdot\left(\frac{9}{8}, \frac{9}{2}\right) \)
в. (2,-4)
\( ^{\mathbf{C}} \cdot\left(-\frac{9}{8}, \frac{9}{2}\right) \)
D. (2,4)


The characteristic that is shared by urea, uric acid and ammonia is /are
(A) They are nitrogenous wastes.
(B) They all need very large amount of water for excretion.
(C) They are all equally toxic.
(D) They are produced in the kidneys.
A . A and C
B. \( A, C \) and \( D \)
c. A and
D. A only


State the law of conservation of mass.
Give one example to illustrate this law.


Give scientific reason:
Danger signals are red in color.


Common origin of man and chimpanzee is best shown by
A. Dental formula
B. Cranial capacity
c. Binocular vision
D. chromosome number


Two particles of masses \( m \) and \( 2 m \) moving in opposite directions collide elastically with velocity \( 2 \nu \) and \( \nu \) respectively. Find their velocities after collision.
\[
n \stackrel{2 v}{\longrightarrow} \quad \stackrel{v}{-2 m}
\]


State whether given statement is True or False.
A five rupees coin has more inertia
than a one-rupee coin.
A. True
B. False


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


A parallel beam of natural light is
incident at an angle of \( 58^{\circ} \) on a plane glass surface. The reflected beam is
completely linearly polarized(tan \( 58^{\circ}= \)
1.6). The angle of refraction of the transmitted beam and the refractive
index of the glass are :
A \( \cdot 32^{\circ}, 1.6 \)
B. 3.2^,1.6
c. \( 32^{\circ}, 1.3 \)
D. 3.2?, 1.3


The solution of \( y \frac{d y}{d x}=1+y^{2} \) is:
A \( \cdot 2 x=\log \left[c\left(1+y^{2}\right)\right] \)
в. \( x=c y^{2} \)
c. \( c\left(1+y^{2}\right)=x \)
D \( \cdot 2 y=\log \left\{c\left(1+x^{2}\right)\right\} \)


A string breaks if its tension exceeds 10 newtons \( A \) stone of mass 250 gm tied to
this string length \( 10 \mathrm{cm} \) is rotated in a horizontal circle The maximum angular velocity of rotation can be.


A plant that possess vascular tissues
is
A. Funaria
B. Equisetum
c. Polytrichum
D. Sphagnum


6 married couples are standing in a
room. If 4 people are chosen at random, then the chance that exactly one
married couple is among the 4 is?
A \( \cdot \frac{16}{33} \)
в. \( \frac{8}{33} \)
c. \( \frac{17}{33} \)
D. \( \frac{24}{33} \)


A system is taken around the cycle
shown in figure from state \( a \) to state \( b \)
and then back to state \( a \). The absolute
value of the heat transfer during one
cycle is 7200 . \( J \) What is the work \( W \)
done (in \( J \) ) by the system in one cycle?


A particle is acted upon by a force given
by \( \boldsymbol{F}=-\boldsymbol{\alpha} \boldsymbol{x}^{3}-\boldsymbol{\beta} \boldsymbol{x}^{4} \) where \( \boldsymbol{\alpha} \) and \( \boldsymbol{\beta} \) are
positive constants. At the point \( x=0 \)
the particle is
A. In stable equilibrium
B. In unstable equilibrium
c. In neutral equilibrium
D. Not in equilibrium


What are the characteristics
of heterotrophic nutrition?
A. Organisms posses chlorophyll.
B. Organisms are able to build up their own organic food from raw materials.
C. Organisms can not make their own food.
D. None of the above.


Find the maximum value of \( x \) such that
\( \mathbf{5} \boldsymbol{x}+\mathbf{7} \leq \mathbf{3} \boldsymbol{x}+\mathbf{9} \)


Solve the following equations by substitution method.
\( \mathbf{5} \boldsymbol{x}+\mathbf{3} \boldsymbol{y}=\mathbf{2} \mathbf{1} ; \mathbf{2} \boldsymbol{x}-\boldsymbol{y}=\mathbf{4} \)
A. \( x=3, y=2 \)
в. \( x=-3, y=2 \)
c. \( x=3, y=-2 \)
D. None of these


To increase the magnification of a
telescope
A. the objective lens should be of large focal length and eyepiece should be of small focal length.
B. the objective and eyepiece both should be of large focal length.
C. both the objective and eyepiece should be of smaller focal lengths
D. the objective should be of small focal length and eyepiece should be of large focal length


If \( 0 \leq \arg z \leq \frac{\pi}{4}, \) then the least value of \( \sqrt{\mathbf{2}}|\mathbf{2} z-\mathbf{4}| \) is
A. 6
B.
\( c \cdot 4 \)
D.


