vanasthalischool.invanasthalischool.in/pdfs/science-XII.pdfDraft an advertisement in not more than 50 words to be published in The Times of India, New Delhi, under the Classified columns.

Dear Children, Congratulations! New session, new friends and new books have already taken their place in this new academic session…….. And now it’s time for a long vacation!!!!!!!! Summer vacation beckons you to freak out, have fun, fast food and of course savor a large dollop of lazy time. However all play and no work can make you lag behind. So the answer is to plan a balanced vacation in a sensible manner with a little of everything lest you get carried away and the books and mind gather dust. We know you are disciplined enough to effectively juggle your time between the idiot box, Apps mania, and social networking….. Have a wonderful time and cherish the memories of being with friends and family!!!! Some pointers for students to follow: • Plan your vacations that you promptly attend school on the first day. • Manage your time and dispense the work for quick completion. • Do not hustle yourself at the last minute. • Be independent and honest in doing your work. • Pick up a new activity for leisure time.

Vision

Empowering citizens & leaders oftomorrow.

Mission

To be a learning institution where students,parents and teachers work in collaborationto provide value based education in a conducive environment that promotes personal excellence without gender bias.

Values

• Nationalism• Conservation of Environment• Compassion & Respect• Pursuit of Excellence• Honesty & Integrity

SUMMER HOLIDAY HOME WORK SESSION : 2016 – 17

CLASS – XII

English 1. You are the General Manager of a leading industrial concern. You need a Chartered Accountant for your office. Draft an advertisement in not more than 50 words to be published in The Times of India, New Delhi, under the Classified columns. 2. You are the manager, of Excel Pharma Ltd. Draft an advertisement for your company for the post of Sales Executive (two) mentioning all details as per your requirement. 3. The cultural club of DAV Public School Noida is organising Talent Hunt Evening. Pt. Ravi Shankar, the eminent vocalist will be the guest of honour. Mridul/ Mridula the secretary of the cultural club drafts a notice to inform and invite the names of the students about the same. 4. Your school AVB Bal VIdyalaya Sirsa, has completed 50 years of meritorious service to the society. As president of the students council of your school write a notice informing and inviting the names of the students council of your school. Write a notice informing and inviting the names of the students to participate in the Golden Jubilee Celebration of the school in not more than 50 words. You are Ram/Radhika. 5. You are Zeenat/Zeeshan, Manager of VGC Firm Sahibabad, dealing with readymade clothes.

You have got letters of enquiry form Vision Costume and Accessories, Vivek Vihar about your products. Write a letter providing necessary information in response to the enquiry.

6. You are Ameena/Aman from NSCB hostel, Dehradun. You and your friends are planning a holiday. You come across the following advertisement in a newspaper. Read the advertisement and on the basis of your choice of destination write a letter to the tour operator enquiring about aspects of the tour. 7. You are Sudhr/Sudhir, a counsellor in BBP school, Palam. You come across cases of domestic

violence frequently. You found through your interaction with the victims that children are affected most by this. Write an article in 150-200 words on the "Impact of Domestic Violence on Young Minds".

8. You are Veer/Veena, a student of class XII of SPS school Aligarh. While watching many reality shows on T.V. you felt that they are harmful for children. Write an article in 150-200 words on Negative impact of reality shows on children.

9. Watch the movie " The Invisible Man" or "Silas Marner" and write down the book review in not more than 400 words.

Physics

Q1. The electric potential V at any point (x, y, z) in space is given by V = 4X2 volt. Calculate electric intensity at the point (1m, 0, 2m). Ans: -8Vm-1 along negative direction of x axis. Q2. What is work done in moving a 2 µ C point charge from corner A to corner B of a square ABCD, when a 10 µ C charge exists at the center of the square in the figure? Ans : Zero

Q3. If a point charge + q is taken first from A to C, and then from C to B of a circle drawn with another point charge + q at the center in the figure. Then along which path, more work will be done? Ans: WAC =WCB

Q4. (a) Calculate the potential at a point P due to a charge of 4 x 10-7 C located 9 cm away. (b) Hence obtain the work done in bringing a charge of 2 x 10-9 C from infinity to the point P. Does the answer depend on the path along which the charge is brought?

Ans: 8 x10-5 J, NO Q5. An infinite number of charges each numerically to q and of the same sign are placed along

the x-axis at x=1, x=2, x=4, x=8 and so on. Find electric potential at x=0. Ans: 𝟐𝒒

𝟒𝝅ℇ𝝄

Q6. Two Charges 3 x 10-8 C and -2 x 10-8 C are located 15 cm apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero. Ans: x= 9cm, 45 cm from 3 x 10-8 C

Q7. The kinetic energy of a charged particle decreases by 10 J as it moves from a point at potential 100 V to a point at potential 200 V. find the charge on the particle. Ans: 0.1 C

Q8. Four charges are arranged at the corners of a square ABCD of side d, as shown in figure:

Find the work required to put together this arrangement (b) A charge qo is brought to the center E of the square, the four charges being held fixed at the corners. How much extra

work is needed to do this? Ans : –𝐪𝟐

𝟒𝝅ℇ𝝄𝒅 𝟒 − 𝟐 , zero

Q9. (a) Determine the electrostatic potential energy of a system consisting of two charges 7 µ C and – 2 µ C ( and with no external field) placed at (-9 cm, 0, 0) and (9 cm, 0, 0) respectively. (b) How much work is required to separate the two charges infinitely away from each other? (c ) Suppose that the same system of charges is now placed in an external electric field E = A x 1/r2 ,where A=9 x 105 C m-2. Ans: -0.7 J, 0.7 J, 49.3J Q10. The electric field components in figure are Ex = αx ½ , Ey = Ez = 0 in which α = 800 N/C – m ½ . Consider the cube shown in figure. Calculate: (a) The flux φE through the cube, and (b) The charge within the cube. Assume that a = 0.1 m. Ans: 1.05 Nm2C-1 , 9.27 x 10 -12 C

Q11. Two charges 4 µC and – 4 µC are placed at (-3, 0, 0) and (3,0,0) cm respectively in an

external field given by E = 9 𝑥 106

𝑟2 C m-2 . Find the energy of the system in this external field.

Ans: 2.4 J Q12. A particle of mass 5 x 10-6 g is kept over a large horizontal sheet of charge density 4 x 10-6

C/m2. What charge should be given to this particle, so that if released, it does not fall down? How many electrons are to be removed to give this charge?

Ans: 2.16 x 10 -13C, 1.355 x 10 6 Q13. An electric dipole consists of charges of 2.0 x 10-8 C separated by a distance of 2 mm. it is

placed near a long line charge of density 4.0 x 10-4 Cm-1 as shown in figure such that the negative charge is at a distance of 2 cm from the line charge. Calculate the force acting on the dipole.

