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If \( \boldsymbol{x}=\boldsymbol{a}\left(\boldsymbol{1}-\cos ^{3} \boldsymbol{\theta}\right), \boldsymbol{y}=\boldsymbol{a} \sin ^{3} \boldsymbol{\theta}, \) prove
that \( \frac{\boldsymbol{d}^{2} \boldsymbol{y}}{\boldsymbol{d} \boldsymbol{x}^{2}}=\frac{\boldsymbol{3} \mathbf{2}}{\mathbf{2 7} \boldsymbol{a}} \) at \( \boldsymbol{\theta}=\frac{\boldsymbol{\pi}}{\boldsymbol{6}} \)
| 2 |
Maths
|
A conic passes through the point (2,4) and is such that the segment of any of its tangents at any point contained between the coordinate axes is bisected
at the point of tangency. Then equation of auxiliary circle of the conic is
A \( \cdot x^{2}+y^{2}=16 \)
B . \( x^{2}+y^{2}=25 \)
c. \( x^{2}+y^{2}=4 \sqrt{2} \)
D. none of these
| 2 |
Maths
|
What do you mean by a solenoid?
| 3 |
Physics
|
Isotopes are atoms with the same number of protons, but differing numbers of neutrons. Isotopes are different forms of a single element.
A. True
B. False
| 1 |
Chemistry
|
In YDSE of equal width slits, if intensity
at the centre of screen is \( I_{0}, \) then
intensity at a distance of \( \beta / 4 \) from the
central maxima is \( (\beta \) is the fringe
width) :
A \( \cdot I_{0} \)
в. \( \frac{I_{0}}{2} \)
c. \( \frac{I_{0}}{4} \)
D. \( \frac{I_{0}}{3} \)
| 3 |
Physics
|
In how many years will a sum of Rs. 800 at \( 10 \% \) per annum compounded, semiannually become Rs. 926.10 ?
A \( \cdot 1 \frac{1}{3} \)
в. \( 1 \frac{1}{2} \)
c. \( _{2} \frac{1}{3} \)
D. \( _{2} \frac{1}{2} \)
| 2 |
Maths
|
The plates of a parallel plate capacitor are charged upto \( 100 V . \) now, after removing the battery, a \( 2 m m \) thick plate is inserted between the plates. Then, to maintain the same potential difference, the distance between the
capacitor plates is increased by \( 1.6 m m \) The dielectric constant of the plate is :
A . 5
B. 1.25
\( c \cdot 4 \)
D. 2.5
| 3 |
Physics
|
The value of \( \sin ^{-1}(\sin 12)- \)
\( \cos ^{-1}(\cos 12)= \)
\( \mathbf{A} \cdot \mathbf{0} \)
в.
\( c \cdot 8 \pi+24 \)
D. \( 8 \pi-24 \)
| 2 |
Maths
|
If a current increases from zero to one
ampere in 0.1 second in a coil of \( 5 \mathrm{mH} \)
then the magnitude of the induced e.m.f. will be
A . 0.005 volt
B. 0.5 volt
c. 0.05 volt
D. 5 volt
| 3 |
Physics
|
Arrange according boiling point:
\( \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C H}_{3}, \boldsymbol{C H}_{3} \boldsymbol{C H O}, \boldsymbol{C H}_{3} \boldsymbol{C H}_{2} \boldsymbol{C} \)
| 1 |
Chemistry
|
\( n \) charged drops, each of radius \( r \) and
charge \( q, \) coalesce to form a big drop of
radius \( R \) and charge \( Q . \) If \( V \) is
the electric potential and \( \boldsymbol{E} \) is the electric field at the surface of a drop,
then :
A \( \cdot E_{\text {big}}=n^{2 / 3} E_{\text {small}} \)
B. \( V_{\text {big}}=n^{1 / 3} V_{\text {small}} \)
C. \( E_{\text {small}}=n^{2 / 3} E_{\text {big}} \)
D. \( V_{\text {big}}=n^{2 / 3} V_{\text {small}} \)
| 3 |
Physics
|
In the series \( 20,18,16, \ldots \ldots \ldots,-2 \) is the
term
\( \mathbf{A} \cdot 10^{t h} \)
B. \( 11^{\text {th }} \)
\( \mathbf{c} \cdot 12^{t h} \)
D. \( 13^{\text {th }} \)
| 2 |
Maths
|
Define roasting.
