Solutions published in same issue
12. Oil floating on water looks coloured due to interference of light. What should be the approximate thickness of the film for such effects to be visible ?
13. Draw a graph showing the variation of intensity with angle in a single slit diffraction experiment.
14. A parallel plate air filled capacitor has capacitance 5 µF. If plate separation made twice and whole space is filled with medium, capacitance becomes 20 µF.
Find dielectric constant of the medium.
15. Suppose you have two bars of identical dimensions, one made of paramagnetic substance and the other of diamagnetic substance. If you place these bars along a uniform magnetic field, show diagramatically, what modifications in the field pattern would take place in each case.
16. In a plane e.m. wave, the electric field oscillates with a frequency of 2 × 1010s–1 and an amplitude of 40 Vm–1. (i) What is the wavelength of the wave and (ii) What is the energy density due to the electric field ?
17. A solenoid has self-inductance 2 mH and current in it is 5 amp. Find magnetic energy stored in it.
18. Find power factor of the adjacent circuit.
L = 30 mH
~
R = 4 Ω
V = 200 2 sin 100 t
19. Experimental observations have shown that X-rays (i) travel in vacuum with a speed of 3 × 108 ms–1, (ii) exhibit the phenomenon of diffraction and can
the polarized.
What conclusion can be drawn about the nature of X-rays from each of these observations ?
20. A radioactive material is reduced to 16
1 of its original amount in 4 days. How much material should one begin with so that 4 × 10–3 kg of the material is left after 6 days.
21. Why are apertures of camera lenses so small while the apertures of telescopes are as large as feasible ? 22. In adjacent circuit, if current in 5 Ω resistance is
zero, find resistance R.
R 6Ω 5Ω
10Ω 20Ω
1Ω
12V
23. The self inductance of a solenoid is 5 mH and current flowing in it depends on time t as i = t2. (where i → In Amp., t → In second). Find induced emf in it at t = 4 s.
24. Derive an expression for magnetic field inside a long solenoid.
25. What is Wheatstone bridge ? Deduce the condition for which Wheatstone bridge is balanced.
26. Explain the differences between diamagnetic, paramagnetic and ferromagnetic substances.
27. Describe the method to obtain Reverse Bias characterstics of a P-N junction diode. Define reverse resistance. Draw necessary circuit diagram and also the reverse characterstic curve.
28. A student has to study the input and output characteristics of a n-p-n silicon transistor in the Common Emitter configuration. What kind of a circuit arrangement should she use for this purpose ? Draw the typical shape of input characteristics likely to be obtained by her. What do we understand by the cut off, active and saturation states of the transistor?
In which of these states does the transistor not remain when being used as a switch ?
OR
Input signals A and B are applied to the input terminals of the ‘dotted box’ set-up shown here. Let Y be the final output signal from the box.
Draw the wave forms of the signals labelled as C1 and C2 within the box, giving (in brief) the reasons for getting these wave forms, Hence draw the wave form of the final output signal Y. Give reasons for your choice.
What can we state (in words) as the relation between the final output signal Y and the input signals A and B ?
A u1
0 1 2 3 4
0 1 2 3 4
B B
C2 C1 A
B
29. Draw a labelled ray diagram of an astronomical telescope. Write mathematical expression for its magnifying power. How does the magnifying power get affected on increasing the aperture of the objective lens and why ?
30. Derive an expression for the energy density of a capacitor.
OR
An electric flux of –6 × 103 Nm2/C passes normally through a spherical Gaussian surface of radius 10 cm, due to a point charge placed at the centre.
(i) What is the charge enclosed by the Gaussian surface ?
(ii) If the radius of the Gaussian surface is doubled, how much flux would pass through the surface ?
CHEMISTRY
1. Which of the following lattices has the highest packing efficiency (i) simple cubic (ii) body centered cubic and (iii) hexagonal close packed lattice ?
2. What is meant by 'specific surface area' of a solid ? 3. Give the IUPAC name of Li [AlH4]
4 What is formula of siderite ore ? 5. Name the monomer units of Bakelite 6. What are antiseptics. Give two example : 7. What are basic amino acids. Give a example ? 8. Arrange the following in the order of their
increasing reactivity in nucleophilic substitution reactions :
CH3F, CH3I, CH3Br, CH3Cl
9. The half life for radioactive decay of 14C is 5730 y.
An archaeological artefact contained wood had only 80% of the 14C in a living tree. Estimate the age of the sample.