Q14. Electric potential of earth is taken to be zero. Why? Q15. The electrostatic field due to a point charge depends on the distance ‘r’ as (1/r2). Similarly

indicate how each of the following quantities depends on r: (a) Intensity of light from a point source (b) Electrostatic potential due to a point charge and (c) Electrostatic potential at a distance r from the center of a charged metallic sphere of radius R(r < R). Q16. Figure shows the variation of electric potential V with 1/r, where r is the distance from the

two charges Q1 and Q2 Determine (i) Signs of two charges Q1 and Q2 (ii) Which of the two charges has a larger magnitude? Justify.

Q17. Figure shows three point charges + 2 q, - q and + 3 q. what is the electric flux due to this

configuration through the surface S? Ans:q/𝝐0

Q18. What is the amount of work done in moving a 200 nC charge between two points 5 cm

apart on an equipotential surface? Q19. Do electrons tend to go to regions of high potential or low potential? Ans: high potential Q20. Does the line integral of gravitational field due to a mass over a path from A to B depend

upon the path? Ans:No Q21. Does the electric potential increase or decrease along the electric line of force? Q22. A charge of + 1 C is placed at the center of a spherical shell of radius 10cm. what will be the

work done in moving a charge of + 1 µC on its surface through a distance of 5 cm? Ans: zero

Q23. The middle point of a conductor is earthed and its ends are maintained at a potential difference of 220 V. what is the potential at the two ends and at the middle point? Ans: +110V, -110V and zero

Q24. A metallic solid sphere is placed in a uniform electric field Figure. Which path is followed by the lines of force? Ans : path 4

Q25. Two protons A and B are placed between two parallel plates having a potential difference V

as shown in Figure. Will these protons experience equal or unequal force? Ans: equal

Q26. Figure shows lines of constant potential in an electric field. Out of the three given points P,

Q, R where is electric field intensity maximum and where is it minimum? Ans: max. at P and min. at R

Q27. A test charge qo is moved without acceleration from A to C over the path ABC as shown in

Figure:Calculate potential difference between A and C. Ans: Ed

Q28. Electric potential at a point O due to a number of point charges equidistant O is V1 when

charges are uniformly distributed and it is V2 when charges are non-uniformly distributed, Figure. Is V1 = V2? Justify. Ans: yes, because it is a scalar quantity.

Q29. A hemispherical body is placed in a uniform electric field E. What is the flux linked with the

curved surface, if field is (i) parallel to base, Figure (a) and (ii) perpendicular to base, Figure (b). Ans: zero, EπR2

Q30. Two point charges 4 µ C and -2 µ C are separated by a distance of 1 m in air. Calculate at

what point on the line joining the two charges is the electric potential zero? Ans: 2/3 m from 4 µ C

Q31. The electric field at a point due to a point charge is 30 N/C, and the electric potential at that point is 15 J/C. Calculate the distance of the point from the charge and the magnitude of the charge. Ans: 0.5m, 0.83 x 10 -9 C

Q32. Two point charges A and B of value + 15 µ C and + 9 µ C are kept 18 cm apart in air. Calculate the work done when charge B is moved by 3 cm towards A. Ans: 1.35 J

Q33. Set up an arrangement of three point charges: + q, + 2q and xq separated by equal finite distances so that electric potential energy of the system is zero. What is x?

Ans: charge + q, + 2q and + 2/3q at vertices of an equilateral triangle ; x= -2/3

CHAPTER 2 -CAPACITANCE Q1. What is the area of the plates of a 2 farad parallel plate capacitor, given that the separation

between the plates is 0.5 cm? Ans: 1.13x 109m2 Q2. Calculate equivalent capacitance between the points A and B in Figure: Ans: 5 µ F

Q3. In figure, the values of capacitances are as follows: C1 = C2 = C3 = C4 = 4 µ F, C5 = 5 µ F. Ans: 4 µ F ,20µ C, C5=0

Calculate the equivalent capacitance between the points P and Q. If a battery of 10 volt is

capacitance between the point P and Q. If a Battery of 10 volt is connected between these points, what will be the charge on each capacitor?

Q4. (i) A 900 pF capacitor is charged by 100 V battery. How much electrostatic energy is stored in the capacitor?

(ii) The capacitor is disconnected from the battery and connected to another 900 pF capacitor. What is the electrostatic energy stored by the system? Ans: 4.5 x 10 -6 J, 2.25 x 10-6 J

Q5. Keeping the voltage of the charging source constant, what would be the percentage change in the energy stored in a parallel plate capacitor, If the separation between its plates were to be decreased by 10%? Ans: 11.1 %

Q6. Two identical metal plates are given charges q1 and q2 (< q1 ) respectively. If they are now brought close together to form a parallel plate capacitor with capacitance C, what will be

the potential difference between the plates? Ans: 𝒒𝟏−𝒒𝟐

𝟐𝑪

Q7. Can ever the whole charge of a body be transferred to the other? If yes, how and if not, why not? Ans: yes,When A is enclosed in B and is connected by a metallic wire.

Q8. Two spheres of radii R and 2 R are charged, so that both of these have same surface charge density σ. The spheres are located away from each other and are connected by a thin conducting wire. Find the new charge density on the two spheres.

Ans: ς 1 = 2/5 ς, ς 2 = 5/6 ς Q9. Sketch a graph to show how charge Q given to a capacitor of capacity C varies with the

potential difference V. Q10. For a given potential difference, does a capacitor store more or less charge with a dielectric

than it does without a dielectric. Ans: more as C increases. Q11. Is there any conductor which can be given almost unlimited charge? Ans:Yes, earth Q12. Can you place a parallel plate capacitor of one farad capacity in your house? Ans: No Q13. Can there be a potential difference between two conductors of same volume carrying equal

positive charges? Ans: yes, because of different value of C Q14. If the plates of charged capacitor be suddenly connected to each other by a wire, what will

happen? Ans: capacitor will discharge immediately. Q15. What are the dimensions of capacitance? Ans: [ M-1L-2A2T4] Q16. Why does the electric conductivity of earth’s atmosphere increase with altitude?

Ans:because of ionization of cosmic rays hitting the atmosphere of earth. Q17. A parallel plate capacitor has a capacity of 6 µ F in air and 60 µ F when dielectric medium is

introduced. What is dielectric constant of medium. Ans: K= 10 Q18. How much work must be done to charge 24 µ F capacitor, when the pot. Diff. between the

plates is 500 V? Ans: 3J Q19. A spherical shell of radius b with charge Q is expanded to radius a. find the work done by

the electrical forces in the process? Ans: Q2/8π𝝐o [1/a -1/b] Q20. On inserting a dielectric between the plates of a capacitor, its capacitance is found to

increase 5 times. What is the relative permittivity of the dielectric?

