Q paper I puc-2014(MATHEMATICS)

ATTENTION!!! For PUC-I to PUC-II moving students

VACATION BATCHES ( II- PUC- CBSE STREAM - PCMB)

CLASSES START FROM 10 - march -2013 GIRLS BATCH: 6:00 TO 8:00 AM & BOYS BATCH: 8:15 TO 10:00 AM

Your vision. Our Mission mob: 9845222682 ANNUAL EXAM – 2013 SUBJECT: MATHEMATICS PROGRAMMES: K-CET JEE(MAIN) JEE(ADV)

PART- A

I. Answer any TEN questions: 10 1 10× =

1. Write (6,12] in Set-builder form. 2. Determine the domain and Range of the Relation R defined by ( ) { }{ }, 5 : 0,1, 2,3, 4,5R x x x= + ∈ 3. If sin 3/ 5x = , x lies in 2nd tan x quadrant then find the value of . 4. Solve 5 3 7x − < Graphically when x R∈ 5. How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated? 6.Write the first five terms of the sequence whose nth ( ) 1 11 5n n

na + += − • term is

7. Find the values of " "k , if the line ( )2 2( 3) 4 7 6 0k x k y k k− − − + − + = is to x axis− .

8. Find the equation of the circle whose centre 1 1,2 4

and radius is 12

.

9. Find the distance between the points ( ) ( )2,3,5 & 4,3,1 .

10. Find the derivative of 2 2 10x at x− = . 11. The sentence “Answer this question” is a statement or not? Give reason for your Answer. 12. Find the mean deviation about the mean for the data 4,7,8,9,10,12,13,17. PART-B II. Answer any ELEVEN(11) Questions: 11 2 22× = 13. In a Group of 65 People , 40 like cricket, 10 like both cricket and Tennis. How many like Tennis only and not cricket ? How many like Tennis? 14. If { } { } { }1,2,3 , 6 , 8A B C= = = Find ( ) ( ) ( ))i A B C and A B A C× − × − × what do you conclude?

15. Find the domain and Range of 2

1 3) ( ) ) ( )46

i f x ii f xxx

= =−−

.

16. In a circle of diameter 40cm the length of a Chord is 20cm . Find the length of minor arc of Chord. 17. Prove that cos 9 cos 5 sin 2

sin17 sin 3 cos10x x xx x x−− = : 18. Find General solution of sin 2 cos 0x x+ = .

19. Find modulus and argument of 1 3i− − . 20. Solve 221 9 1 0x x+ + = . 21. Solve 2 6x y+ ≥ Graphically. 22. In how many ways 4 boys and 3 girls may be arranged for Photograph. So that all the 3girls are shown together. 23. Find the number of straight lines that can be drawn from 12 points of which 4 are collinear.

24. Find the middle terms in ( )3 7

63 x− .

25. Which term of the following sequence is 2, 2 2,4,........... 128?is (OR) Find the angle between the line 3 1& 3 1x y x y+ = + =




26. Find the Coordinates of the point which divides the line joining the points (-2,3,5) and (1,-4,6) Internally in the ratio 2:3 ii) also externally in the same ratio. (OR) Show that the following statement is true by the method of Contra positive P: If x is an integer and 2x is even, then x is also even. PART – C III. Answer any ELEVEN Questions: 11 3 33× = 27. In a Science course,all students offered atleast one of the subjects Maths,Physics,Chemistry. 162 took Maths 153 took Physics, 198 took Chemistry, 99 took Maths and Physics, 90 took physics and chemistry, 117 took Maths and Chemistry and 72 took all the three i) what number of students offered all the three subjects. ii) How many took maths and Chemistry but not Physics. 28. The Fig- I shows a relation between the sets P and Q. Write this relation i) in set-builder form, (ii) in roster form. What is its domain and range? 29. Let A= {1,2,3,4}, B={1,5,9,11,15,16} and f={(1,5),(2,9),(3,1),(4,5),(2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B.Justify your answer in each case.

30. If 4tan3

θ = where 32ππ θ< < find the value of sec cos

2sec 3cosec

ecθ θθ θ++

31. Solve sin sin 3 sin 5 0θ θ θ+ + = (OR) Three coins are tossed once,Find the Probability of getting (i) 3 heads (ii) 2 heads (iii) atleast 2 heads (iv) no head.

32. If ,p iq x iym in+

= ++

then Prove that p iq x iym in−

= −−

and 2 2

2 22 2

p q x ym n

+= +

+

33. Convert 52 3

ii

−−

into Polar form.

34. Solve : 2 8, 2 10x y and x y+ ≥ + ≥ Graphically. 35. Find the sum to n terms of the series 1 2 2 3 3 4 ...........× + × + × + .