A shown in figure there is a spring block
system. Block of mass \( 500 \mathrm{g} \) is pressed against a horizontal spring fixed at one
end to compress the spring through 5.0
cm. The spring constant is \( 500 \mathrm{N} / \mathrm{m} \) When released, the block moves
horizontally till it leaves the spring Calculate the distance where it will hit
the ground 4 m below the spring?
\( A \cdot 6 m \)
в. \( 4 m \)
\( c .8 m \)
\( D \cdot \sqrt{2} m \)


Non-functional stamens are called
A. Assessory stamens
B. Staminodes
c. supplementary stamens
D. Staminates


Express in radians \( 47^{\circ} 25^{\prime} 36^{\prime \prime} \)
A \( \cdot \frac{3472}{38921} \pi^{c} \)
B \( \cdot \frac{3247}{13562} \pi^{c} \)
c. \( \frac{3557}{13500} \pi^{c} \)
D. \( \frac{6582}{25700} \pi^{c} \)


Which is the correct assignment of
chirality at \( C 2 \) and \( C 4 \) of the following
molecule?
A \( .2 S, 4 S \)
в. \( 2 R, 4 R \)
c. \( 2 S, 4 R \)
D. \( 2 R, 4 S \)


What is a parent chain?
A. Longest carbon chain
B. Shortest carbon chain
C. Chain with a bent
D. Chain with side chains


There are two wires \( a b \) and \( c d \) in a
vertical plane as shown in figure.Direction of current in wire \( a b \) is
rightwards.Choose the correct options
This question has multiple correct options
A. If wire \( a b \) is fixed then wie \( c d \) can be kept in equilibrium by the current in \( c d \) in leftward direction
B. Equilibrium of wie \( c d \) will be stable equilibrium
C. If wire \( c d \) is fixed,then wire \( a b \) can be kept in equilibrium by flowing current in \( c d \) in rightward direction
D. Equilibrium of wire \( a b \) will be stable equilibrium


Find odd one out:
\( \mathbf{A} \cdot \) Coal
B. Petroleum
C. Natural gas
D. Wind


By dropping a drop of water on a glowing electric bulb, it bursts. This is because
glass is a
A. good conductor of heat
B. bad conductor of heat
c. transparent substance
D. good conductor of electricity


Add
\( (-7)+(-8)+(-90) \)


\( \int \frac{\sqrt{\cot x}-\sqrt{\tan x}}{\sqrt{2}(\cos x+\sin x)} d x \) equals to
A \( \cdot \sec ^{-1}(\sin x+\cos x)+c \)
B. \( \sec ^{-1}(\sin x-\cos x)+c \)
c. \( \ln |(\sin x+\cos x)+\sqrt{\sin 2 x}|+c \)
D. \( \ln |(\sin x-\cos x)+\sqrt{\sin 2 x}|+c \)


Assertion: \( C a C l_{2} \) can't be used for
drying ethyl alcohol
Reason: Calcium chloride can form an
addition compound with ethyl alcohol
A. Both Assertion and Reason are true and Reason is the correct explanation to Assertion
B. Both Assertion and Reason are true and Reason is not the correct explanation to Assertion
c. Assertion is true but Reason is false
D. Assertion is false but Reason is true


Which of the following is/are not false?
This question has multiple correct options
A. The mid point of the line segment joining the foci is called the centre of the ellipse.
B. The line segment through the foci of the ellipse is called the major axis.
C. The end points of the major axis are called the vertices of the ellipse.
D. Ellipse is symmetric with respect to Y-axis only.


Substances such as metal, their
sulphites form Iyophobic sols.
If true enter 1 , else enter 0 .
\( A \)


Chromatid bodies occur
in Entamoeba during
A. Precyst stage
B. Early cysts
c. Tetranucleate cysts
D. Trophozoites


A bag contains 5 balls of unknown colors, two balls are drawn at random
from the bag and are found to be red. The probability that the bag contains exactly 4 red balls is.
A \( \cdot \frac{3}{5} \)
B. \( \frac{3}{10} \)
c. \( \frac{5}{13} \)
D. \( \frac{4}{13} \)


An inductor of 2 henry and a resistance of 10 ohms are connected in series with
a battery of 5 volts. The initial rate of
change of current is:
A. 0.5 amp/sec
B. 2.0 amp/sec
c. 2.5 amp/sec
D. 0.25 amp / sec