Q21. What should be the capacitance of a capacitor capable of storing 1 joule of energy, when used with a 100 V d.c supply? Ans:2 x10-4 F

Q22. A capacitor is charged through a potential difference of 200 V, when 0.1 C charge is stored in it. How much energy will it release, when it is discharged? Ans: 10 J

Q23. The dielectric constant of a conductor can be taken as infinitely large. Why? Q24. By what factor does the capacity of a metal sphere increase if its volume is tripled? Q25. The battery remains connected to a parallel plate capacitor and a dielectric and a dielectric

slab is inserted between the plates. What will be the effect on its(i) capacity (ii) charge, (iii) potential difference (iv) electric field (v) energy stored ? Justify your answer.

Q26. In the above question, if battery is removed after charging the condenser & dielectric slab introduced, how are all the five parameters affected?

Q27. What are dielectric substances? Which of the following is a dielectric: Silicon, mica, carbon? Q28. An uncharged insulated conductor A is brought near a charged insulated conductor B. what

happens to charge and potential of B? Q29. Two capacitors of capacitance 6 µ F and 12 µ F are connected in series with a battery. The

voltage across the 6 µ F capacitor is 2 V. Compute the total battery voltage. Ans:3V Q30. Derive expression for energy stored in a parallel plate capacitor of capacitance C with air as

medium between the plates having charges Q and – Q. Show that this energy can be

expressed in terms of electric field as 1

2€𝑜 E2 Ad, where is area of each plate and d is the

separation between the plates. How will the energy stored in a fully charged capacitor change when the separation between the plates is doubled and the dielectric medium of constant 4 is introduced between the plates?

Q31. A parallel plate capacitor is filled with two dielectrics as shown in fig. What is its capacity? A

d

A/2 A/2

Ans: ℇ0A(k1+K2)/2d Q32. A parallel plate capacitor is filled with dielectrics as shown in Fig. what is its capacitance?

d d/2

Ans: 2 ℇ0A(k1K2/ k1+K2)/d Q33. Two parallel plate capacitors X and Y have the same area of plates and same separation

between them. X has air between the plates and Y contains a dielectric medium of €r = 4, Fig.

X Y

12 V

K1 K2

K1

K2

Calculate : (i) Capacitance of X and Y if equivalent capacitance of combination is 4 µ F. (ii) pot. Diff. between the plates of X and Y (iii) what is the ratio of electrostatic energy stored in X and Y?

Ans: Cx =5 µ F, Cy =20 µ F,Vx=9.6 V, Vy= 2.4 V, Ratio =4:1 Q34. A capacitor of capacitance 20 µ F is charged to a potential of 500 volt. Calculate the charge

and energy stored in the capacitor. Q35. Two capacitors of capacitances C1 = 3 µ F and C2 = 6 µ F arranged in series are connected in

parallel with C3 = 4 µ F. The arrangement is connected to a 6.0 V battery. Calculate the total energy stored in capacitors. Ans: 1.08x10 -4J

CHAPTER 3 – CURRENT ELECTRICITY

Q1. If 3.2 x 1017 electrons pass through a wire in 0.5 s, calculate the current through it. Charge

on each electron is 1.6 x 10-19 C. Ans: 0.1024 A

Q2. In the bohr model of hydrogen atom, the electron circulates around the nucleus in a path radius 5.1 x 10-11 m at a frequency of 6.8 x 1015 revolution per second. Calculate the equivalent current. Ans: 1.088 x 10-3 A

Q3. A steady beam of ∝- particles travelling with kinetic energy E = 83.5 ke V carries a current of I = 0.2 𝜇A. Mass of ∝- particle = 6.68 x 10-27 kg. If this beam strikes a plane surface at an angle θ = 60 0 with normal to the surface, how many ∝- particles strikes the surface in t = 4 second? Ans: 2.5 x 1012

Q4. A current of 6.4 A is maintained in a conductor of cross section of 10-4 m2. If the number of free electrons is 8 x 1028 m-3, calculate the drift velocity of free electrons. Given that charge on electron is 1.6 x 10-19 C. Ans: 5 x 10-6 ms-1

Q5. A potential difference of 12 V is across a conductor of length 0.2 m. If the drift velocity of electrons is 3 x 10-4 ms-1 , calculate the electron mobility. Ans: 5 x 10-6 mV-1s-1

Q6. Calculate the resistivity of the material of wire 1.0 m long 0.4 mm in diameter and having resistance of 2.0 ohm. Ans:2.514 x 10 -7 Ωm

Q7. Find the relaxation time for free electrons in copper, if the density of mobile electrons 8.4 x 1028 m-3. The resistivity of copper at room temperature is 1.7 x 10-8 Ωm. Given mass of electron = 9.11 x 10-31 kg and charge on electron = 1.6 x 10-19 C. Ans: 2.49 x 10 -14 s

Q8. A wire of resistance 5 Ω is drawn out so that its length is increased by twice its original length. Calculate its new resistance. Ans: 45Ω

Q9. A wire of resistance 5 Ω is drawn out so that its length is increased to twice its original length. Calculate its new resistance and resistivity. Ans: 20Ω , same

Q10. A copper wire is stretched to make it 0.2% longer. What is the percentage change in its resistance? Ans:0.4 %

Q11. Calculate the electrical conductivity of the material of a conductor of length 3 m, area cross – section 0.02 mm2, having a resistance of 2 ohm. Ans: 7.5 x 107 ms-1

Q12. A conductor has a cross section of 15 cm2 and a specific resistance of 7.6 𝜇 Ω cm at 00 C. If the temperature coefficient of resistance of the material is 0.005O C-1, estimate its resistance in Ω per 2 km, when its temperature is 50O C. Ans: 0.126 Ω

Q13. The resistance of a tungsten filament at 150O C is 133 Ω. What will be its resistance at 500O

C? The temperature coefficient of resistance of tungsten is 0.0045OC-1 at 0OC. Ans: 258 Ω Q14. The resistance of a conductor at 20OC is 3.15 Ω and at 100O C is 3.75 Ω. Determine the

temperature coefficient of resistance of the conductor. What will be the resistance of the conductor at 0OC? Ans: ∝= 𝟎.𝟎𝟎𝟐𝟓0C-1 ,3 𝛀

Q15. Resistivity of the material of a conductor of uniform cross – section varies along the length as ρ= ρo (1 + ∝ 𝑥 ).Find the resistance if its length is L and area of cross – section is A. Ans: ρo/A[L + 1/2 ∝ L2]

Q16. The resistance of two conductors in series is 40 Ω and their resistance becomes 6.4 Ω, when connected in parallel. Find the resistance of individual conductors. Ans:8 𝛀 or 32 𝛀