A. Heating of sulphide ores in the presence of excess air to convert them into oxides
B. Heating of carbonate ores in the limited supply of air to convert them into oxides
C. Heating of oxides of metals to turn them into metal
D. Heating of carbonate ores in the limited supply of air to convert them into sulphide
| 1 |
Chemistry
|
When calyx and corolla are not
distinguishable, then member of their collective whorl termed as
A. Perianth
B. Sepal
c. Petal
D. Tepal
| 0 |
Biology
|
The fluid mosaic model of plasma
membrane was given by
A. Robertson
B. Robert Hooke
c. singer and Nicholson
D. Gorter and Grende
| 0 |
Biology
|
Liquid is used in rocket
fuels.
A. nitrogen.
B. oxygen
c. hydrogen
D. both B and C
| 1 |
Chemistry
|
Which term of the sequence 3,6,12 is \( 1536 ? \)
| 2 |
Maths
|
Trans \( -1,2- \) dibromo \( -1- \)
methylcyclohexane.
\( A \)
| 1 |
Chemistry
|
Give the differences between right and left lungs of humans.
| 0 |
Biology
|
If an earthworm is left in \( 40 \% \) KOH
solution for a long time, which part would be left undissolved?
A . Setae
B. Spermatheca
c. sand particles
D. circular muscles
| 0 |
Biology
|
The function of zymase is to:
A. change starch into sugar
B. ferment glucose to alcohol and carbon dioxide
c. change malt sugar into glucose
D. change starch into malt sugar and dextrin
| 1 |
Chemistry
|
Let \( \boldsymbol{f}(\boldsymbol{x})= \)
\( \left\{\begin{array}{cc}2 a-x, & \text { if }-a<x<a \\ 3 x-2 a, & \text { if } a \leq x\end{array} . \) Then \right.
which of the following is true?
A. \( f(x) \) is discontinuous at \( x=a \)
B. \( f(x) \) is not differentiable at \( x=a \)
c. \( f(x) \) is differentiable at \( x \geq a \)
D. \( f(x) \) is continuous at all \( x<a \)
| 2 |
Maths
|
In the mechanism of action of a protein hormone, one of the second messengers is?
A. Cyclic AMP
B. Insulin
\( c \cdot T_{3} \)
D. Gastrin
| 0 |
Biology
|
\( y=(x-8)^{4}(x-9)^{5}, 0 \leq x \leq 10, \) In
this interval \( y \) will attain max. and min.
value at \( \boldsymbol{x}= \)
\( A \cdot 8,9 \)
в. \( _{8, \frac{76}{9}} \)
\( \mathrm{c} .9,10 \)
D. \( _{9, \frac{76}{9}} \)
| 2 |
Maths
|
When the distance covered by an object is directly proportional to the time interval, it is said to travel with:
A. Constant speed
B. Zero velocity
c. Constant acceleration
D. Uniform velocity
| 3 |
Physics
|
When zinc reacts with very dilute
\( H N O_{3}, \) the oxidation state of nitrogen
changes from:
A. +5 to +1
B. +5 to -3
\( c \cdot+5 t o+4 \)
D. +5 to +3
| 1 |
Chemistry
|
Solve the inequality and show the graph
of the solution on number line:
\( 3 x-2<2 x+1 \)
| 2 |
Maths
|
\( \sigma_{i}^{i} \)
\( \Phi_{i}^{i} \)
\( \Phi_{i-i}^{i-1} \)
\( \sigma_{i}^{i} \)
| 1 |
Chemistry
|
Which one of the following species does not represent cationic species of vanadium formed in aqueous solution?
A \( \cdot V O_{2}^{+} \)
B. \( V O^{2+} \)
c. \( \left[V\left(H_{2} O\right)_{6}\right]^{3+} \)
D. \( V O_{2}^{2+} \)
| 1 |
Chemistry
|
A pure capacitor is connected in an \( A C \) circuit.The power factor of the circuit will be
\( A \)
B. infinity
c. zero
D. 0.5
| 3 |
Physics
|
The amount of oil available for use are
from oil
A . reserve
B. reservoir
c. resources
D. barrelss
| 3 |
Physics
|
A \( 1000 \Omega \) resistance and a capacitor of
100 \( \Omega \) resistance are connected in
series a \( 220 V \) source. when the
capacitor is \( 50 \% \) charged, the value of the displacement current is.
