12S-1

S.B.P. D.A.V. Centenary Public School, Fatehabad. Website: www.davfatehabad.in E. Mail: sbpdavftb@yahoo.co.in, Ph. 01667-222664

Holidays’ Assignments for Summer Vacations (2019-20) for Class XII (Medical)

General Instructions:

1. Get up early in the morning and go out for a walk daily. Play some outdoor game to remain fit.

2. Learn all the prayers and mantras given in student diary.

3. Raise a small kitchen garden by planting seeds.

4. The summer break for Nursery to XII will be from May 24, 2019 to July 1, 2019 (Both days inclusive). School

will reopen on July 2, 2019.

5. Revise the syllabus of all subjects done before summer vacations for Unit Tests to be arranged after

summer break.

6. Submit home work to your teachers on July 2, 2019.

7. Register & Participate in 1st

stage of 5th

Online International Humanity Olympiad by accessing through

our web portal – www.humanityolympiad.org or Android App - Awake Humanity (play store). Every

individual passing the exam (i.e. scoring minimum 40%) will get an e-certificate through e-mail

immediately on their emails. School code is : FATE001

English 1) REVISE syllabus for U.T.:-

Flamingo- Lessons- 1 to 5, Poems- 1 & 2

Advertisements, Notice, Invitation & Replies and Letter Writing

Note Making & Summarizing

2) Write 30 new words along with the synonym, antonym and usage of the word.

3) (i) Make a beautiful collage on classified advertisements(any 8) ---------Roll Nos. 1 to 10

(ii) Make a beautiful collage on different posters (any 8) --------- Roll Nos. 11 to 20

(iii) Draft beautiful invitations (formal& informal both) on any family Function, School Function,

Inauguration and a Birthday Party. ------------ Roll Nos. 21 to 30

(iv)Write any 8 notices on A4 sheets. ------------Roll Nos. 31 onwards

4) Complete Modules from Devjyoti Bravia in good Handwriting.(Use Pencil)

a. Booklet- 1 Worksheet 1 to 8 (Reading Comprehension)

b. Booklet- 1 Worksheet 19 to 23 (Note-Making)

c. Booklet- 2 Worksheet 29,30,33,34,39 to 42, 44 to 47,53,54,60,61, 68 to 70,73,74, 82 to 84

d. Booklet- 3 Worksheet 88 to 93,97,98

e. ASL- Listening Assignment- 1 to 3,

5) Read any one book written by any of the following authors and write its review in 150-200 words. 1. Satyajeet Ray 2. R.K. Narayan 3. Sudha Murthy 4. Ismat Chugtai

5. Vikas Swaroop 6. A.P.J. Abdul Kalam 7. Mark Twain

6) Visit the following links, watch the videos and practice the same for ASL:

https://www.youtube.com/watch?v=1Dax90QyXgI

https://www.youtube.com/watch?v=TdtUjWb0O9w

https://www.youtube.com/watch?v=3LoTF_B8vrU

https://www.youtube.com/watch?v=7kRQlYSqw_g

Physics

• Do all the NCERT Exemplar questions of chapters completed in class

• Investigatory Project Report to be made on the topics allotted in class.

• Do following assignment in your holidays’ homework notebook.

12S-2

SUBJECTIVE QUESTIONS

01. Define dipole moment of an electric dipole. Show mathematically that the electric field intensity due to a short

dipole at a distance ‘d’ along its axis is twice the intensity at the same distance along the equatorial line.

02. Find expression for electric field at a point due to axial line and equatorial line. Hence show that the ratio of electric

field intensity is two.

03. Define electrostatic potential energy & derive an expression for electrostatic potential energy of three point

charges.

04. Find an expression for electric intensity due to a short electric dipole at any point situated along a line inclined at an

angle θ to the dipole axis

05. A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law,

derive an expression for an electric field at a point outside the shell. Draw a graph of electric field with distance r

from the centre of the shell for 0 ≤ r ≤∞.

