Q paper I puc-2014(MATHEMATICS)

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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 R = {( x, x + 5) : x ∈ {0,1, 2,3, 4,5}}
3. If sin x = 3 / 5 , x lies in 2nd quadrant then find the value of tan x .
4. Solve 5 x − 3 < 7 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 term is an =1) • 5n +1
(−
n +1

7. Find the values of " k " , if the line (k − 3) x − ( 4 − k 2 ) y + k 2 − 7 k + 6 = is  to x − axis .
0
1 1 1
8. Find the equation of the circle whose centre  ,  and radius is .
2 4 2
9. Find the distance between the points ( 2,3,5 ) & ( 4,3,1) .
10. Find the derivative of x 2 − 2 at x =
10 .
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.= {1, 2,3} , B {= {8} Find i ) A × ( B − C ) and ( A × B ) − ( A × C ) what do you conclude?
If A = 6} , C
1 3
=
15. Find the domain and Range of i ) f ( x) = ii ) f ( x) .
x−6 4 − x2
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 sin17xx−−cos 5 x = cos10xx :
cos 9
sin 3 x
sin 2
18. Find General solution of sin 2 x + cos x =
0.
19. Find modulus and argument of −1 − 3i . 20. Solve 21x 2 + 9 x + 1 = .
0
21. Solve 2 x + y ≥ 6 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.
( ).
7
24. Find the middle terms in 3 − x3
6

25. Which term of the following sequence is 2, 2 2, 4,...........is 128? (OR) Find the angle between
the line 3 x + = 1& x + 3= 1
y y
ATTENTION!!! For PUC-I to PUC-II moving students
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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 x 2 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.
4 3π sec θ + cos ecθ
30. If tan θ = where π < θ < find the value of
3 2 2sec θ + 3cos ecθ
31. Solve sin θ + sin 3θ + sin 5θ = 0 (OR) Three coins are tossed once,Find the Probability of
getting (i) 3 heads (ii) 2 heads (iii) atleast 2 heads (iv) no head.
p + iq p − iq p2 + q2
32. If = x + iy, then Prove that = x − iy and 2 = x2 + y 2
m + in m − in m + n2
5−i
33. Convert into Polar form.
2 − 3i
34. Solve : 2 x + y ≥ 8, and x + 2 y ≥ 10 Graphically.
35. Find the sum to n terms of the series 1 × 2 + 2 × 3 + 3 × 4 + ........... .
x2 y 2
36. Find, foci, vertices, length of major axis, length of latus rectum of the conic + = 1
36 16
37. Derive the equation of the straight line in the slope intercept form = mx + c .
y
38. Find the image of the point (3,8) with respect to the line x + 3 y = 7 assuming the line to
be a plane mirror.
x
 ,x ≠ 0
39. Evaluate lim f ( x) where f ( x) =  x
x →0
0, x = 0


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( A + B) sin A cos B + cos A sin B by Geometrically.
=
n(4n 2 + 6n − 1)
42.Prove by Mathematical induction 1.3 + 3.5 + 5.7 + ...... + (2n − 1)(2n + 1) =
3
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 x − 2= 5 & 3 x + 2= 5 are equal is a straight line.
y y
47. Derive the equation of the parabola in the form y 2 = 4ax .Prove that length of latus rectum
for the parabola is equal to 4a.
48. Derive the formula for distance between two points P( x1 , y1 , z1 ), Q( x2 , y2 , z2 ) hence find the
distance between P(2,3,1) from origin.

PART – E
V. Answer any one question: 1 × 10 =
10

 sin θ   sin 3θ 
49. a) Prove that lim   = 1 where θ is measured in radians and hence find lim   = 1.
θ →0
 θ  θ →0
 θ 
 1   1  
b) Differentiate 1 +  ÷ 1 −   w.r.t.x
 x  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

sin 9 x + sin 7 x + sin 3 x + sin 5 x
b) Prove that = tan 6 x
cos 9 x + cos 7 x + cos 3 x + cos 5 x
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2
(b) Solve by Method of separation of Variables xy (1 + x 2 )
dy
− y 2 = 1given that when x = 1, y = o .
dx

PART - E
Answer any one question: 10 × 1 =10

( )
39. a) Find the fourth roots of the complex number −1 + i 3 and represent them in an Argand diagram.
b) Find the length of the common chord of the intersecting circles x 2 + y 2 − 4 x − 5 =0
and x + y − 2 x + 8 y + 9 =.
2 2
0
(c) Find the remainder obtained when 2301 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.

x+2
3
dy
(b) Evaluate ∫
0 x+2 + 5− x
dx ; (c) If y = sec3x ,find
dx
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Q paper I puc-2014(MATHEMATICS)

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