A \( .11 . \sqrt{2} A \)
в. \( 2.2 A \)
\( c .11 A \)
D. \( 4.4 A \)
| 3 |
Physics
|
If \( P(1,4), Q(9,-2), \) and \( R(5,1) \) are collinear
then
A. P lies between \( Q \) and \( R \)
B. Q lies between P and R
c. R lies between P and Q
D. none of these
| 2 |
Maths
|
A rock is \( 12.5 \times 10^{9} \) years old. The rock
contains \( ^{238} U \) which disintegrates to
form \( ^{206} U . \) Assume that there was no
\( ^{206} P b \) in the rock initially and it is the only stable product formed by the decay
The ratio of number of nuclei of \( ^{238} U \) to that of \( ^{206} P b \) in the rock is \( \frac{1}{2^{1 / x}-1} \)
Find \( x \) (Approximately). Half-life of \( ^{238} \boldsymbol{U} \) is \( 4.5 \times 10^{9} \) years.\( \left(2^{1 / 3}=1.259\right) \)
| 3 |
Physics
|
Which of the following are paramagnetic? This question has multiple correct options
\( A \cdot B_{2} \)
в. \( O_{2} \)
\( c \cdot N_{2} \)
D. \( H e_{2} \)
| 1 |
Chemistry
|
If you dilute \( 25.0 \mathrm{mL} \) of \( 1.5 \mathrm{M} H C l \) to \( 500 \mathrm{mL}, \) then the molar concentration of
each ions becomes \( \boldsymbol{Y} \times \mathbf{1 0}^{-\mathbf{3}} \boldsymbol{M} . \) Here \( \boldsymbol{Y} \)
is:
| 1 |
Chemistry
|
What is the shape of f-orbital?
A. spherical
B. dumb bell
c. double dumb bell
D. no definite shape
| 1 |
Chemistry
|
If \( i z^{3}+z^{2}-z+i=0, \) then \( |z|=? \)
B . |z| = 2
c. \( |z|=3 \)
D. \( |z|=4 \)
| 2 |
Maths
|
Which among the following is/are
correct?
This question has multiple correct options
A. If an operations can be performed in 'm' different ways and a second operation can be performed in 'n different ways, then both of these operations can be performed in \( ^{\prime} m \times n^{\prime} \) ways together
B. The number of arrangements of n different objects taken all at a times is n!
C. The number of permutations of n different things taken \( r \) at a time, when each thing may be repeated any number of times is \( n \)
D. The number of circular permutations of 'n' different things taken all at a time is \( \frac{1}{2}(n-1) ! \). if clockwise and anticlockwise orders are taken as different.
| 2 |
Maths
|
Freons are:
A. chlorofluorocarbons of methane
B. chlorofluorocarbons of ethane
C. both chlorofluorocarbons of methane and
chlorofluorocarbons of ethane
D. chlorofluorocarbons of butane
| 1 |
Chemistry
|
If \( A \) is any event in a sample space then \( P\left(A^{\prime}\right) \) is
\( A \cdot P(A) \)
B. \( 1+P(A) \)
c. \( 1-P(A) \)
D. 1-2P(A)
| 2 |
Maths
|
State True or False.
\( 1+\frac{1}{5}+\frac{3}{5^{2}}+\frac{5}{5^{3}}+\ldots . . \infty=\frac{13}{8} \)
A . True
B. False
| 2 |
Maths
|
From a survey of 100 college students, a marketing research company found
that 75 students owned stereos, 45
owned cars, and 35 owned cars and stereos. How many students owned either a car or a stereo?
A . 85
B. 47
\( c .68 \)
D. None of these
| 2 |
Maths
|
The equi-potential surface for an
electric dipole is:
A. the dipole axis
B. the perpendicular bisector of the dipole axis
C. a line parallel to the dipole axis
D. a line passing through one of the charges
| 3 |
Physics
|
Describe the following:
Carius method for the estimation of
halogens in an organic compound.
| 1 |
Chemistry
|
Maximum value of \( r \) where \( \frac{c^{2}}{r^{2}}= \) \( \frac{\mathbf{a}^{2}}{\sin ^{2} \theta}+\frac{b^{2}}{\cos ^{2} \theta} \) where \( c, a, b \)
are constants is
A. \( \frac{c}{a+b} \)
B. \( \frac{c}{a-b} \)
c. \( \frac{a^{2}+b^{2}}{c^{2}} \)
D. \( \frac{c^{2}}{a^{2}+b^{2}} \)
| 2 |
Maths
|
What is intensive property? Give one example.