10. What is the effect of temperature on the rate constant of reaction ? How can this temperature effect on rate constant ? Explain using collision theory ?
11. Explain the following :-
(i) S.H.E.; (ii) Kohlrausch's law
12. Why Actinides show much higher oxidation states as compared to Lanthanides ?
13. How group I radicals like Ag+ and Hg22+ are seperated by complex formation with NH4OH ? 14. What is Roasting ?
15. Give the structure and monomer units of biodegradable polymer PHBV ?
16. Name the purine and pyrimidine bases in DNA and RNA .
17. What are detergents. Give a example of Cationic &
Anionic detergents
18. A sweet smelling organic compound 'A' is slowly oxidised by air in the presence of light to a highly poisonous gas. On warming with silver powder, it forms gaseous substance 'B' which is also formed by the action of calcium carbide on water. Identify 'A' and 'B' and write the equations of the reactions involved .
19. (a) Gold (atomic radius = 0.144 nm) crystallises in a face centred unit cell. What is the length of a side of the cell ?
(b) Classify each of the following as being either a p-type or an n-type semiconductor
(i) Ge doped with In (ii) Si doped with As.
20. Two liquids A and B form ideal solution at 323 K. A liquid mixture containing one mole of A and two moles of B has a vapour pressure of 250 bar. If one more mole of A is added to the solution, the vapour pressure increases to 300 bar. Calculate the vapour pressures of liquids A and B at 323 K.
21. (a) In which of the following does adsorption take place and why ?
(i) Silica gel placed in the atmosphere saturated with water.
(ii) Anhydrous CaCl2 placed in the atmosphere saturated with water.
(c) Give an example of shape-selective catalysis 22. Explain the order of basic character in hydrides of
nitrogen family ?
23. Give structure of Cr2O72– ? 24. How will you convert ?
(i) Phenol to p-hydroxyazobenzene (ii) Ethyl alcohol to methyl alcohol.
25. Write the IUPAC name of the following : CH3 – O – C (CH3)3
26. Give a suitable colour reaction test to distinguish between
(i) 2-Pentanone and 3-Pentanone (ii) Acetone and acetaldehyde ?
27. An organic compound A(C3H6O) is resistant to oxidation but forms compound B(C3H8O) on reduction which reacts with HBr to form the bromide (C). C forms a Grignard reagent which reacts with A to give D (C6H14O). Give the structures of A, B, C and D and explain the reactions involved.
28. (a) What are ideal and non-ideal solutions ? What type of non-idealities are exhibited by cyclohexane-ethanol and acetone-chloroform mixtures ? Give reasons for your answers.
(b) A solution containing 30 g of a nonvolatile solute exactly in 90g water has a vapour pressure of 2.8 kPa at 298 K. Further 18 g of water is then added to solution, the new vapour pressure becomes 2.9 kPa at 298 K. Calculate,
(i0 Molecular mass of the solute;
(ii) Vapour pressure of water at 298 K.
29. Give structure of :-
(a) Hypophosphorus acid (b) Pyrophosphoric acid (c) Dithionic acid (d) Marshall acid (e) Hypophosphoric acid
30. (a) An optically inactive compound (A) having molecular formula C4H11N on treatment with HNO2
gave an alcohol (B). (B) on heating at 440 K gave an alkene (C). (C) on treatment with HBr gave an optically active compound (D) having the molecular formula C4H9Br. IdentifyA, B, C and D and write down their structural formulae. Also write equations involved.
(b) Explain why Alkyl amines are stronger bases
than arylamines.
MATHEMATICS
Section A
1. Show that relation R on the set A = {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
2. If x2/3 + y2/3 = a2/3 then find
5. The projection of a vector on the coordinate axes are 6, –3, 2. Find its length and direction cosines.
6. Find the values of x for which the angle between the vectors ar = 2x2iˆ+ 4x jˆ+ kˆand br
= 7iˆ–2jˆ+ xkˆis obtuse.
7. A plane meets the coordinate axes in A, B, C such that the centroid of triangle ABC is the point (p, q, r). Show that the equation of the plane is
10. Using determinant, find k so that points (k, 2 –2k), (–k + 1, 2k) and (– 4 – k, 6 –2k) are collinear.
Section B
11. In two successive throws of a pair of dice, determine the probability of getting a total of 8, each time.
12. If f : R → R is given by
f(x) = sin2 x + sin2(π/3 + x) + cos x . cos (π/3 + x) ∀ x ∈ R. g : R → R be such that g(5/4) = 1 then prove that gof is constant function.