Q17. A resistor of 5 Ω is connected in series with a parallel combination of a number of resistors each of 5 Ω. if the total resistance of the combination is 6 Ω, how many resistors are in parallel? Ans: 5

Q18. In the circuit shown in figure , find the potential difference across capacitor. Ans: 12 V

Q19. In figure, current through 3 Ω resistances is 0.8 A, then find potential drop through 4 Ω

resistance. Ans :4.8V

Q20. Three cells of emf 2.0 V, 1.8 V and 1.5 V are connected in series. Their internal resistances

are 0.05 Ω, 0.7 Ω and 1 Ω respectively. If this battery is connected to an external resistance of 4 Ω, calculate (i) the total current flowing in the circuit. (ii) the potential difference across the terminals of the cell of emf 1.5 V while in use. Ans: 0.92A ,0.58V

Q21. A battery of emf 6 V and internal resistance 1 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of resistor? What is the terminal voltage of the battery when the circuit is closed? Ans: 11Ω,5.5 V

Q22. A cell of emf ∈ and internal resistance r gives a current of 0.5 A with an external resistance of 12 Ω and a current of 0.25 A with an external resistance of 25 Ω. Calculate ( a ) internal resistance of the cell and ( b ) emf of the cell. Ans: 1 Ω,6.5V

Q23. Two identical cells, whether joined together in series or in parallel give the same current, when connected to external resistance of 1 Ω . Find the internal resistance of each cell. Ans: 1Ω

Q24. A wire is carrying a current. Is it charged? Ans: No Q25. A large number of free electrons are present in metals. Why is there no current in the

absence of electric field across it, but there is a current in the presence of electric field? Q26. Clarify your elementary notions about current in metallic conductor by answering the

following queries: (a) The electron drift speed is estimated to be only a few mm s-1 current in the range of a few

amperes. How then is current established almost the instant a circuit is closed?

(b) The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady drift speed?

(c) If the electron drift speed is so small, and electron’s charge is small, how can we still obtain large amounts of current in a conductor?

(d) When electrons drift in a metal from lower to higher potential does it mean that all the “free “electrons of the metal are moving in the same direction?

(e) Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the (i) Absence of electric field, (ii) presence of electric field?

Q27. What happens to drift velocity ( Vd ) of electrons and the resistance R if the length of a conductor is doubled (keeping potential difference unchanged ) ? Ans: Vd become half.

Q28. The standard resistance coils are made of manganin. Why? Q29. Two square metal plates are of same thickness and material. The side of B is twice that of

A. These are connected in series, fig . if the resistance of A and B are denoted by RA and RB, find RA/RB. Ans: 1

Q30. A copper wire of resistance RO is stretched till its length is increased to n times of its original

length. What will be its new resistance? Ans: n2 RO

CHAPTER 3 – CURRENT ELECTRICITY

Q31. A cell of emf E and internal resistance r is connected across a variable resistor R. Plot a graph showing the variation of terminal potential V with resistance R. Predict from the graph the condition under which V becomes equal of E.

Q32. A battery has an emf E and internal resistance r. A variable resistance R is connected across the terminals of the battery. Find the value of R such that

( a ) the current in the circuit is maximum ( b ) the potential difference across the terminals in maximum.

Q33. Two cells each of emf E and internal resistances r1 and r2 are connected in series to an external resistance R. can a value of R be selected such that the potential difference at the first cell be zero?

Q34. Is electric current a vector or scalar quantity? Explain. Q35. How can the current flow in an electric circuit? Q36. What is the order of the number of free electrons in metals? What is their function? Q37. What is the effect of temperature on the relaxation time of electrons in ametal? Q38. What do you mean by a linear resistor? Q39. What is the effect of rise in temperature on the electrical resistivity of semiconductor? Q40. What is the internal resistance of a cell due to? Q41. By what factor the resistivity of a typical insulator (e.g amber ) is greater than that of a

metal ? Q42. A 4 Ω non insulated resistance wire is bent in the middle by 180O and both the halves are

twisted with each other. What will be its new resistance? Q43. Can the terminal potential difference of a cell exceed its e.m.f? Q44. Will the drift speed of free electrons in a metallic conductor increase of decrease with the

increase in temperature? Q45. A wire of resistance 4R is bent in the form of a circle. What is the effective resistance

between the ends of diameter? Q46. If the electric current is passed through a nerve, the man is excited, why?

Q47. Is it possible that there is no potential difference between the plates of a cell? If yes, under what condition?

Q48. What will be the bands of colours in sequence on carbon resistor, if its resistance is 0.1 Ω ± 5%.

Q49. Two different wires X and Y same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ration of drift velocity of electrons in the two wires.

Q50. Draw temperature – resistivity graph for an ohmic resistor. Q51. State the factors on which (i) internal resistance (ii) emf of a cell depend. Q52. Why is it unsafe to turn a light switch on or off while talking bath? Q53. The resistivity of semiconductors and insulators decrease with increase of temperatures.

Why? Q54. While making a standard resistance, the coil is made of manganin. The coil is double folded

and is wound over non – conducting frame. Why ? Q55. Lights of a car are dimmed when the starter is operated, why? Q56. A wire is drawn into double its length and half its original cross – section. What will be

increase in its (i) resistance and (ii) resistivity? Q57. After long use of car, as given in question 25, the internal resistance of the storage battery

increases to 500 Ω. What maximum current can be drawn from the battery? Assume the emf of the battery to remain unchanged.

Q58. Three identical cells each of emf 2 V and unknown internal resistance are connected in parallel. This combination connected to a 5 ohm resistor. If the terminal voltage across the cells is 1.5 volt, what is the internal resistance of each cell?

Q59. Explain how does the resistivity of a conductor depend upon (i) number density ‘n’ of free electrons, and (ii) relaxation time 𝜏.

Q60. Draw V – I graph for ohmic and non – ohmic materials. Give one example for each. Q61. Define the term temperature coefficient of resistivity. Show graphically the variation of

resistivity with temperature for nichrome. Q62. Explain how electron mobility changes for a good conductor, when (i) the temperature of

the conductor is decreased at constant potential difference and (ii) applied potential difference is doubled at constant temperature.