The mean kinetic energy of a gas
molecule is proportional to
\( \mathbf{A} \cdot \sqrt{T} \)
B . \( T^{3} \)
\( c . T \)
D. None of the above


Cylinder \( A \) has diameter \( 14 \mathrm{cm}, \) and the
height is \( 7 \mathrm{cm}, \) and cylinder \( B \) has
diameter \( 7 \mathrm{cm} \) and height is \( 14 \mathrm{cm} \)
Without calculation tell volume of
which cylinder is more? Verify the
answer by calculation


Choose the correct answer from the
alternatives given
Phosphorus is a structural element in:
A. nucleic acids
B. carbohydrates
c. proteins
D. lipids


Fog is an example of colloidal system with liquid dispersed in gas.
A. True
B. False


The value of \( x \) in the expression
\( \left(x+x^{\log _{10} x}\right)^{5}, \) if the third term in the
expansion is \( 10,00,000, \) is This question has multiple correct options
A \( \cdot 10^{-1} \)
B . \( 10^{\text {। }} \)
\( \mathbf{c} \cdot 10^{-5 / 2} \)
D. \( 10^{5 / 2} \)


State Henry's law and mention some
important applications?


The \( E_{1} \) of \( H \) is \( 13.6 e V . \) It is exposed to electromagnetic waves of \( 1028 \dot{A} \) and gives out induced radiation. Find the
wavelengths of these induced radiation.

This question has multiple correct options
A \( \cdot \lambda_{3}=1216 \hat{A} \)
B . \( \lambda_{2}=6568 \AA \)
c. \( \lambda_{2}=1000 \dot{A} \)
D. \( \lambda_{2}=2432 \hat{h} \)


Infinite number of cells having emfs and internal resistances \( (\boldsymbol{E}, \boldsymbol{r}),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}}, \frac{\boldsymbol{r}}{\boldsymbol{n}}\right),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}^{2}}, \frac{\boldsymbol{r}}{\boldsymbol{n}^{2}}\right),\left(\frac{\boldsymbol{E}}{\boldsymbol{n}^{3}}, \frac{\boldsymbol{r}}{\boldsymbol{n}^{3}}\right) \)
ara connected in series in same manner
\( \operatorname{across} \) an external resistance of \( \frac{\boldsymbol{n} \boldsymbol{r}}{\boldsymbol{n}-\mathbf{1}} \)
Current flowing through the external
resistor is:
A \( \cdot \frac{E}{2 r} \)
B. \( \frac{E}{(n+1) r} \)
c. \( \frac{(n-1) E}{r} \)
D. \( \frac{(n-1) E}{2 r} \)


Attainment of equilibrium in a coloured gaseous reversible reaction is detected
by the constancy of:
A. colour
B. density
c. pressure
D. all the above properties of the mixture


Find the number of solutions of the
equations;
\( |\cos x|=2[x](\text { where }[] \) denotes
greatest integer function


What is the multiplicative inverse of -6
\( ? \)
A. -6
B. 6
c. \( \frac{-1}{6} \)
D. \( \frac{1}{6} \)


Chipko movement was launched for the protection of
A. Wetlands
B. Forests
c. Grasslands
D. Livestock


A carom board \( (4 f t \times 4 f t \text { square }) \) has
the queen at the centre. The queen, hit by the striker moves to the front edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen
(i) from the centre to the front edge
\( (i i) \) from the front edge to the hole and
(iiii) from the centre of the hole.
A.
\( (i) \frac{2}{3} \sqrt{10} f t(i i) \frac{4}{3} \sqrt{10} f t(i i i) 2 \sqrt{2} f t \)
в.
(i) \( \frac{4}{3} \sqrt{10} f t(i i) \frac{4}{3} \sqrt{10} f t(i i i) 2 \sqrt{2} f t \)
\( c \)
(i) \( \frac{4}{3} \sqrt{10} f t(i i) \frac{2}{3} \sqrt{10} f t(i i i) 2 \sqrt{2} f t \)
\( D \)
\( (i) \frac{2}{3} \sqrt{10} f t(i i) \frac{2}{3} \sqrt{10} f t(i i i) 2 \sqrt{2} f t \)


Assertion
Carbon and its compounds used as fuels for most applications.
Reason
When carbon is heated in presence of excess of air or oxygen, it forms carbon dioxide. During its formation, a large amount of heat and light are released.
Further, once ignited, carbon and its
compounds keep on burning without needing additional heat energy.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect


If \( z=\frac{2-i}{i}, \) then \( \quad R e\left(z^{2}\right)+I m\left(z^{2}\right) \)
is equal to
A . 1
B. -
\( c \cdot 2 \)
D. - -
\( E \)


A planet's density is 3 times that of the Earth. But the acceleration due to
gravity on its surface is exactly the same as on the Earth's surface. The
radius of the planet in terms of the Earth's radius \( R \) is
A \( .2 . R \)
в. \( 3 R \)
c. \( \frac{R}{3} \)
D. none of the above


Identify whether the following sequence is a geometric sequence or not. \( \frac{1}{2}, \frac{2}{4}, \frac{4}{8}, \frac{8}{16} \)


The equilibrium constant \( \left(\boldsymbol{K}_{\boldsymbol{p}}\right) \) for the reaction \( \boldsymbol{P} \boldsymbol{C l} \boldsymbol{l}_{5}(\boldsymbol{g}) \rightleftharpoons \boldsymbol{P} C l_{3}(\boldsymbol{g}) \) is \( 16 . \) If
the volume of the container is reduced
to one-half its original volume, the value
of \( K_{p} \) for the reaction at the same
temperature will be:
A . 32
B. 64
\( c \cdot 16 \)
D. 4


enthalpy stabilises an ionic compound the most.
A. low ionization
B. high electron affinity
c. lattice
D. none of them


Trapezoidal rule for evaluation of \( \int_{a}^{b} f(x) d x \) requires the interval \( (a, b) \) to
be divided into
A. \( 2 n \) sub-intervals of equal width
B. any number of sub intervals of not equal width
C . any number of sub intervals of equal width
D. \( 3 n \) sub-intervals of equal width


Read the following statements and answer whether the given statement is true or false.
S.I. unit of magnetic flux is weber. It is a vector quantity
A. True
B. False


Ornithorhynchus is an example of
A. Dinosaur
B. Monotreme mammal
c. Marsupial mammal
D. Eutherian mammal


Pressure exerted by static fluid does not depends on
A. Shape of the liquid
B. Total mass of liquid
c. Surface area of liquid
D. All of these


Calculate the volume of \( C O_{2} \) evolved by
the combustion of \( 50 \mathrm{ml} \) of a mixture
containing 40 per \( C_{2} H_{4} \) and 60 per
\( \boldsymbol{C H}_{4} \) (by volume)
\( \mathbf{A} \cdot 70 \mathrm{ml} \)
B. \( 75 \mathrm{ml} \)
c. \( 80 \mathrm{ml} \)
\( \mathbf{D} \cdot 82 \mathrm{m} \)


State the number of protons, electrons
\& neutrons in atom \( B \) whose atomic
number is 11 and mass number is 23 .
A. 11,11,12
B. 11,12,12
c. 11,11,11
D. 12,11,11


is an example of Hemichordata.
A. Balanoglossus
B. Star fish
c. Echinus
D. Dog fish


Cell wall in cork is impervious to water
and gases due to presence of
A. Lignin
B. Pectin
c. suberin
D. Cellulose


Choose that set of numbers from the
option set that is similar to the given \( \operatorname{set}\{10,15,65\} \)
B . \{124,5,3\}
c. \{95,25,5\}
D. \{168,15,4\}


The medicines which relieve pain are
called


If \( \vec{a} \) and \( \vec{b} \) are not perpendicular and \( \vec{c} \) and \( \vec{d} \) are such that \( \vec{b} \times \vec{c}=\vec{b} \times \vec{a} \) and \( \vec{a} \cdot \vec{d}=0 \) then \( \bar{d} \)
is equal to
A \( \cdot \vec{c}-\left(\frac{\vec{a} \cdot \vec{c}}{\vec{a} \cdot \vec{b}}\right) \cdot \vec{b} \)
B \( \cdot \frac{\vec{a}}{p}-\frac{(\vec{c} \vec{c} \vec{a})}{p^{2}} \vec{b} \)
C \( \cdot \frac{\vec{b}}{p}-\frac{(\vec{a} \cdot \vec{\alpha}) \bar{c}}{\bar{p}^{2}} \bar{c} \)
D. \( \frac{\vec{p}}{p^{2}}-\frac{(\vec{b} \cdot \vec{c})}{\vec{p}} \vec{a} \)


Find the degree of following polynomial \( 4 x-\sqrt{5} \)
A \( \cdot \frac{1}{2} \)
B.
\( c \cdot 2 \)
D.