06. Find expression for loss of energy on sharing charges.

07. Find expression for energy stored in charged capacitor.

08. Find expression for capacitance of an isolated spherical conductor.

09. Find expression for the capacitance when a number of capacitors are joined in parallel.

10. Three capacitors of equal capacitance are connected in i. series ii. Parallel. What happens to capacitance in each

case? Explain.

11. What happens to the energy stored in a capacitor if after disconnecting the battery, the plates of charged capacitor

are moved farther.

12. What happens to the energy stored in a capacitor, if the plates of charged capacitor are moved farther the battery

remaining connected.

13. A proton & an electron are placed freely in an electric field. Which of these particles have greater acceleration &

why?

14. Is elective flux a scalar or vector quantity? Write electric flux on a scalar product of two vectors.

15. A charge q is placed at the centre of a cube. What would be the flux through one face?

16. Define electric flux. Write its S.I unit. A spherical rubber balloon carries a charge that is uniformly distributed over

the surface. As the balloon is blown up & increases in size, how does the total flux coming out of the surface

charge? Give reason

17. State Coulomb’s law in electrostatics. Express it in vector form what is importance of expressing it in vector force.

18. State the limitations of coulomb’s law.

19. An electric dipole with moment is placed in a uniform electric field of intensity Derive an expression for

torque experienced by the dipole. Show diagrammatically the orientation of the dipole in the field for which the

torque is (i) maximum (ii) half the maximum value (iii) zero.

20. Can we give any amount of charge to a capacitor? Why?

21. Is there any material which when inserted betn the plates of capacitor reduces its capacitance?

22. How will you obtain maximum capacitance by combining three capacitors?

23. Which of the following is a dielectric substance : germanium, mica, carbon?

24. Write the principle of capacitor.

25. State Coulomb’s law in vector & prove that

21 = - 12

26. Give six properties of electric charge.

27. Show that the capacitance of capacitor increases on introducing the conducting slab.

28. Electrostatic force between two charges is called central force. Comment.

29. What is the least possible value of charge?

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30. What orientation of an electric dipole in a uniform electric field corresponds to its stable equilibrium?

31. The distance of the field point, on the equatorial plane of small electric dipole is halved, By what factor does the

electric field due to dipole change?

32. At what points is the electric dipole field intensity parallel to the line joining the charges?

33. A positively charged particle is true to move in an electric field. Will it always move along the line of force?

34. A proton & an electron are placed freely in an electric field. Which of these particles have greater acceleration &

why?

35. Derive expression for application of Gauss`s law.

36. Find an expression for electrostatics potential and potential difference.

37. Find an expression for electric potential gradient.

38. What is drift velocity? Derive an expression for it.

39. Define SI unit of current.

40. State ohm’s Law. Explain how it fails.

41. How does the drift velocity of electrons in a metallic conductor vary with increase in temperature?

42. The potential difference across a given copper wire is increased. What happens to the drift velocity of the

charge carriers?

43. What is non-ohmic device? Give one example.

44. Define resistivity of the material of a wire.

45. Find expression for relation between relaxation time and resistivity.

46. If a wire is stretched to double of its original length without loss of mass, how will the resistivity of the

wire be influenced?

47. Name the units of conductance of conductor.

48. Derive relation between internal resistance, e m f and terminal potential difference.

49. Explain with graph, the variation of conductivity with temperature for a metallic conductor.

50. How does the conductance of a semiconductor material change with rise in temperature?

Numericals 1. Which is bigger, a coulomb or charge on an electron? How many electronic charges form one coulomb of charge?

2. The force between two electrons when placed in air is equal to 0.5 times the weight of an electron. Find the distance

between two electrons. Given: mass of electron = 9.1 × 10–31

kg.

3. The electrostatic force on a small sphere of charge 0.4 C due to another small sphere of charge – 0.8 C in air is 0.2

N. (a) What is the distance between two spheres? (b) What is the force on the second sphere due to the first?

4. An electric dipole, when held at 30° with respect to a uniform electric field of 104 N C–1 experiences a torque of 9 ×

10–26

N m. Calculate the dipole moment of the dipole.