INVESTIGORY PROJECT OF PHYSICS

NOTE: 1. APART FROM BELOW SUGGESTED PROJECTS, STUDENT MAY ALSO WORK ON ANY

RELEVANT TOPIC FROM NCERT PHYSICS GRADE 12. 2. AFTER CHOOSING THE RELEVANT TOPIC STUDENT WILL SEND A PROJECT REPORT ON

SOFT COPY FOR APPROVAL TO EMAIL: [email protected] BEFORE 15TH OF JUNE 2016. 3. ONE SAMPLE OF INVESTIGATORY PROJRCT IS ALSO ATTACHED. Suggested Investigatory Projects for holiday: 1. To study various factors on which the internal resistance/EMF of a cell depends. 2. To study the variations, in current flowing, in a circuit containing an LDR, because of a

variation. (a) in the power of the incandescent lamp, used to 'illuminate' the LDR. (keeping all the lamps

at a fixed distance). (b) in the distance of a incandescent lamp (of fixed power) used to 'illuminate' the LDR. 3. To find the refractive indices of (a) water (b) oil (transparent) using a plane mirror, an equi-

convex lens, (made from a glass of known refractive index) and an adjustable object needle.

4. To design an appropriate logic gate combination for a given truth table. 5. To investigate the relation between the ratio of (i) output and input voltage and (ii) number

of turns in the secondary coil and primary coil of a self designed transformer. 6. To investigate the dependence of the angle of deviation on the angle of incidence, using a

hollow prism filled, one by one, with different transparent fluids. 7. To estimate the charge induced on each one of the two identical styrofoam (or pith) balls

suspended in a vertical plane by making use of Coulomb's law. 8. To set up a common base transistor circuit and to study its input and output characteristic

and to calculate its current gain. 9. To study the factor on which the self inductance of a coil depends by observing the effect of

this coil, when put in series with a resistor/(bulb) in a circuit fed up by an A.C. source of adjustable frequency.

10. To construct a switch using a transistor and to draw the graph between the input and output voltage and mark the cut-off, saturation and active regions.

11. To study the earth's magnetic field using a tangent galvanometer.

Chemistry Q.1 Write the IUPAC name of

Br |

(i) CH2CHCH2 (ii) CH3CH2CCHCH2Cl | | | | | OH OH OH OH Cl

Q.2 Write the IUPAC name of

CH3CHCHCHCH3 | | | Cl Br OH Q.3 Write the IUPAC name of CH3 CH3

| |

CH2=CCCHCOH | | | | OH CH3 Br CH3

Q.4 How is cumene prepared from benzene? Q.5 How many sigma bonds are present in 3-Methylphenol? Q.6 How will you obtain Ethane-1, 2-diol from ethanol? Q.7 How is that alcohol and water miscible in all proportions?

Q.8 How is the COH bond in phenol stabilized? Q.9 Out of the two hydroxyl organic compounds ROH and R’OH, the first one is basic and other is acidic in behaviour. How is R different from R? Q.10 Mention an Industrial product manufactured from methanal. Q.11 Mention two important uses of methanol. Q.12 Why are higher ethers insoluble in water? Q.13 How is the presence of peroxides in ethers detected? Q.14 How is the presence of peroxide in ethers removed? Q.15 How are the following conversions carried out (i) Propan-2-ol to 1-Bromopropane. (ii) 2-Chlorobutane to Butan-2-ol.

Q.16 What happens when (i) Propan-1-ol reacts with thionyl chloride. (ii) Ethylene is treated with an alkaline solution of potassium permanganate. Q.17 Write chemical equations and reaction conditions for the conversion of (i) Chlorobenzene to phenol. (ii) Propan-2-ol to iodoform. Q.18 Show with the help of chemical equations, what happens when (i) Ethanol is treated to distinguish between (ii) Cumene hydroperoxide is treated with phosphoric acid. Q.19 Give chemical tests to distinguish between (i) Ethanol and methanol (ii) Propan-1-ol and 2-Methylpropan-2-ol. Q.20 What happens when primary, secondary and tertiary alcohols are oxidised using alkaline’ potassium permangate. Q.21 Discuss the mechanism of acid catalysed dehydration of ethanol at high temperature. OR What happens when ethanol is heated with concentrated sulphuric acid at 453 K? Explain the mechanism of this reaction. OR

Explain the mechanism of the following reaction: C2H5OH Conc . H2SO 4

453 K CH2=CH2 + H2O

Q.22 Explain the mechanism of the following reaction:

2C2H5OH H2 SO 4

413 K C2H5OC2H5 + H2O

Q.23 Phenols are more acidic than alcohols. Q.24 Write the structure of the main products of each of the following reaction: (i) Action of excess of bromine on phenol. (ii) Action of alkaline potassium permanganate on ethane. Q.25 What are glycerides? How is glycerol obtained commercially. Q.26 What do you mean by Trans-esterification. Q.27 Account for the following: (i) Phenol has a smaller dipole moment than methanol. (ii) Phenols do not give protenation reactions readily. Q.28 How are the following conversions carried out (write reactions with conditions) (i) Propan-2-ol to Propan-1-ol (ii) Ethene to Ethane-1, 2-diol (iii) Phenol to Salicylaldehyde Q.29 How will you bring about the following conversions? (i) Ethanol to ethanoic acid (ii) Phenol to 2-Acetoxy benzoic acid (Aspirin) (iii) Acetone to 2-Methylpropan-2-ol. Q.30 Write chemical equations for what happens when: (i) 2-Methylpropan-2-ol vapours are passed over heated copper. (ii) A glyceride is treated with sodium hydroxide solution. Q.31 Write chemical equations for what happens when: (i) Ethyl bromide is treated with sodium methoxide. (ii) Benzene is heated with propene in the presence of phosphoric acid. Q.32 Write the IUPAC names of the following compounds:

CH3 CH3

| |

(i) CH3CCH2CH2OH (ii) CH3CH2CCHCH2CH2OH | | | CH3 Br Br

Q.33 Write the reaction and state the condition for each of the following conversions:

(i) Ethene to ethanol (ii) Chlorobenzene to phenol

(iii) Ethanal to propan-2-ol

Q.34 Write the reactions and their conditions only for the commercial preparation of phenol from Cumene.

Q.35 Phenol is acidic while cyclohexanol is neutral. Justify.

Q.36 Complete the following reaction:

(i) (CH3)2 CO LiAIH 4

(ii) OH |

COOH

(CH 3CO )2O

Q.37 How can ethers be prepared (i) From alcohol (ii) By Williamson’s synthesis. Q.38 How do you justify the following: (i) Order of reactivity of halogen acids with ethers is HI > HBr > HCl. (ii) Phenyl methyl ether reacts with Hl to give phenol and methyl iodide but not iodobenzene and methyl alcohol. Explain by using chemical reactions involved. Q.39 (a) How will you prepare 2-Methylbutan-2-ol from (i) Acetone (ii) Butan-2-one (b) What happens when Glyol is treated separately with (i) alkaline KMnO4 (ii) terephthalic acid (c) Give equation for he preparation of iodoform from Propan-2-ol. Q.40 (a) Write the chemical equations and reaction conditions for the conversion of (i) Ethene to Ethanol (ii) Phenol to phenyl ethanoate (iii) Ethanal to propan-2-ol (b) Give an example for each of the following reactions: (i) Kolbe’s reaction (ii) Reimer-Tiemann reaction. Q.41 (a) Write the reaction and state the condition for each of the following conversions: (i) Ethene to ethanol (ii) Chlorobenzene to phenol (iii) Ethanol to propan-2-ol (b) Write the reactions and their conditions only for the commercial preparation of phenol from Cumene. Q.42 An organic compound ‘A’ having molecular formula C6H6O gives a characteristic colour with aqueous FeCl3 solution. When ‘A’ is treated with CO2 and NaOH at 400 K under pressure, ‘B’ is obtained. The compound B on acidification gives compound ‘C’ which react with acetylchloride to form ‘D’ which is a popular pain killer. Deduce the structure of A, B, C and D.