The gas absorbed during photosynthesis is
A. oxygen
B. Nitrogen
c. Ammonia
D. carbon dioxide


An object, moving with a speed of \( 6.25 m s^{-1}, \) is decelerated at a rate given by \( \frac{d v}{d t}=-2.5 \sqrt{v} \) where \( v \) is the instantaneous speed. The time taken by the object, to come to rest, would be
A . \( 1 s \)
B . 2 s
c. \( 4 s \)
D. 8


Some stars appear red in colour and
some blue in colour. Which one of the
statements is true?
A. Star with blue colour has more temperature than red colour star
B. Temperature of blue colour star is less than red colour star
c. There is no relation between colour of the star and temperature
D. Blue colour star and red colour star has equal temperature


Differentiate between homogeneous
and heterogeneous catalysis with one example of each.


Find the equivalent resistance between \( A \) and \( E \) (The resistance of each
resistor is \( R \).)
\( A \cdot \frac{7}{12} F \)
3. \( \frac{7}{13} \) f
\( c \cdot \frac{7}{15} \)
D. \( \frac{8}{13} R \)


Write the formula for each of the
following complexes:
(a) tetraamminecopper (II) sulphate
(b) potassium tetracyanonickelate (0)
(c) bis (cyclopentadiehyl)iron(II)
(d) tetrathicyanato -N-zinc (II)
(e) diamminebis (ethylenediamine) cobalt (III) chloride
\( (f) \)
tetraammineddithiocyanatochromium
\( (\| I) \)
(g) potassium tetraoxomanganate (VII)
(h) potassium terioxalatoalumminate
\( (\| I) \)
(i) tetrapyridineplatinum (II) tetrachloroplatinate (II)


What are bio-hard and bio-soft
detergents? Give one-one illustration of
each.


A spherical half of volume \( 1000 \mathrm{cm}^{3} \) is
subjected to a pressure of 10 atmosphere. The change in volume is \( 10^{-3} \mathrm{cm}^{-3} . \) If the ball is made of iron
find its bulk modulus.(Atmospheric
pressure \( \left.=1 \times 10^{3} N m^{-2}\right) \)
\( \mathbf{A} \cdot 3 \times 10^{11} N / m^{2} \)
B . \( 2 \times 10^{11} N / m^{2} \)
c. \( 1 \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)
D. \( 4 \times 10^{11} \mathrm{N} / \mathrm{m}^{2} \)


A charged drop of radius \( 1.92 \mathrm{mm} \) is kept stationary by the application of an electric field of \( 1.65 \times 10^{6} \mathrm{N} / \mathrm{C} \) in
Millikans oil drop experiment. The charge, if the density of oil is 920 \( K g / m^{3}, \) is
A \( \cdot 1.72 \times 10^{-18} \)
В. \( 16.2 \times 10^{-19} \)
c. \( 1.82 \times 10^{-17} \)
D. \( 1.92 \times 10^{-17} \)


Find the area of the semicircle with
diameter \( 6 \mathrm{cm} \)
A . \( 3.5 \pi \) sq.units
в. \( 4.5 \pi \) sq.units
\( \mathrm{c} .5 .5 \pi \) sq.units
D. \( 6.5 \pi \) sq.units


When a light of wavelength \( 4000 A \) in vacuum travels through the same thickness in diamond and water
separately, the difference in the number of waves is \( 200 . \) Find the thickness, if refractive indices of diamond and water \( \operatorname{are} \frac{5}{2} \) and \( \frac{4}{3} \) respectively.
\( \mathbf{A} \cdot 0.685 m m \)
B. \( 0.0685 \mathrm{mm} \)
\( \mathbf{c} .68 .5 \mathrm{mm} \)
D. \( 6.85 \mathrm{mm} \)


Rank the arrangements of masses given in the table below according the
force between masses, greatest first. The first column in the table tells the
mass of one of the objects in each arrangements, the second column gives the mass of the second object, and the third column gives the distance between the centers of the objects.
\( \boldsymbol{m}_{1} \) , an a \( m_{2} \)
Arrangement 1 M м
М 2M 1 Arrangement 2
зм 1 Arrangement 3 1 М
A .1,2,3
B. 1,2 and 3 tie
c. 1,3,2
D. 3, 2,1
E. 2 and 3 tie,


Choose the correct answer from the
alternatives given. In a closed circulatory system, blood is completely enclosed within:
A . Heart
B. vessels
c. sinuses
D. coelom


Assertion
The electric bulbs glows immediately
when switch is on.
Reason
The drift velocity of electrons in a
metallic wire is very high.
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 phenomenon due to which white light splits into seven colours on passing through a prism is called
A. reflection
B. refraction
c. dispersion
D. all the above