5. In a certain region of space, electric field is along the Z-direction throughout. The magnitude of the electric field is,

however, not constant but increases uniformly along the positive Z-direction at the rate of 105 N C

–1 m

–1. What are

the force and torque experienced by a system having a total dipole moment equal to 10–7

C m in the negative Z-

direction?

6. Calculate the capacitance of a parallel plate capacitor having 0.20m × 0.20m square plates separated by a distance

of 1 × 10–3

m.

7. A parallel plate capacitor having plate area of 25 cm2 and plate separation of 1 mm is connected to a battery of 6 V.

Calculate the work done by the battery during the process of charging.

8. An uncharged capacitor of capacity C is connected to a battery of emf V. Prove that half of the energy supplied by

the battery is loss as heat while charging the capacitor.

9. 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?

10. Calculate the equivalent capacity of the system shown in Fig.

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11. Find the capacity of the combination shown in figure.

12. Three capacitors, each of capacitance 9 pF, are connected in series. (a) What is

the total capacitance of the combination? (b) What is the potential difference

across each capacitor, if the combination is connected to a 120 V supply?

13. A point charge of 2 µC is situated at the centre of a sphere of radius 0.2 m.

Calculate the electric flux through its surface given to 8.854 x 10-12

C2/N/m

2.

14. Two equal charges placed in air and separated by a distance of 2m repel each other with a force of 10-4

kgf. Calculate

the magnitude of either of the charges.

15. Find the capacitance of the infinite ladder between the points x& y.

16. Find the resultant capacitance between the points. X & Y of the combination of capacitors as shown.

17. A system has two charges qA = 2.5 × 10–7

C and qB = – 2.5 × 10–7

C located at points A: (0, 0, – 0.15 m) and B: (0, 0 +

0.15 m) respectively. What is the total charge and electric dipole moment of the system?

12S-5

18. Point charges having values + 0.1 C, + 0.2 C, –0.3 C and –0.2 C are placed at the corners A, B, C and D

respectively of a square of side one metre. Calculate the magnitude of the force an a charge of + 1 C placed at the

centre of the square.

19. An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 104 V m

–1 in Millikan oil

drop experiment. The density of oil is 1.26 × 103 kg m

–3. Estimate the radius of the drop. Given: g = 9.81 ms

–2 and e =

1.6 × 10–19

C.

20. Two point charges of + 16 C and – 9 C are placed 8 cm apart in air. Determine the position of the point at which

the resultant electric field is zero.

21. Two charges, each of 5 C but opposite in sign, are placed 4 cm apart. Calculate the electric field intensity at a point

distant 4 cm from the mid-point on the axial line of the dipole.

22. (a) Calculate the potential at a point P due to a charge of 4 × 10–7

C located 0.09 m away.

(b) Hence obtain the work done in bringing a charge of 2 × 10–9

from infinity to the point P. Does the answer depend

upon the path along which the charge is brought?

23. A parallel plate capacitor having plate area of 25 cm2 and plate separation of 1 mm is connected to a battery of 6 V.

Calculate the work done by the battery during the process of charging.

24. Three capacitors of equal capacitance, when connected in series, have a net capacitance of C1. When connected in

parallel, they have a capacitance of C2. What is the value of

2

1

C

C?

25. Two fixed point charges 4Q and 2Q are separated by a distance x. Where should be a third point charge q be placed

for it to be in equilibrium.

Multiple choice Questions 1. The work done in moving a positive charge on an equipotential surface is:

a. Finite and positive b. Infinite

c. Finite and negative d. Zero

2. At a large distance r, the electric field due to a dipole varies as:

a.1/r b.1/r2

c. 1/r3 d. 1/r

4

3. A and B are two spherical conductors of the same extent and size. A is solid and B is hollow. Both are

charged to the same potential. If the charges on A and B are QA and QB respectively, then:

a. QA is less than QB b. QA is greater than QB but not double c.