| 1 |
Chemistry
|
If ovaries from a pregnant woman are removed in \( 4^{t h} \) month of pregnency,
then
A. Development of embryo becomes abnormal
B. Abortion occurs after some time
C. Embryo develops normally till birth
D. None of the above
| 0 |
Biology
|
Two circular loops \( P \) and \( Q \) are
concentric and coplanar as shown in
figure. The loop \( Q \) is smaller than \( P . \) If
the current \( I_{1} \) flowing in loop is decreasing with time, then the current
\( I_{2} \) in the \( \operatorname{loop} Q \)
A. flows in the same direction as that of \( P \)
B. flows in the opposite direction as that of \( Q \)
c. is zero
D. None of these
| 3 |
Physics
|
In the following figure, \( \Delta A B C \) is an isosceles triangles with perimeter
\( 40 \mathrm{cm} . \) The base \( A C \) is of length \( 10 \mathrm{cm} \)
Side \( A B \) and side \( B C \) are congruent. \( A \)
circle touches the three sides as shown
in the figure below. Find the length of
the tangent segment from point \( B \) to
the circle.
| 2 |
Maths
|
Which of the following hypotheses was made by Newton?
A. Heavier body in the universe exerts a gravitational force on the lighter bodies.
B. Every body in the universe exerts a gravitational force on every other body.
c. Only the sun gravitational force is responsible for all the motion in this universe
D. None of the above
| 3 |
Physics
|
Assertion
Collision between two billiard's ball are
inelastic.
Reason
Momentum remains conserve during
the collision.
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
| 3 |
Physics
|
If coulomb's law involved \( 1 / r^{3} \) instead
of \( \left(1 / r^{2}\right), \) would Gauss's law still be
true?
| 3 |
Physics
|
Find common difference of the following \( 8,15,22,29, \dots \)
A. 5
B. 6
c. 7
\( D \)
| 2 |
Maths
|
Which \( \beta-k e t o \) acid shown will not
undergo decarboxylation?
\( A \)
B.
\( c \)
D.
| 1 |
Chemistry
|
State one way to obtain a greater
moment of a force about a given axis of
rotation.
| 3 |
Physics
|
The hybridization and shape of \( X e F_{2} \) is
\( \mathbf{A} \cdot s p^{3}, \) bent
B. \( d s p^{2}, \) linear
c. \( s p^{3} d^{2}, \) linear
D. \( s p^{3} d, \) linear
| 1 |
Chemistry
|
Which of the following statements
is/are correct regarding inter-halogen
compounds of ABX types?
This question has multiple correct options
\( A \cdot X \) may be 1,3,5 and 7
B. A is a more-electronegative halogen than B
\( \mathrm{C} \cdot F B r_{3} \) is a stable inter-halogen compound
D. the structures of \( C I F_{3} \) and \( I F_{2} \) show deviation from
normal structures and could be explained on the basis of VSEPR theory
| 1 |
Chemistry
|
Assertion
Air bladder is absent in fishes.
Reason
Fishes generally respire through gills.
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect Reason is correct.
| 0 |
Biology
|
On reduction of glycolic acid with \( \boldsymbol{H} \boldsymbol{I} \) the product formed is:
A . acetic acid
B. iodo aectic acid
c. formic acid
D. none of these
| 1 |
Chemistry
|
The mixture of \( X \) and \( Y \) were taken in a
condenser flask and were then heated.