If \( P\left(E_{k}\right) \propto k \) for \( 0 \leq k \leq n, \) the \( P(A) \)
equals
A. \( 3 n /(4 n+1) \)
B. \( (2 n+1) / 3 n \)
c. \( 1 /(n+1) \)
D. \( 1 / n^{2} \)


\( \int_{0}^{2 \pi} \sin ^{4} x d x \) is equal to
This question has multiple correct options
\( \mathbf{A} \cdot 2 \int_{0}^{\pi} \sin ^{4} x d c \)
B. \( 8 \int_{0}^{\frac{\pi}{4}} \sin ^{4} x d x \)
C \( \cdot 4 \int_{0}^{\frac{\pi}{2}} \cos ^{4} x d x \)
D. \( 3 \int_{0}^{\frac{2 \pi}{3}} \sin ^{4} x d x \)


Two atoms are said to be isobars if ?
A. They have same atomic number but different mass number
B. They have same number of electrons but different number of neutrons
C. They have same number of neutrons but different number of electrons
D. Sum of the number of protons and neutrons is same but the number of protons is different.


Mean proportion of 64 and 225 will be -
A \( \cdot 120 \)
B. 90
\( c \cdot 60 \)
D. 30


\( 5 \times 10^{7} \mu s \) is equivalent to
A . \( 0.5 \mathrm{s} \)
B. 5 s
\( c .50 \mathrm{s} \)
D. 500 s


Find the values of \( x, \) if \( \left|\begin{array}{ll}\mathbf{3} & \boldsymbol{x} \\ \boldsymbol{x} & \mathbf{1}\end{array}\right|=\left|\begin{array}{ll}\mathbf{3} & \mathbf{2} \\ \mathbf{4} & \mathbf{1}\end{array}\right| \)


What is the mean deviation about the
mean for the data 4,7,8,9,10,12,13,17
\( ? \)
A . 2.5
B. 3
\( c .3 .5 \)
D. 4


The heat of formation of HI from the
equation \( H_{2}+I_{2} \rightarrow 2 H I, \Delta H=+52 K J \) is
A . -26 KJ
B. +26 KJ
c. -52 К」
D. +52 KJ


A child staying in a coastal region tests
the drinking water and also the seawater with his tester. He finds that
the compass needle deflects more in the case of seawater. Can you explain the reason?


How is the equal genetic contribution of male and female parents ensured in
the progeny?


The specific heat capacity of water is:
A. 1 calorie \( g^{-1} \)
B. 10 calories \( g^{-1} \)
c. 2 calories \( g^{-1} \)
D. 30 calorie \( g^{-1} \)


If \( 0 \leq x \leq 1, \) then \( \sin \left\{\tan ^{-1} \frac{1-x^{2}}{2 x}+\cos ^{-1} \frac{1-x^{2}}{1+x^{2}}\right\} \)
equal to
\( \mathbf{A} \cdot \mathbf{1} \)
B. -
\( c \cdot 0 \)
D. none of these


Cellulose is a condensation polymer of:
A. Maltose
B. \( \beta- \) Glucose
c. \( \alpha- \) Glucose
D. \( \beta \) - Fructose


If the distance between earth and the
sun were
half of its present value, then how many
number of days will be there in at year?


Assertion
Conversion of potassium ferrocyanide to potassium is an oxidation process.
Reason Oxidation is the additon of oxygen 1 electronegative element to a substance or removal of hydrogen / electropositive element from a substance.
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


If the G.M of two numbers is 24 and their
\( \mathrm{H.M} \) is \( \frac{72}{5}, \) Find the numbers


The equilibrium constants for the
stepwise formation of \( M C l, M C l_{2} \) and
\( M C l_{3} \) are \( a, b \) and \( c \) respectively. If the equilibrium constant of formation of
\( M C l_{3} \) is \( K, \) which of the following is
correct?
A \( . \log K=\log a+\log b+\log c \)
в. \( K=a+b+c \)
c. \( \frac{1}{K}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \)
D. \( \frac{1}{K}=\frac{1}{a} \times \frac{1}{b} \times \frac{1}{c} \)


A round uniform body of radius \( R \), mass \( M \) and moment of inertia \( I, \) rolls down
(without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is :
A. \( \frac{g \sin \theta}{1+I / M R^{2}} \)
B. \( \frac{g \sin \theta}{1+M R^{2} / I} \)
c. \( \frac{g \sin \theta}{1-I / M R^{2}} \)
D. \( \frac{g \sin \theta}{1-M R^{2} / I} \)


Two charges equal in magnitude and opposite in polarity are placed at a certain distance apart and effective
force between them is \( F \). If \( 75 \% \% \)
charge of one is transferred to another, then the effective force between the
charges becomes:
A \( \cdot \frac{F}{16} \)
в. \( \frac{9 F}{16} \)
\( c . F \)
D. \( \frac{15}{16} \)


Overall the contribution of carbon
dioxide to global warming is
A . 20\%
B. 14\%
\( c \cdot 6 \% \)
D. 60\%


A pair of bullocks exerts a force of \( 140 N \) on a plough. The field being
ploughed is 15 m long. How much work
is done in ploughing the length of the field?