QA = QB d. QA = 2QB

4. Three point charges, each + q, are placed at the corners of a equilateral triangle of side r. the electric field at the

circumcentre will be (k = 1/4 ):

a.3kq/r2 b. kq/r

2 c. d. Zero

5. A capacitor of 20 µµµµF, charged to 500 V, in connected in parallel with another capacitor of 10 µµµµF

charged to 200 V. The common potential difference across the combination is:

a. 300 V b. 350 V

c. 400 V

d. 700 V

6. According to Coulomb’s law, the electrostatic force between two charges is:

a. Inversely proportional to the product of the charges

b. Inversely proportional to the square of the distance between the charges

c. Directly proportional to the cube of the distance between the charges

d. Directly proportional to the product of the two charges and also the distance between them

Energy of an electrical condenser of capacity C, when subjected to a potential V, is given by:

a. CV2 b. C

2V c.

d.

12S-6

7. Electron volt (eV) is a unit of:

a. Energy b. Potential c. Current d.Charge

8. Which of the following is not true:

a. For a point charge, the electrostatic potential varies as 1/r

b. For a dipole, the potential depends on the position vector and dipole moment vector

c. The electric dipole potential varies as 1/r at large distance

d. For a point charge, the electrostatic field varies as 1/r2

9. A hollow metal sphere of radius 10 cm is charged such that the potential on its surface becomes 80 V. The

potential at the centre of the sphere is:

a. 80 V b. 800 V c. 8 V d. Zero

10. A capacitor of capacitance C1 is charge to a potential V and then connected in parallel to an

uncharged capacitor of capacitance C2. The final potential difference across each capacitor will be:

a. b.

c. 1 + d. 1 -

11. Two identical conducting balls A and b have positive charge q1 and respectively but . The balls are

brought together so that they touch each other and then kept in their original positions, the force between them

is:

A .Less than that before the balls touched b. Greater than that before the balls touched

c. Same as that before the balls touched d. Zero

12. A charged particle of mass m and charge q is released from rest in uniform electric field E.

Neglecting the effect of gravity, the kinetic energy of the charged particle after t second is:

a. b. c. d.

13. A particle of mass 2 x 10-3

kg, charge 4 x 10-3

C enters in an electric field of 5 V/m, then its kinetic

energy after 10 s is: a. 0.1 J b.1 J c. 10 J d. 100 J

14. The electric field and the potential of an electric dipole vary with distance r as:

a. and b. and c. and d. and

15. The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r

from the centre is:

a. for points outside and for points inside the shell

b. for both points inside and outside the shell

c. Zero for points outside and for points inside the shell

d. Zero for both points inside and outside the shell

16. The electric flux for Gaussian surface A that encloses the charged particles in free is

(Given = -14 nC, = 78.85 nC, = -56 nC):

a.10

3 Nm

2C

-1 b.10

3 CN

-1C

-2

c. 6.32 x 103Nm

2C

-1

d.6.32 x 10

3 CN

-1m

-2

12S-7

17. Work done in placing a charge of 8 x 10-18

C on a condenser of capacity 100 µµµµF is:

a.16 x 10-32

J b.31 x 10-26

J c. 4 x 10-10

J d.32 x 10-32

J

18. A charge Q is placed at the corner of a cube. The electric flux through all the six faces of the cube is:

a. Q/ b. Q/6 c. Q/8 d. Q/3

19. If q is the charge per unit area on the surface of a conductor, then the electric field intensity at a

point on the surface is:

a. normal to surface b. normal to surface

c. tangential to surface d. tangential to surface

20. When an electric dipole p is placed in a uniform electric field E then at what angle between the value of torque

will be maximum?