13. f(x) =
15. Differentiate tan–1
16. The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm/sec. How fast is the area decreasing when the two sides are equal to the base.
OR
Use lagrange's Mean Value theorem to determine a point P on the curve y = x− where the tangent is 2
19. Solve : 21. Find the foot of the perpendicular from the point
(0, 2, 3) on the line find the length of the perpendicular.
OR
Find the particular solution of the differential equation
and hence factorize.
OR
23. Two persons A and B throw a die alternately till one of them gets a 'six' and wins the game. Find their respectively probabilities of winning.
24. Find the area bounded by the curves y = x and y = x3.
25. Find the shortest distance between the lines 2
system of linear equations x – 2y = 10
ex by first principle method
29. There is a factory located at each of two places P and Q. From these locations, a certain commodity is delivered to each of the three depots situated at A, B and C. The weekly requirements of the depots are respectively 5, 5 and 4 units of the commodity while the production capacity of the factories at P and Q are 8 and 6 units respectively. The cost of transportation per unit is give below.
From
To COST (In Rs.)
A B C
P 16 10 15
Q 10 12 10
How many units should be transported from each factory to each depot in order that the transportation cost is minimum. Formulate the above as a linear programming problem.
OR
A brick manufacturer has two depots, A and B, with stocks of 30,000 and 20,000 bricks respectively. He receives orders from three builders P, Q and R for 15, 000, 20,000 and 15000 bricks respectively. The cost in Rs. transporting 1000 bricks to the builders from the depots are given below.
From
To P Q R
A 40 20 30
B 20 60 40
How should the manufacturer fulfill the orders so as to keep the costs of transportation minimum?
• Pluto lies at the outer edge of the planetary system of our sun, and at the inner edge of the Kuiper Belt, a belt of icy comets that are the remnants of the formation of the solar system.
• Gamma ray bursts - mysterious explosions at the edge of the Universe - were first detected in 1969 by military satellites monitoring the Test Ban Treaty.
• Titan is the largest moon of Saturn and the second largest moon in the entire solar system.
PHYSICS
1. p = q × 2l
It's a vector quantity 2. Sensitivity ∝
gradient Potential
1
3. Gamma rays, X-rays, ultraviolet, Infrared 4. λ =
p h =
mk h 2
∴ The proton will have a higher K.E.
(mass of proton is slightly less than that of the neutron)
5. The ionization energy of silicon gets (considerably) reduced compared to that of carbon. Silicon (a semi-conductor), therefore, becomes a (much) better conductor of electricity than carbon (an insulator)
6. (0 to t1), (t3 to t4)
7. No, when the refractive index of prism material is same as that of the surrounding, then there is no dispersion.
8. As, P ∝ f
1 , so lens of smaller focal length is more powerful and more magnifying power.
9. F = qvB sinθ
(i) θ = 90°, Fmax = q v B (ii) θ = 0°, 180°, F = 0 10. S =
g g
i i
G i
–
×
11. V1 = 2 V V2 6 µF 12 µF
V
V1 = 2 = 12 6
12 + × V V = 3 volt
OR d
0 A
∈ = 8
C' =
2 ) 5
0( d
∈ A
= 10 × d
0 A
∈
= 10 × 8 = 80
12. The region containing the uncompensated acceptor and donor ions is called depletion region there is a barrier at the junction which opposes the movement of majority charge carriers.
– ° – ° – ° – – + + + + +
– ° – ° – ° – ° – ° – ° – ° – ° – °
– –
– –
– –
+ + + + + +
+ + +
+ + +
+ + +
P N
Depletion region
Formation of depletion region in PN junction diode
The physical distance from one side of the barrier to the other is called the width of the barrier. The width of the depletion region or barrier depends upon the nature of the material. Its typical value is nearly 10–6 m. The difference of potential from one side of the barrier to the other side is called potential barrier or height of the barrier. Its value is nearly 0.7 V for a silicon PN junction and 0.3 V for a germanium diode.
13. Reasons : (i) Size of antenna
(ii) Effective power radiated by the antenna
14. The activity of a radioactive element at any instant, equals its rate of decay at that instant. Its SI unit is Becquerel (Bq) (= 1 decay per second)
Activity R = – dt
dN = λN = T
e2 log N
∴
2 1
R R =
1 1
T N +
2 2
T N =
1 2
2 1
T N
T N