After keepint it for cooling, crystals of \( Y \) were found on the walls of the flask and
X was present as such at the bottom of
flask. Identify \( X \) and \( Y: \)
A. \( X=N a C l, Y=K C l \)
B. \( X= \) Anthracene, \( Y= \) Naphthalene
c. \( X=N a C l, Y= \) Naphthalene
D. \( X= \)Anthracene, \( Y=N a C l \)
| 3 |
Physics
|
Two soap bubbles of radii \( a \) and \( b \)
combine under isothermal conditions to
form a single bubble of radius \( c \) without
any leakage of air. If \( \boldsymbol{P}_{\mathbf{0}}= \)
atmospheric pressure and \( \boldsymbol{T}= \) surface
tension of soap solution, show that \( \boldsymbol{P}_{0}=\frac{\boldsymbol{4} \boldsymbol{T}\left(\boldsymbol{a}^{2}+\boldsymbol{b}^{2}-\boldsymbol{c}^{2}\right)}{\boldsymbol{c}^{3}-\boldsymbol{a}^{3}-\boldsymbol{b}^{3}} \)
| 3 |
Physics
|
If impulse \( I \) varies with time \( t \) as
\( f\left(k g m s^{-1}\right)=20 t^{2}-40 t . \) The change in
momentum is minimum at
\( \mathbf{A} \cdot t=1 s \)
B . \( t=2 s \)
c. \( _{t=\frac{1}{2} s} \)
D. \( t=\frac{3}{2} s \)
| 3 |
Physics
|
If the \( 10^{t h} \) term of a G.P. is 9 and \( 4^{t h} \)
term is \( 4, \) then its \( 7^{t h} \) term is
A. 6
B. 14
c. \( \frac{27}{14} \)
D. \( \frac{56}{15} \)
| 2 |
Maths
|
Chemical hypothesis first emerged in Classical Greece by:
A. Einstein
B. Louis Pasteur
C. Aristotle
D. Leuweenhock
| 1 |
Chemistry
|
State whether true or false.
Ebonite is a good conductor of electricity.
A. True
B. False
| 3 |
Physics
|
When two charged objects attract each other, the objects carry:
A. same charges
B. opposite charges
c. no charges
D. none of the above
| 3 |
Physics
|
Find the temperature of Hydrogen gas which has the same velocity as that of
oxygen at a temperature of \( 0^{0} C \)
A. \( 273 \div 16 K \)
В . \( 273 \times 8 K \)
c. \( 273 \times 32 K \)
D. \( 273 \times 4 K \)
| 1 |
Chemistry
|
In a first order reaction, the concentration of product 'x' at time 't' is given by the expression:
(where,a = initial concentration, \( \mathbf{k}= \)
rate constant, \( n=\text { order }) \)
A \( \cdot x=a\left(1-e^{-k t}\right) \)
в. \( x=\frac{1}{(a-x)} \)
c. \( _{x}=\frac{1}{2^{n-1}} \)
D. \( x=\frac{a}{(a-x)} \)
| 1 |
Chemistry
|
When a mixture to \( t- \)butyl alcohol and
ethyl alcohol is heated with conc.
\( H_{2} S O_{4} \) a single ether product is obtained. Identify the product giving
proper reasons.
| 1 |
Chemistry
|
STATEMENT - 1: If tangents OR, PR, PQ and drawn respectively at \( A, B, C \) to the circle circumscribing an acute-angled
\( \Delta A B C \) so as the form another \( \Delta P Q R \) then the \( \angle R P Q=\angle B A C \)
STATEMENT - 2: \( \Delta A B C \) is similar to \( \Delta \)
CPB.
A. Statement - 1 is True, Statement - 2 is True, Statement 2 is a correct explanation for Statement - 1
B. Statement-1 is True, Statement - 2 is True : Statement 2 is NOT a correct explanation for Statement- -
c. Statement - 1 is True, Statement- - 2 is False
D. Statement-1 is False, Statement - 2 is True
| 2 |
Maths
|
If tangents \( \boldsymbol{P} \boldsymbol{A} \) and \( \boldsymbol{P} \boldsymbol{B} \) from a point \( \boldsymbol{P} \)
to a circle with centre \( O \) are inclined to
each other at angle of \( 80^{\circ}, \) then \( \angle P O A \) is equal to.