a.90o b.0

o c. 180

o d. 45

o

21. Gauss’s law is valid for: a .Any closed surface b.Only regular close surface

c.Any open surface d. Only irregular open surface

22. An air capacitor is charged with an amount of charge ‘q’ and dipped into an oil tank. If the oil is

pumped out, the electric field between the plates of capacitor will: a. Increase b.Decrease c. Remain the same d. Become zero

23. What is the magnitude of a point charge which produces an electric field of 2 N/C at a distance of 60 cm?

a.8 x 10-11

coulomb b.2 x 10-12

coulomb

c.3 x 10-11

coulomb d. 6 x 10-10

coulomb

24. A conducting sphere of radius R = 20cm is given a charge Q = 16µµµµC. What is E at centre:

a.3.6 x 104 N/C

b.1.8 x 104 N/C

c. Zero

d.0.9 x 104 N/C

CHEMISTRY 1) Revise Lesson 1,2,3,4 (NCERT) exemplar.

2) Do following assignment:

1) Explain Vapour pressure and Raoult’s law for a solution containing volatile components. How does

Raoult’s law become a special case of Henry’s law?

2) What are Ideal and non ideal solutions. Give example with graph.

3) How relative lowering in Vapour pressure is a colligative property?

4) Determine relation between elevation in boiling point and molality.

5) How can you determine Molecular Mass of solute using Depression in freezing point.

6) Show that osmotic pressure is a colligative property.

7) What is Henry’s Law? What are its conditions and applications?

8) What is Henry’s Law? What are its conditions and applications?

9) Determine Rate of a Reaction and unit of rate of reaction.

10) What are the factors influencing rate of a reaction?

11) Difference between Order and Molecularity of a reaction.

12) Describe zero, Ist and 2nd

order reaction including integrated rate equation, units and graphs

13) Determine rate of reaction using Initial rate method.

14) Explain points of Collision theory and Activated complex theory.

15) Copper is conducting as such, while copper sulphate is conducting in molten state or in aqueous solution,

Why?

12S-8

16) Differentiate between molarity and molality for a solution. How does a change in temperature influence

their values?

17) Calculate the molarity and molality of 15%solution(by weight) of sulphuric acid of density 1.02g/cm3.

18) 15 gm of unknown material is dissolved in 450 gm of water. The resulting solution freezes at -0.34oC.

What the molar mass of the material (Kf for the water is 1.86K Kg/mol)

19) A solution of glucose in water is labelled as 10% by weight. What would be the molality of the

solution?(molar mass of glucose is 180)

20) A first order reaction is found to have a rate constant k=5.5*10-14

sec-1

. Find the half life of the reaction.

21) What are pseudo first order reactions? Give example.

22) A first order reaction has a rate constant value of 0.00510min-1

. If we begin with 0.10 M concentration of

the reactant, how much of the reactant will remain after 3 hr.

23) A first order reaction is 15% completes in 20 min. how long it will take to be 60% complete?

24) Copper is conducting as such, while copper sulphate is conducting in molten state or in aqueous solution,

Why?

25) What type of point defect is produced when AgCl is treated with CdCl2?

26) Differentiate between molarity and molality for a solution. How does a change in temperature influence

their values?

27) Calculate the molarity and molality of 15%solution(by weight) of sulphuric acid of density 1.02g/cm3.

28) 15 gm of unknown material is dissolved in 450 gm of water. The resulting solution freezes at -0.34oC.

What the molar mass of the material (Kf for the water is 1.86K Kg/mol)

29) A solution of glucose in water is labelled as 10% by weight. What would be the molality of the

solution?(molar mass of glucose is 180)

30) A first order reaction is found to have a rate constant k=5.5*10-14

sec-1

. Find the half life of the reaction.

31) What are pseudo first order reactions? Give example.

32) A first order reaction has a rate constant value of 0.00510min-1

. If we begin with 0.10 M concentration of

the reactant, how much of the reactant will remain after 3 hr.

33) A first order reaction is 15% completes in 20 min. how long it will take to be 60% complete?