Q.43. An organic compound ‘X’, containing C, H and O is unreactive towards sodium. It does not add up bromine. It does not react with Schiff’s reagent either on refluxing with excess of hydroiodic acid, ‘X’ yields only one organic product, Y. On hydrolysis, yields a new compound ‘Z’, which can be converted back to ‘Y’ by reaction with red phosphorus and iodine. The compound ‘Z’ on oxidation with potassium permanganate gives carboxylic acid. The molecular mass of the acid is 60 g mol-1 and it smells like vinegar. What are the compounds X, Y and Z? Write chemical equations leading to the conversion of X to Y and then to Z. Q.44 Arrange the following set of compounds in order of their increasing boiling points. Pentan-1-ol, butan-1-ol, butan-2-ol, ethanol, propan-1-ol, methanol. Q.45 Arrange the following set of compounds in order of their increasing boiling points. Pentan-1-ol, n-butane, pentanal, ethoxyethane. Q.46 Explain why is propanol higher boiling than butane. Q.47 Explain why are alcohols comparatively more soluble in water than the corresponding hydrocarbons. Q.48 While separating a mixture of ortho and para nitrophenols by steam distillation, name the isomer which is steam volatile. Give reason. Q.49 Write the IUPAC names of the following compounds:

Q.50 Write IUPAC names of the following compounds:

CH3 CH3 CH3 CH3

(i) OH (ii) (iii) (iv) OH

OH OH CH3 CH3

Q.51 Write IUPAC names of the following compounds:

(i) CH3OCH2CHCH3 (ii) C6H5OC2H5

(iii) C6H5OC7H15 (iv) CH3CH2OCHCHCH2CH3 | CH3

Q.52 Write structures of the compounds whose IUPAC names are as follows: (i) 2-Methylbutan-2-ol (ii) 1-Phenylpropan-2-ol (iii) 3, 5-Dimethylhexane-1, 3, 5- triol (iv) 2, 3-Diethylphenol. Q.53 Write structures of the compounds whose IUPAC names are as follows: (i) 1-Ethoxypropane (ii) 3-Methyl-2-ethoxypentane (iii) Cyclohexylmethanol. Q.54 Draw the structures of all isomeric alcohols of molecular formula C5H12O and give their IUPAC names. Classify them as primary, secondary and tertiary alcohols. Q.55 Write equations for preparation of Propan-2-ol from (i) Alkene and (ii) a Grignard reagent. Q.56 Write notes on (i) Oxymercuration-demercuration and (ii) Hydroboration.

Q.57 Give the structures and IUPAC names of the products expected from the following reactions:

(i) Catalytic reduction of butanal (ii) Hydroboration of but-1-ene (iii) Hydration of propane in the presence of dilute sulphuric acid. (iv) Reaction of propanone with methyl magnesium bromide followed by hydrolysis of the adduct.

Q.58 Give the equations of the following reactions: (i) reaction of propene with mercuric acetate followed by hydrolysis. (ii) oxidation of propan-1-ol with alkaline KMnO4 solution. Q.59 How are the following conversions called out? (i) Propene Propan-1-ol (ii) Benzyl chloride Benzyl alcohol (iii) Ethyl magnesium chloride Propan-1-ol (iv) Methyl magnesium bromide 2-Methylpropan-2-ol. Q.60 Name the reagent used in the following reactions. (i) Oxidation of a primary alcohol to carboxylic acids. (ii) Oxidation of a primary alcohol to an aldehyde. (iii) Dehydration propan-2-ol to propene. (iv) Butan-2-one to butan-2-ol. Q.61 Give the equation of reaction of preparation of phenol from Cumene. Q.62 Give two reactions that show the acidic nature of phenol. Q.63 Compare the acidity of phenol with that of ethanol. Q.64 Explain why is ortho-nitrophenol more acidic than ortho-methoxy phenol. Q.65 Explain how does the – OH group attached to a carbon of benzene ring activates it towards electrophilic substitution. Q.66 Arrange the following compounds in increasing order of their acid strength. Propan-1-ol, 2, 4, 6-trinitrophenol, 3-nitrophenol, 3, 5- dinitrophenol, phenol, 4-methylphenol. Q.67 Give the equations of the following reactions: (i) Reaction of bromine in CS2 with phenol. (ii) Action of dilute HNO3 with phenol.

(iii) Treating phenol with chloroform in the presence of aqueous NaOH at 343 K. Q.68 Give the IUPAC name of the following ethers:

(i) CH3OCH2CHCH3 (ii) CH3OCH2CH2Cl | CH3

(iii) O2NC6H4OCH3 (p) (iv) CH3CH2CH2OCH3 Q.69 Write the names of reagents and equations for the preparation of the following ethers by Williamson synthesis. (i) 1-Propxypropane (ii) Ethoxybenzene (iii) 2-Methyl-2-methoxypropane (iv) 1-Methoxyethane. Q.70 Illustrate with examples the limitations of Williamson synthesis for the preparation of certain types of ethers. Q.71 How is 1-Propxypropane synthesised from propan-1-ol. Q.72 Preparation of ethers by acid dehydration of secondary or tertiary alcohols is not a suitable method. Give reasons. Q.73 Write the equation of the reaction of hydrogen iodide with (i) 1-Propxypropane (ii) Methoxybenzene acid (iii) Benzylethyl ether. Q.74 Explain the fact that in aryl alkyl ethers. (i) The alkoxy group activities the benzene ring towards electrophilic substitution and (ii) It directs the incoming substituents to ortho and para position in the benzene ring. Q.75 (a) How is Ethan-1, 2-diol prepared with (i) Ethylene oxide (ii) Ethene and (iii) 1, 2-Dibromoethane. (b) How is glycerol obtained as a by product of soap industry? Write the equation of nitration of glycerol. Q.76 (a) Write the structures of the major products expected from the following reactions: (i) Mononitration of 3-Methylphenol. (ii) Dinitration of 3-Methylphenol. (iii) Mononitration of phenyl ethanoate. (b) Account for the following:

(i) The bond angle COH in alcohols is slightly less than the tetrahedral angle (109o-28’). (ii) The carbon-oxygen bond length in phenol is slightly less than that in methanol. Q.77 Write equation for the following reactions:

(i) Friedel Craft reaction – alkylation of anisole. (ii) Nitration of anisole. (iii) Bromination of anisole in ethanoic acid medium. (iv) Friedel Craft acetylation of anisole.