Which of the following is/are peroxide(s)?
This question has multiple correct options
\( \mathbf{A} \cdot P b O_{2} \)
в. \( H_{2} O_{2} \)
\( \mathrm{c} \cdot \operatorname{Sr} \mathrm{O}_{2} \)
D. \( B a O_{2} \)


The most abundant metal ion present in the human body is
A \( . Z n^{2} \)
the \( ^{2} n^{n^{n}} \)
в. \( C a^{2} \)
c. \( N a^{+} \)
D. \( F e^{2} \)


\( 18.4 \mathrm{g} \) mixture of \( \mathrm{CaCO}_{3} \) and \( \mathrm{MgCO}_{3} \)
on strongly heating gives \( 8.8 \mathrm{g} \) of \( \mathrm{CO}_{2} \)
gas. Calculate mole percentage of
\( M g C O_{3} \) in the mixture


Complete the following:
\( 4 F e C l_{3}+3 N a_{4} F e(C N)_{6} \longrightarrow \)


Heat of solution of anhydrous \( C u S O_{4} \) is
\( -15.9 \mathrm{kcal} \) and heat of hydration of
anhydrous \( C u S O_{4} \) is -18.9 kcal. The
heat of solution of \( C u S O_{4} .5 H_{2} O \) is


Match List I with List II
List-I
a) Dalton's Law
e) \( P V= \)
constant \( (T=\text { constant }) \)
b) Charle's Law-I
\( f) P / T= \)
constant \( (\mathrm{V}=\text { constant }) \)
c) Charle's Law-II
\( g) \vee / T= \)
constant \( (\mathrm{P}=\text { constant }) \)
d) Boyle's Law
h) \( P=P_{1}+ \)
\( P_{2}+\ldots \ldots P_{\infty} \)
A \( \cdot a-f, b-h, c-g, d-e \)
B. a-g, b-h,c-e, d-f.
c. a-f, b-e,c-g,d-h.
D. a-h, b-g,c-f,d-e.


A pendulum clock is 5 sec fast at
temperature of \( 15^{\circ} \mathrm{C} \) and 10 sec slow at
a temperature of \( 30^{\circ} \mathrm{C} \). At temperature
does it give the correct time-
A \( \cdot 18^{\circ} \mathrm{C} \)
B . \( 20^{\circ} \mathrm{C} \)
c. \( 22.5^{\circ} \mathrm{C} \)
D. \( 25^{\circ} \mathrm{C} \)


The bond between chlorine and bromine
in \( \boldsymbol{B} \boldsymbol{r} \boldsymbol{C} \boldsymbol{l} \)
A. ionic
B. non polar
c. polar with negative end on \( B r \)
D. polar with negative end on \( C l \)


Consider the following statement:
There exists a pair of straight lines that are everywhere equidistant from one another.
Is this statement a direct consequence of Euclid's fifth postulate? Explain
A. True
B. False


Prove that in a parallelogram the opposite angles are equal.


Find the common difference of the A.P.
\( \boldsymbol{y}-\mathbf{7}, \boldsymbol{y}-\mathbf{2}, \boldsymbol{y}+\mathbf{3} \)


During lactic acid fermentation
\( A \cdot O_{2} \) is used, \( C O_{2} \) is not liberated.
B. \( O_{2} \) is not used, \( C O_{2} \) is liberated.
\( \mathrm{C} \cdot \mathrm{O}_{2} \) is used, \( \mathrm{CO}_{2} \) is liberated.
D. Neither \( O_{2} \) is used, nor \( C O_{2} \) is liberated.


\( \frac{\sqrt{x}}{\frac{x}{3}} \)


Find the odd one out.
A . Meat
B. Fish
c. Eggs
D. cheese


Write down a unit vector in \( X Y \) - plane,
making an angle of \( 30^{\circ} \) with the
positive direction of \( \boldsymbol{x} \) - axis.