34) Can an electrochemical cell act as electrolytic cell? How?

35) Single electrode potential cannot be determined. Why?

36) Explain construction and working of standard Hydrogen electrode?

37) Explain construction and working of standard Hydrogen electrode?

38) Explain construction and working of standard Hydrogen electrode?

39) What are the factors on which conductivity of an electrolyte depend?

40) Conductivity of 0.00241M acetic acid solution is 7.896 ´10-5 S cm-1. Calculate its molar

conductivity in this solution. If Lm for acetic acid is 390.5 S cm2 mol-1, what would be its

dissociatconstant?

12S-9

Maths

Note : (i) Do all the assignments in holidays’ Homework Notebook.

(ii) Prepare yourself for Unit Test (Ch.1-Ch.5)

(iii) Draw the graphs of inverse trigonometric function and compare it with trigonometric

functions

ASSIGNMENT

(MATRICES & DETERMINANTS)(MATRICES & DETERMINANTS)(MATRICES & DETERMINANTS)(MATRICES & DETERMINANTS) Q.No. Sums Answer

1 If X + Y =

52

07 and X – Y =

30

03 then the sum of the elements of the matrix 3X -4Y

is………….

14

2

If

−+

+−

−

=

+−

−+

−++

02142

2232

2360

233

0164

7243

b

cx

y

czbb

ax

yzx

then the value of a + b + c + x + y +z

is ……….

-16

3 The matrix X is equal to what such that 3A -2B + X = 0 , where A =

31

24 ; B =

−

23

12 …

−

−−

53

416

4 If A = ,

11

0

α B = ,

15

01

whenever A

2 = B, then find the value of α

no real

value of α

5 If A = diag [ ]321 ,, ddd , then find An. diag

[ ]nnn ddd 321 ,,

6

If

=

014

312A and

−

=

05

20

11

B , verify that ( ) '''ABAB =

7 Let B and C be two square matrices such that BC = CB and C2 = 0 . If A = B+C , then show

that

CBBA 233 3−− is equal to 0 .

8

Show that

−=

−

−−

θθθθ

θ

θ

θ

θ

cossin

sincos

12

tan

2tan1

12

tan

2tan1

1

9

If ,

cos0sin-

010

sin0cos

)G( and ,

100

0cossin

0sincos

)(

=

−

=

θθ

θθθαα

αααF show

that [ ] )()()()(1 αθθα −−=−

FGGF

10

Show that – ( a + b + c ) is one root of the equation 0=

+

+

+

bxac

bcxb

cbax

and solve the

12S-10

equation completely.

11 Using properties of determinates, prove that

(ii) abc

bacc

bacb

aacb

4=

+

+

+

(iii) ( )wvu

pca

qdb

x

wvu

qpxdcxbax

qxpdxcbxa

14222

222

−=+++

+++

(iv) abc

bacc

bacb

aacb

4=

+

+

+

(v) 3)(2

2

2

2

cba

bacac

bacbc

bacba

++=

++

++

++

12 Using properties determinants, solve the following for x:

(-7/3)

13

If a +b +c and

bac

acb

cba

then Using properties of determinants prove that a = b = c

14 Solve the following system of equations

(i) x + 2y – 3 z = -4, 2x +3y + 2z =2, 3x - 3y - 4z = 11. Ans 3.-2 ,1

(ii) 2x – y + 3z = 5 , 3x + 2y – z = 7 , 4x + 5y – 5z = 9 Ans. x = ,

y = , z =k

15

Solve by matrix method:

13213

10111

10332

=+−

=++

=+−

zyx

zyx

zyx

16

Determine the product

−−

−

−−

−

−

312

221

111

135

317

444

and use it to solve x-y +z = 4,

x-2y-2z = 9, 2x +y +3z =1

17 If f (x) = ax2 + bx + c is a quadratic function such that f(1) = 8 , f(2 ) = 11 and f( -3) = 6 , find f (x )

by using matrices. Also find f (0)