A \( .50^{\circ} \)
B. \( 60^{\circ} \)
\( c \cdot 70^{\circ} \)
D. \( 80^{\circ} \)
| 2 |
Maths
|
Examine the table. (Each figure is
divided into triangles and the sum of the angles deduced from that)
What can you say about the angle sum
of a convex polygon with number of \( \operatorname{sides}(n)=10 ? \)
\begin{tabular}{|l|c|c|c|c|}
\hline Figure & & & & & \\
\hline side & 3 & & & & \\
\hline Ange sum & \( 180^{\circ} \) & \( 2 \times 180^{\circ} \) & 5 & 6 \\
\hline
\end{tabular}
A \( .720^{\circ} \)
B. \( 960^{\circ} \)
\( c \cdot 1080^{\circ} \)
D. \( 1440^{\circ} \)
| 2 |
Maths
|
\( p H \) of a dilute solution of \( H C l \) is 6.95
Calculate molarity of \( H C l \) solution. \( \left[\begin{array}{c}10^{-6.95}=11.22 \times 10^{-8} \\ 10^{-7.05}=8.90 \times 10^{-8}\end{array}\right] \)
| 1 |
Chemistry
|
Number of chiral centre present in cyclic structure of glucose:
| 1 |
Chemistry
|
Small chromosomes which do not
produce any detectable phenotypic expression are termed as
A. Heterochromatic chromosomes
B. Supernumerary chromosomes
c. Nonsense chromosomes
D. Nucleoids
| 0 |
Biology
|
Two thin, long, parallel wires, separated by a distance 'd' carry a current of 'i' A in
the same direction. They will
A \( . \) repel each other with a force of \( \mu_{0} i^{2} /(2 \pi d) \)
B. attract each other with a force of \( \mu_{0} i^{2} /(2 \pi d) \)
C . repel each other with a force of \( \mu_{0} i^{2} /\left(2 \pi r d^{2}\right) \)
D. attract each other with a force of \( \mu_{0} i^{2} /\left(2 \pi d^{2}\right) \)
| 3 |
Physics
|
Masses of neutron, proton and electron are \( 1.0087 \cup, 1.0073 \mathrm{u} \) and \( 0.0005 \mathrm{u} \)
respectively. If a neutron decays into a proton and an electron, the energy released would be about.
A. \( 0.68 \mathrm{MeV} \)
B. 0.84 Mev
c. \( 0.75 \mathrm{MeV} \)
D. \( 1.22 \mathrm{MeV} \)
| 3 |
Physics
|
Assertion:PV/T=constant for 1 mole of gas.
This constant is same for all gases.
Reason: 1 mole of different gases at \( \mathrm{NTP} \)
Occupy same volume of 22.4 litres.
A. Both assertion (A) and reason (R) are correct and R gives the correct explanation
B. Both assertion (A) and reason (R) are correct but R doesnt give the correct explanation
C. A is true but R is false
D. A is false but R is true
| 3 |
Physics
|
Which term of the following sequences:
\( \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots \) is \( \frac{1}{19683} ? \)
| 2 |
Maths
|
If \( Q_{1} \) and \( Q_{2} \) are the energies released in the fusion of hydrogen in Carbon nitrogen cycle and proton - proton cycle respectively, then
A \( \cdot Q_{1}>Q_{2} \)
в. \( Q_{1}=Q_{2} \)
c. \( Q_{1}<Q_{2} \)
D. \( Q_{1}=2 Q_{2} \)
| 3 |
Physics
|
During the discharge of a lead storage battery, the density of sulphuric acid
fell from 1.294 to \( 1.139 g m L^{-1} . H_{2} S O_{4} \) of
density \( 1.294 g m L^{-1} \) is \( 39 \% \) and that of
density \( 1.139 g m L^{-1} \) is \( 20 \% \)
by weight.The battery holds 3.5 L of acid and the volume practically remains constant during discharge. The number of ampere hours for which the battery must have been used are..
The discharging and charging reactions
are:
\( \boldsymbol{P b}+\boldsymbol{S O}_{4}^{2-} \rightarrow \boldsymbol{P b S O}_{4}+\boldsymbol{2} \boldsymbol{e}^{-} \)
(charging) \( \boldsymbol{P b O}_{2}+\mathbf{4 H}^{+}+\boldsymbol{S O}_{4}^{2-}+\boldsymbol{2 e}^{-} \rightarrow \)
\( P b S O_{4}+2 H_{2} O \) (discharging)
| 1 |
Chemistry
|
The number of steps in which orthophosphoric acid is ionized is :
A.
B. 2
\( c \cdot 3 \)
\( D \)
| 1 |
Chemistry
|
a speparanationa
varies as follows.