36. Find, foci, vertices, length of major axis, length of latus rectum of the conic 2 2

136 16x y

+ =

37. Derive the equation of the straight line in the slope intercept form y mx c= + . 38. Find the image of the point (3,8) with respect to the line 3 7x y+ = assuming the line to be a plane mirror.

39. Evaluate 0

lim ( )x

f x→

where , 0( )0, 0

xxf x x

x

≠=

=

40. Find the derivative of ‘ sin x ’ . . .w r t x by First Principle method. PART – D IV. Answer any Five Questions : 5 5 25× = 41. Prove that ( ) sin cos cos sinSin A B A B A B+ = + by Geometrically.

42.Prove by Mathematical induction 2(4 6 1)1.3 3.5 5.7 ...... (2 1)(2 1)

3n n nn n + −

+ + + + − + =

43. State and Prove Binomial theorem for Positive integral index ‘n’.




44. A group consists of 7 boys and 5 girls. Find the number of ways in which a team of 5 members can be selected so as to have at least one boy and one girl. 45.Find the sum to n terms of the series 5 11 19 29 41 .......+ + + + + 46. Show that the path of a moving point such that its distances from two lines 3 2 5 & 3 2 5x y x y− = + = are equal is a straight line. 47. Derive the equation of the parabola in the form 2 4y ax= .Prove that length of latus rectum for the parabola is equal to 4a. 48. Derive the formula for distance between two points 1 1 1 2 2 2( , , ), ( , , )P x y z Q x y z hence find the distance between P(2,3,1) from origin. PART – E V. Answer any one question: 1 10 10× =

49. a) Prove that 0

sinlim 1θ

θθ→

=

where θ is measured in radians and hence find0

sin 3lim 1θ

θθ→

=

.

b) Differentiate 1 11 1x x

+ ÷ − . . .w r t x

50. a) Find the mean deviation about the mean for the following data Marks obtained 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Number of students 2 3 8 14 8 3 2

b) Prove that sin 9 sin 7 sin 3 sin 5 tan 6cos9 cos 7 cos3 cos5

x x x x xx x x x+ + +

=+ + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Attention!!!. For PUC-I TO PUC-II moving students VECATION BATCH CLASSES ON PHYSICS, CHEMISTRY , MATHEMATICS & BIOLOGY START FROM 10 – MARCH- 2013 Fee Structure:

P C M Rs. 8000 P C M B Rs. 11000

Last Date to take admission without late fee is on or before 28-feb-2013 Admissions will be closed with fine on 04-March- 2013 ( Only 75 students will be admitted)

P C M

For the students who are appearing CET -2013 CET CRASH COURSE ON P C M B CLASSES START FROM 29/MARCH/2013 TO 30/APRIL/2013 Fee structure for CET

Rs. 3300 Last date to take admission 01-march- 2013 P C M B Rs. 4300 Last date to take admission with fine Rs.500 is 10-march- 2013

For Details : Trin 9845222682/9972774040. E-mail: [email protected] (OR) [email protected]




2

(b) Solve by Method of separation of Variables ( )2 21 1 1,dyxy x y given that when x y odx

+ − = = = .

PART - E Answer any one question: 10 1 10× = 39. a) Find the fourth roots of the complex number ( )1 3i− + and represent them in an Argand diagram.

b) Find the length of the common chord of the intersecting circles 2 2 4 5 0x y x+ − − = and 2 2 2 8 9 0x y x y+ − + + = . (c) Find the remainder obtained when 3012 is divided by 7.Using Congruence Method. 40. (a) Show that among all the right-angled triangles of a given hypotenuse, the isosceles triangle has the Maximum Area.




(b) Evaluate 3

0

22 5x dx

x x+

+ + −∫ ; (c) If sec3y x= ,find dydx

- - - - - - - - - - - - - - - - - - - - - - - - BEST OF LUCK - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Attention!!!

VECATION BATCH (II- PUC- CBSE STREAM-PCMB) CLASSES START FROM 10-MARCH-2013 & Good opportunity for the students who are Appearing CET- 2013.

- Features -

1. Daily 8 Hrs coaching with 2. Best experience Faculties from North Karnataka will handle CET. 3. Weekly twice CET Mock test on P C M B. 4. Printed study material will be provided on subjects. Note:- Admission for CET Crash course starts from 01-Feb-2013.And admission closes on 20-Feb-2013

For Details: Trin : 9845222682 / 9972774040 E-Mail : [email protected] (OR) [email protected]




A.NAGARAJ, CO ORDINATOR, SREE SUSHEELA TUTORIALS, MOB: 9845222682. e-mail: [email protected]

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Q paper I puc-2014(MATHEMATICS)