INVERSE TRIGONOMETRYINVERSE TRIGONOMETRYINVERSE TRIGONOMETRYINVERSE TRIGONOMETRY

12S-11

1 Evaluate : (i) ( )4/sinsin 1 π− (ii) ( ))6tan(tan 1 −−

(iii) ( )}2/1sin2/sin{ 1−−π

(iv)

+

−=

62

3coscos 1 π

(v) ( )x1cotsin − (vi) ( ))4/3cos(tan 1−

Ans (i) 4/π (ii) -6 (iii) (iv) -1 (v) 21

1

x+ (vi) 4/5

2 (i) If

= −−

2

1sintan 11 x ,find the value of x.

(ii) If ,3

1tan

4tan 11

−= −− πx then x is ………… ½

(iii) If cos thenxx ,tan 11 −− = ..............)sin(cos 1 =− x 2

15 −

(iv) If 3tan,2tan 11 −− are two angles of a triangle, then find the third angle. 3π/4

3 Solve: (i) sin-1[ cos( sin-1 )] (ii) sin[2 cot-1 ( ] (iii) cos [sin-1 +sec -1 ]

(iv) sec (tan-1 (v) ( )3tan2tan1tan2 111 −−− ++ .

Ans. (i) π/6 (ii) -120/169 (iii) - .

4 Prove that (i) sec2 (tan -1 2) + cosec2 (cot -1 3) = 15. (ii) 2sin-1 – tan-1 = π/4

(iii) 3cot18cot8cot7cot 1111 −−−− =++ (iv) sin ( )22tancos3

1tan2 11 −− +

=.

15

14

5 Solve the equation: (i) sin–16x + sin–1 6 = (ii) sin–1 x + sin–1 (1 – x) = cos–1 x

Ans.(i) x= 1/12 (ii) x= 0 or ½

6 If ,

46

51tan6

51tanπ

=

+

+−+

−

−−x

x

x

x then find the value of x.

RELATION & FUNCTIONSRELATION & FUNCTIONSRELATION & FUNCTIONSRELATION & FUNCTIONS

1 Check the following functions for one-one and onto.

(a) 7

32)(,:

−=→

xxfRRf Bijective

(b) f : R → R, f(x) = |x + 1| ( neither 1-1 nor onto )

(c) { }2

13)(,2:

−−

=→−x

xxfRRf ( 1−1 but onto )

(d) f : R → [–1, 1], f(x) = sin 2 x ( neither 1-1 nor onto )

2 Show that f : R+ → R+ defined by

xxf

2

1)(, = is bijective where R+ is the set of all non-

zero positive real numbers.

3 f : R → R, g : R → R given by f(x) = [x], g(x) = |x| then find ( ) ( )

−

−3

2 and

3

2, goffog

0 ;1

4 let A be the set of all students of class XII in a school and R be the relation, having the same sex

on A, and then prove that R is an equivalence relation

5 Show that the relation R defined by (a, b) R(c, d) ⇔ a + d = b + c on the set N × N is an equivalence relation.

12S-12

6 Let N be the set of all natural numbers & R be the relation on N × N defined by (a , b) R (c ,d)

if ad(b+c) = bc(a + d). Show that R is an equivalence relation.

7 Show that the relation R in the set A = { }9,8,7,6,5 given by ( ){ },2by divisible is :, babaR −= is an

equivalence relation. find all the elements related to elements 6.

8 Let f : N N be a function defined by f(x) = 9x2 + 6x - 5. Show that f : N S , where S is

the range of f , is invertible. Find the inverse of f. Hence find (i) f-1

(43) (ii) f-1

( 163) Ans.

( ) ,3

16 1 −+

=− xxf (i) 2 (ii) 4

9 If f: R+ R be a function defined as f(x) = x

2 +4x+6. Show that f is one one but not onto.

Find the range of S of f .Also show that f: R+ S defined by f(x) =x

2 +4x+6 is invertible.