\( 1 / 1 \)
What
1
\( M \)
| 3 |
Physics
|
Write one merit and one de-merit of
alternating current in comparison of direct current. Obtain expression for
following in a pure inductive alternating current circuit
i) Instantaneous value of current
ii) Reactance of circuit
iii) Peak value of current Draw curve for
power in pure inductive circuit.
| 3 |
Physics
|
The value of \( k \) for which the system of equations \( 3 x+5 y=0 \) and \( k x+ \)
\( 10 y=0 \) has a non-zero solution, is
\( A \cdot 0 \)
B . 2
\( c \cdot 6 \)
D. 8
| 2 |
Maths
|
Chloral is :
A \( \cdot C C l_{3} C O C H_{3} \)
в. \( C C l_{3} \) СН \( _{2} \) ОН
c. \( C C l_{3} C H O \)
D. \( C C l_{3} \) СОСС\( l \)
| 1 |
Chemistry
|
A light year is unit of
A. acceleration
B. distance
\( \mathbf{C} \cdot \) speed
D. velocity
E . time
| 3 |
Physics
|
The diagonals of a rectangle \( A B C D \)
intersect each other in \( O . \) If angle \( A O D \)
is \( 30^{0}, \) then find angle \( O C D \)
| 2 |
Maths
|
A spherical capacitor has an inner sphere of radius \( 12 \mathrm{cm} \) and an outer
sphere of radius \( 13 \mathrm{cm} . \) The outer sphere is earthed and the inner sphere is given
a charge of \( 2.5 \mu C . \) The space between
the concentric spheres is filled with a liquid of dielectric constant 32
(a) Determine the capacitance of the capacitor.
(b) What is the potential of the inner sphere?
(c) Compare the capacitance of this capacitor with that of an isolated
sphere of radius 12 cm. Explain why the latter is much smaller.
| 3 |
Physics
|
Assertion
Stress is the internal force per unit area
of a body.
Reason
Rubber is more elastic than steel.
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
| 3 |
Physics
|
What will happen to the volume of the cube, if its edge is
(a) tripled (b) reduced to one-fourth?
| 2 |
Maths
|
The resistance of \( n \) wires each of
resistance \( r \) ohms is \( R \), when they are connected in parallel. When these resistance are connected in series the
resultant resistance will be :-
A \( \cdot \frac{R}{n} \)
в. \( \frac{R}{n^{2}} \)
\( c \cdot n R \)
D. \( n^{2} R \)
| 3 |
Physics
|
(a) Two identical vessels \( A \) and \( B \)
containing equal volume of water are placed in sun. The outer surface of one vessel A is blackened, while of other
vessel B is polished. Thermometer \( \boldsymbol{T}_{1} \)
and \( T_{2} \) are used to measure the
temperature of vessel \( A \) and \( B \) respectively. Which thermometer will
record a higher temperature? Give a reason for your answer
(b) If the two vessels \( A \) and \( B \) as
described in part (a) are filled with
boiling water and placed inside the room, which thermometer will show a
higher temperature after 15 minutes? Give a reason for your answer
| 3 |
Physics
|
Find the slope of a line. Which bisects the first quadrant angle.
| 2 |
Maths
|
Hormone involved in discharge of pancreatic secretions is
A. Gastrin
B. cholecystokinin
c. secretin
D. Both B and C
| 0 |
Biology
|
find the value
\( \tan 11 \frac{\pi}{3} \)
| 2 |
Maths
|
A student prepared methanol in the laboratory by the addition of \( 266 g \) of \( C O \) and \( 60 g \) of \( H_{2}, \) as shown below. \( \boldsymbol{C O}(\boldsymbol{g})+\boldsymbol{H}_{2}(\boldsymbol{g}) \rightarrow \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{O} \boldsymbol{H}(\boldsymbol{l}) \)
(a) Find out the limiting reagent
(b) Calculate the amount of methanol produced and the amount of excess reactant remaining after the completion of the reaction.
| 1 |
Chemistry
|
\( A, B, \) and \( C \) are three points on a circle
with centre \( \boldsymbol{O} \) such that \( \boldsymbol{B O C}=\mathbf{3 0}^{\mathbf{o}} \)
and \( \angle A O B=60^{\circ} . \) If \( D \) is a point on the
circle other than the arc \( A B C \), find
\( \angle A D C \)
\( A \cdot 45 \)
В. 60
\( c \cdot 22.5^{\circ} \)
0.30
| 2 |
Maths
|
Which of the following statements is
false?
A. The main reason for river water pollution is industrial and domestic sewage discahrge
B. Surface water contains a lot of organic matter mineral nutrients and radioactive materials
c. oil spills in sea water causes heavy damage to fishery
D. oil slick in a sea water increases DO value
| 1 |
Chemistry
|
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