\( \sin ^{-1}\left(\cos \left(\sin ^{-1} x\right)\right)+ \)
\( \cos ^{-1}\left(\sin \left(\cos ^{-1} x\right)\right) \) is equal to
A.
в. \( \frac{\pi}{2} \)
c. \( \frac{3 \pi}{4} \)
D.


The valence electronic configuration of an element is \( [N e] 3 s^{1} . \) The element is :
A. argon
B. sodium
c. magnesium
D. fluorine


If \( x=\sin ^{-1} 2 t \sqrt{1-t^{2}} \) and \( y=\frac{\pi}{2} \)
\( \cos ^{-1} t, \) then find the value of \( \frac{d^{2} y}{d x^{2}} \) at \( t=\frac{\pi}{3} \)


Number of meiosis for formation of 80
zygotes in the angiosperms will be
A . 40
B. 100
\( c \cdot 160 \)
D. 90


Carbon and oxygen combine to form two oxides, carbon monoxide and carbon
dioxide in which the ratio of the weights of carbon and oxygen is respectively 12: 16 and 12: 32
These figures illustrate the:
A. Law of multiple proportions
B. Law of reciprocal proportions
c. Law of conservation of mass
D. Law of constant proportions


The radius of curvature of a plano-
convex lens is \( 20 \mathrm{cm} \) If the refractive
index of the material of the lens be 1.5 it
will
A. Act as a convex lens only for the objects that lie on its curved side
B. Act as a concave lens for the objects that lie on its curved side
C. Act as a convex lens irrespective of the side on which the object lies
D. Act as a convex lens irrespective of side on which the object lies


Assertion
Four point charges \( \boldsymbol{q}_{1}, \boldsymbol{q}_{2}, \boldsymbol{q}_{3} \) and \( \boldsymbol{q}_{4} \) are
as shown in figure. The flux over the shown Gaussian surface depends only
on charges \( \boldsymbol{q}_{1} \) and \( \boldsymbol{q}_{2} \)
Reason
Electric field at all points on Gaussian
surface depends only charges \( q_{1} \) and \( q_{2} \)
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
c. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct


If the minimum value of \( \left(\sec ^{-1} x\right)^{2}+ \)
\( \left(\operatorname{cosec}^{-1} x\right)^{2} \) is \( \frac{\pi^{a}}{b} . \) Find the value of
\( a+b \)
\( \mathbf{A} \cdot \mathbf{6} \)
B. 8
c. 10
D. 12


\( \boldsymbol{K}, \boldsymbol{C} \boldsymbol{a} \) and \( \boldsymbol{L} \boldsymbol{i} \) metals may be arranged
in the decreasing order of their standard electrode potentials
as
A. \( K, C a \) and \( L i \)
в. \( L i, K \) and \( C a \)
c. \( L i, \) Ca and \( K \)
D. \( C a, L i \) and \( K \)


Name the sweetening agent used in the
preparation of sweets for a diabetic patient.


Positive and negative point charges of equal magnitude are kept at \( \left(0,0, \frac{a}{2}\right) \) and \( \left(0,0, \frac{-a}{2}\right) \)
respectively. The work done by the electric field when another positive
point charge is moved from \( (-a, 0,0) \) to \( (0, a, 0) \) is
A. Positive
B. Negative
c. zero
D. Depends on the path connecting the initial and final positions


If \( a+b+c=3 \) and \( a>0, b>0, c>0 \)
the greatest value of \( a^{2} b^{3} c^{2} \)
\( ^{A} \cdot \frac{3^{10}, 2^{4}}{7^{7}} \)
в. \( \frac{3^{9}, 2^{4}}{7^{7}} \)
c. \( \frac{3^{9}, 2^{5}}{7^{7}} \)
D. \( \frac{3^{10}, 2^{5}}{7^{7}} \)


The back emf in a DC motor is
maximum when
A. the motor has picked up maximum speed.
B. the motor has just started moving.
C. the speed of motor is still on increase.
D. the motor has just been switched off.


Solve \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}} \sin ^{\boldsymbol{n}} \boldsymbol{x} \)


Which one has more free energy?
A. Reactants
B. Transition state of reactants
c. Products
D. Active site of enzyme


The missing particle in the reaction:
\( \underset{99}{253} \boldsymbol{E} \boldsymbol{s}+_{2}^{4} \boldsymbol{H} \boldsymbol{e} \rightarrow_{101}^{256} \boldsymbol{M} \boldsymbol{d}+ \)
A. deuteron
B. proton
c. neutron
D. \( \beta \) - particle