Now find f -1

10 If RRf →: and g RR →: defined as f(x) = xx + and g(x) = xx − ,Then , find fog

and gof . hence , find fog(-3) , fog(5) and gof(-2) . ans ||x|-x| +|x| -x (ii) ||x|+x| - |x| -x

(iii) 12 (iv) 0 (v)0

DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION 1

Find dx

dy If

(i) y = log(sin21 x+ ) (ii) y = sin[ sin(log3x) ] (iii) y = sin(xx) + (sin x)x

(iv) y = (log x)e2

tan xx+ (v) y =( )2

4

53

6

+

+

x

xx (vi) sin y = x sin(a+y)

(vii) y = sec–1

−

+

1

1

x

x + sin–1

1

1

+

−

x

x, (viii) ,

11

11tan

22

221

−++

−−+= −

xx

xxy

(ix) y =

−−−

13

132cos

21 xx

, Ans.(i) ( )

2

2

1

1cot

x

xx

+

+ (ii) ( ) ( )[ ]xx

x3logsincos.3logcos

1

(iii) cos ( ) ( ) ( ) [ ]xxxxxxxxxx sinlogcotsinlog1 +++ (iv) ( )xxex

x

e xxxx

2sec.log 2tantan

2

2

++ ++

(v) ( )2

4

53

6

+

+

x

xx

( )( )

++

++

xxx

xx

53122

240117152

2

(vi)( )

a

ya

dx

dy

sin

sin 2 += (vii) 0

2 if baxyyx =+ , then find .

dx

dy ans

xyxxxy

yyxyxy

log1

1log

+−

−−−−

3 If θθ sincos bax += , θθ cossin bay += , show that 0

2

22 =+− y

dx

dyx

dx

ydy

4 Find

dx

dy , if y = ( ) ( )xxx 1(sinsin −+ Ans. ( ) [ ]

xxxxxxx

−++

12

1sinlogcotsin

5 If ( )

2

dx

dy

2dx

y2

d3thatprove,x y/xe

−==+ yxxbax

6 (i) If

2

dx

dy

2dx

y2

d3thatprove,y

x

log

−==

+

yxxbxa

x

(II) If y =

−=+y

xyx 1tan22log . Show that

xy

xy

dx

dy

+

−=

12S-13

7 If y = 11 −−+ xx . Show that 0

4

1

2

212 =++

− y

dx

dyx

dx

ydx

8 If x = )2cos1(2sin tt +α and y = )2cos1(2cos tt −β ) , show that at t =

4

π,

αβ

=dx

dy

9 If x sin (a + y ) + sina cos (a +y) = 0 , then prove that

( )a

ya

dx

dy

sin

2sin +=

10 Find the derivative of the following function f(x) w.r.t. x :

( )

+

+−

x

xx

361

3.121sin ans

6log62

61

12 x

x

+

11 Differentiate ,

122

11sec

−

−=x

y w.r.t. 21 x− at x = ½ . ans. 4

12 If the function f(x) = |x - 3| + |x - 4|, then show that f(x) is not differentiable at the points x = 3 and x = 4

13 Find the value of k for which f(x) = is continuous at x = 0

14 Determine the value of k , if

=

≠−=

2 x if ,3

2 x if ,

2

cos

)(π

ππ x

xk

xf is continuous at x =

2

π

15 Find a so that f(x ) = is continuous at x = 0.

Physical Education 1. Make a chart on following topics using A3 sheets or make a PPT on following topics.

a) Asanas to cure ‘Diabetes’ : XII Arts

b) Asanas to cure ‘Asthma’ : XII Commerce

c) Asanas to cure ‘Hypertension’ : XII Science

2. Calculate your BMI & Waist Hip Ratio and mention it on last page of your file.

Music 1. Make a chart/collage showing character sketch of Ustad Inayat Khan.

2. Make a PPT on single and double of Tala ‘Rupak’ & ‘Jhap’ and insert music related to these talas in your slides