Q.78 Mention one property of glycerol which is useful in cosmetics. Q.79 How much bromine (in moles) is needed to produce 2, 4, 6- tribromophenol form 1 mole of phenol? Q.80 Compare the acidic character of primary, secondary and tertiary alcohols. Q.81 Why is glycerol more viscous than ethanol? Q.82 Arrange the following in order of decreasing acid strength CH3OH, H2O, C6H5OH Q.83 Phenol is an acid but does not react with sodium bicarbonate solution. Q.84 Why is common phenol more acidic than ethyl alcohol?

Q.85 Anhydrous CaCl2 is not recommenced in decreasing order of their acidic character. Q.86 Arrange the following phenolic compounds in decreasing order of their acidic character.

OH OH OH OCH3 NO2

Q.87 Why is the boiling point of glycol high?

Q.88 Sodium metal can be used for drying diethyl ether and benzene and not ethanol. Why?

Q.89 Complete the following reaction: OH

Excess of Br 2

Q.90 Ether fire is not extinguished by water. Explain?

Q.91 Give one example of coupling reaction.

OR

Convert phenol into 4-Hydroxy azobenzene.

Q.92 Out of HCl (g) and SOCl2, which is preferred for converting ethanol into chloroethane.

Q.93 Discuss dehydration of alcohols at different temperatures.

Q.94 How is phenol prepared from

(i) Benzene (ii) Chlorobenzene (iii) Benzene diazonium chloride.

Q.95 Write a short note on

(i) Kolbe-Schmidt reaction

(ii) Schotten-Baumann reaction

(iii) Reimer Tiemann reaction.

Q.96 How will you distinguish between primary, secondary and tertiary alcohols by Victor Mayor’s test. Give chemical reactions also.

Q.97 How will you distinguish between the following pairs by chemical test?

(i) C2H5OH and OH Or CH3OH and Phenol.

(ii) Propan-1-ol and Propan-2-ol.

Q.98 Phenols are more acidic than alcohols. Explain.

Or

Which of the two, Alcohols or phenols is more acidic and why?

Q.99 What is Lucas test? How will you distinguish between ethanol and methanol?

Q.100 How is glycerol prepared synthetically from propene?

Or

How is Propane-1, 2- 3-triol obtained from propane?

Q.101 How will you convert glycerol into:

(i) Allyl alcohol (ii) Acrolein (iii) Isopropyl iodide.

Q.102 What happens when primary, secondary and tertiary alcohols are passed over heated copper at 570 K?

Or

Give chemical test to distinguish Propan-2-ol and 2-Methylpropan-2-ol.

Or

Give chemical test to distinguish secondary butyl alcohol and tert. butyl alcohol.

Q.103 What is fermentation? How can ethyl alcohol be obtained by this method.

Q.104 How are the following conversions carried out (write equations).

(i) Phenol into phenolphthalein.

(ii) Benzene into picric acid.

Q.105 How will you bring about the following conversions?

(i) Ethers are used as solvent in industry.

(ii) Ethers have low boiling point as compared to alcohols.

(iii) Ethers are soluble in water to an appreciable extent.

Q.107 What happens when:

(i) Isopropyl chloride is heated with dry silver oxide.

(ii) Methoxy benzene is subjected to nitration.

(iii) Phenol dissolved in caustic alkali is heated with ethyl iodide.

Q.108 Write a short note on Haloform reaction.

Q.109 Account for the following:

(i) Unlike phenols, alcohols are easily protonated.

(ii) The water solubility of three alcohols lie in the order:

n-Butyl alcohol > sec – Butyl alcohol ? tert.-Butyl alcohol.

(iii) Which haloalkane must be preferred in Williamson’s synthesis.

(iv) Bond angle COC in ethers is more than HOH in water.

(v) o-Nitrophenol is more acidic than m-Nitrophenol.

Q.110 What happens when Glycerol is treated with

(i) Insufficient HI.

(ii) Oxalic acid at low temp. (383 K)

(iii) Oxalic acid at high temp. (503 K)

(iv) Fenton’s reagent

(v) Bromine water

(vi) KHSO4.

Q.111 Write equations and give IUPAC name of the main product, when propan-1-ol reacts with

(i) excess HBr under reflux.

(ii) a small amount of conc. H2SO4.

(iii) acidified KMnO4

(iv) Ethanoic acid in the presence of conc. H2SO4.

(v) SOCl2.

Q.112 What happens when

(i) Propane is treated with diborane and the product is hydrolysed with alkaline hydrogen peroxide.

(ii) Crotonic acid is heated with sodium borohydride.

(iii) Acetyl chloride is heated with lithium aluminium hydride.

(iv) Propan-1-ol is treated with ethanoic acid in the presence of conc. H2SO4.

Q.113 The treatment of alkyl halide with aqueous KOH leads to the formation of alcohols whereas in the presence of alc. KOH, alkenes are the major product. Give reason.

Q.114 What is the function of anhydrous ZnCl2 in the reaction of alcohols with conc. HCl (or Lucas reagent).

Q.115 Convert (i) C2 + H2 to glycerol.

(ii) Benzene sulphonic acid to resorcinol.

Q.116 Phenol reacts with bromine in non-polar solvents to give only monobromophenol whereas in polar solvents trisubstituted product is formed. Explain.

Q.117 When t-butanol and n-butanol are separately treated with a few drops of dilute KMnO4, in one case only, the purple colour disappears and a brown precipitate is formed. Which of the two alcohols gives the above reaction and what is the brown precipitate.

Q.118 Ethyl alcohol and dimethyl ether are isomeric but alcohol is a liquid at room temperature while ether is gas. Explain.

Q.119 What is the structure of the major product when 3-Ethylpent-2-ene is reacted with Hg(OAc)2/H2O, NaBH4?

Q,120 The coupling of phenol with benzene diazonium chloride is carried in the weakly alkaline medium. Explain.

Q.121 Why are secondary and tertiary alcohols not suitable for preparing ethers by dehydration with conc. H2SO4.

Q.122 Account for the following:

(i) Phenols get coloured on long standing.

(ii) Out of benzene and phenol which is more easily nitrated and why?

Q.123 How do you account for the fact that unlike phenol, 2, 4-Dintrophenol and 2, 4, 6- Trinitrophoneol are soluble in aqueous solution of sodium carbonate?

Q.124 Benzyl chloride is more reactive than Chlorobenzene towards Nucleophilic substitution. Explain.

Q.125 A compound (A) reacts with thionyl dichloride to give compound (B). B reacts with magnesium to form a Grignard’s reagent which is treated with acetone and the product is hydrolysed to give 2-Methylbutan-2-ol. What are (A) and (B) compounds.

Maths Continuity and Differentiability

1. If )11(sin 21 xxxxy find dx

dy

2. If xxxy 1log1 22 , prove that 0112 xydx

dyx

3. If )(11 33366 yxayx , Prove that 6

6

2

2

1

1

x

y

y

x

dx

dy

4. If 011 yxxy , prove that 2)1(

1

xdx

dy

5. If )sin(sin ybxy , prove that b

yb

dx

dy

sin

)(sin 2

6. If 0cossinsin yaayax , prove that

a

ya

dx

dy

sin

sin 2

7. If 172916 yxyx , Prove that x

y

dx

dy 2

8. If xyy ex , Show that

2)log1(

log2

x

x

dx

dy

9. If ttx 2cos23cos and ,sin23sin 2 tty find the value of 4

tat

dx

dy

10. If ttax 2cos12sin and ,2cos12cos ttby find the value of

34

tandtat

dx

dy

11. Differentiate x

x 11tan

21 with respect to

2

1

1

2sin

x

x

12. If t

ty

t

tx

2cos

cos,

2cos

sin 33

Prove that tdx

dy3cot

13. Prove that: 22222

22 log22

xaxaxa

xax

dx

d

14. Prove that: 2212

22 sin22

xaa

xaxa

x

dx

d

15. If 2

2

1

1log1

sinx

x

xxy

prove that 2

32

1

)1(

sin

x

x

dx

dy

16. Differentiate xxx xxx coscos w.r.t. x

17. If ,1

332 x

x

xxf

find xf '

18. If 42 xxf , 1

3

x

xxg and 54 xxh then find xghf '''

19. ,1

sin

2

1

x

xy

show that 0312

22 y

dx

dyx

dx

ydx

20. If ,sinsin 1 xmy prove that 01 2

2

22 ym

dx

dyx

dx

ydx

21. If 01,1 2

2

222 ym

dx

dyx

dx

ydxthatShowxxy

m

22. If 0,log2

22222

dx

dyx

dx

ydaxthatShowaxxy

23. If 11 xey , Show that 2

2

2

dx

dy

dx

yd

24. If ,log1

tan

y

ax 021

2

22

dx

dyax

dx

ydx

25. f 21 )(sin xy , prove that 02)1(2

22

dx

dyx

dx

ydx

26. If xecxy cotcos , prove that 2

2

2

sin ydx

ydx

27. If xxy sectan , prove that xdx

ydx cos)sin1(

2

22

--------------------------------------------------------HOTS:------------------------------------------------------------------

28. If ,logcos 1

n

n

x

b

y

Prove that 02

2

22 yn

dx

dyx

dx

ydx

29. If ,12

2

2

2

b

y

a

x prove that

32

4

2

2

ya

b

dx

yd

30. If 11 xxy , prove that 04

12

22

y

dx

dyx

dx

ydx

31. ,2

11

xyyif mm

prove that 01 2

2

22 ym

dx

dyx

dx

ydx

32. If ,222cbyax for some c > 0, prove that

2

2

2/32

1

dx

yd

dx

dy

is a constant.

33. If ,log

bxa

xxy Prove that .

2

2

23

y

dx

dyx

dx

ydx

34. If xxy , Prove that 01

2

2

2

x

y

dx

dy

ydx

yd.

35. If ktytx sin,sin , prove that 01 2

2

22 yk

dx

dyx

dx

ydx

36. If 33 sin,cos ayax , prove that adx

yd

27

322

2

when 6

37. Differentiate

x

xx

361

32sin

1

w.r.t. x6

38. If

13

1125sin

21 xx

y ,find dx

dy

39. Differentiate 2222

22221tan

xaxa

xaxa

with respect to 2

21cos

a

x

40. If cossec x and nny cossec , then show that 04 2

2

22 yn

dx

dyx

dx

ydx

41. Find the values of a, b and c for which the function

0,2/3

2

0,

0,sin)1sin(

)(

xwhenbx

xbxx

xwhenc

xwhenx

xxa

xf is continuous at x = 0

42. If

4,|4|

4

4,

4,|4|

4

)(

xwhenbx

x

xwhenba

xwhenx

x

xf , is continuous at x = 4, find a and b

43. If the function

1,25

1,11

1,3

)(

xwhenbax

xwhen

xwhenbax

xf is continuous at x = 1, find a and b

44. If the function

1,

0,)1log()1log(

)(

xwhenk

xwhenx

bxax

xf is continuous at x = 0, find the

value of k

45. If the function

0,416

0,

0,2

4cos1

)(

xwhenx

x

xwhena

xwhenx

x

xf is continuous at x =0, find a .

46. Find the value of a and b so that the function

1,1

1,32

xifbx

xifaxxxf is

differentiable at each Rx

47. Find the value of p and q so that the function

1,2

1,3

2

23

xifqx

xifpxxxf

is differentiable at x =1

Inverse Trigonometric Functions

1. Find the domain of 4cos 21 xxf

2. Write the range of 25

5

x

xxf

3. If 2

3sinsinsin 111

zyx find the value of x + y + z

4. If two angles of a triangle are 2tan 1 and 3tan 1 find third angle

5. Solve for x: 12

2cotcot 11 xx

6. Solve for x: xxx cos1sinsin 11

7. Evaluate:

3cot2

4cot 1

8. Evaluate: 22tancos3

1tan2sin 11

9. If

b

y

a

x 11 coscos , then prove that 2

2

2

2

2

sincos2

b

y

ab

xy

a

x

10. Solve: 3

2

2

1cot

1

2tan

21

2

1

x

x

x

x, x>0 [Ans:

3

1x ]

11. Solve 60,43

tan2

tan 11 xxx

[Ans: 1x ]

12. Solve: 2

- 36 sin 6x sin 1-1- x [Ans:

12

1x ]

13. Solve: xxx 111 sin

5

4sin

5

3sin [Ans: 1,0,1x ]

14. Solve: 0tan2cotcos2sin 11 x [Ans: 21,21,1 x ]

15. Prove that: 48

1tan2

7

25sec

5

1tan2 111

16. Find the greatest and least value of the 2121 cossin xx

17. Prove that

2tan

2tantan2

coscos1

coscoscos 11

18. Prove That:

tan4

1tan

2cos35

2sin3tan 11

19. Prove That: 1tantantantan2

2sec2cos2sec2costan 12211

20. Show that

sincos

cossintan

24tan.

2tantan2 11