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Question Paper 2017-2018 MATHEMATICS

HIGHER SECONDARY FIRST YEAR

TIME 2 ½ HOURS MAX. MARKS.90.

PART- I

ALL THE QUESTIONS ARE COMPULSORY 1 x 20 =20

CHOOSE THE CORRECT ANSWER

1. If A is a square matrix of order n, then is……

(1) (2) (3) (4) 2. If the order of a matrix is 3, then the value of det (k A)

(1) (2) (3) k det(A) (4) det (A)

3. If a line makes with positive direction of axes x and y then the angle it makes with

the z axis is

(1) (2) (3) (4)

4. If = 0, then the angle between and is

(1)

(2)

(3)

(4)

5. The number of permutation of the letters of the word APPLE are _________

(i) 120 (ii) 60 (iii) 30 (iv) 5

6. 2 3

( 2)(2 3) 2 2 3

ax

x x x x

then the value of a is

a) 4 b) 20 c) 35 d) 45

7. The largest co efficient in the expansion of (1+x)24

is

a) b) 24

13C c) 24

12C d) 24

11C

8. If a,b,c are in AP then 3a, 3

b, 3

c are in

a) AP b) GP c) HP d) AP and HP

9. If y= 2x + c is a tangent to the circle x2+y

2=5 then the value of c is ___________

a) 5 b) 25 c) 5 d) 2

10.

11.

12. The graph of the Linear function is a

1) Straight line 2) point 3) Circle 4) parabola

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13. The range of Signum function is

1) 1,0 2) 1,0 3) 1,0,1 4) 1,1

14. The value of

3

1

1lim

1x

xis

x

1) 3 2) 1 3) 0 4)

15. y= log e(2x+3) then dy

dx at x= 0 is __________ 1) 0 2) log 3 3)

1

3 4)

2

3

16.

If f(x) = ax

2+bx+12 , f

!(2) = 11, f

! (4) =15 then a and b are ______

1) (7,1) b) (1,7) c) (11,15) d) (15,11)

17.

18.

19. In box containing 10 bulbs, 2 are defective. What is the probability that among 5 bulbs chosen at random

none is defective ?

a) 1/5 b) 4/5 c) 2/3 d) ¾

20. If A B then

a) P(A) < P(B) b) P(A) >P(B) c) P(A)P(B) d) P(A)P(B)

PART II

ANSWER ANY 7 QUESTIONS 7 X 2 =14.

QUESTION NUMBER 30 IS COMPULSORY

21. Find the values of x, y ,z if 3 0 7

2 3 3 20

x x y

x z y w

22. Find the unit vectors parallel to the sum of 3 5 8i j k and 2 2j k

23. If 8 7 7

3 2rC C C- = find r

24. If the point P ( 5t-4, t+1 ) lies on the line 7x-4y+1= 0 Find the value of t Find also the co – ordinates of P

25. If A , B, C , D are angles of a cyclic quadrilateral prove that Cos A + Cos B + Cos C + Cos D =0

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26. Solve 1

0 11

xx

x

27. Differentiate 1 1

2

CosxCos

28. Integrate log(tan )

2

xdx

Sin x

29. An integer is chosen at random from the first fifty positive integer. What is the probability that the

integer is a prime (or) multiple of 4.

30.

PART III

ANSWER ANY 7 QUESTIONS 7 X 3 = 21

QUESTION NUMBER 40 IS COMPULSORY

31.

32. Prove the following by the principle of mathematical induction

2+4 +6 +8 ………………….+ 2n = n (n+1) 33. Insert four arithmetic mean -1 and 14

34. The slope of one of the straight lines of ax2+2hxy+by

2=0 thrice that of the other, Show that 3h

2=4ab

35. Prove that Cos 20o Cos 40

o Cos 80

o =

1

8

36. Show that the graph of x2+y

2=4 is not the graph of the function

37.

38. Evaluate : 2

1

6dx

x x

39. A speaks truth in 80% cases and B is 75% cases. In what percentage of cases are they likely to contradict

each other in stating the same fact?

40.

PART IV

ANSWER ALL THE QUESTIONS 7 X 5 = 35

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41.

(OR)

42. If A+B+C=180o Prove that Sin 2A-Sin 2B+Sin 2C = 4 Cos A Sin B Cos C

(OR)

State and prove sine formula

43. The first 3 terms in the expansion of (1-ax)n are 1-14x+84x

2 find a and n

(OR)

If the pth

and qth

terms of a H.P are q and p respectively Show that (pq)th

term is 1

44. Find the circles which cuts orthogonally each of the circles x2+y

2+2x+17y+4=0 , x

2+y

2+7x+6y+11=0 and

x2+y

2-x+22y+3=0

(OR)

Find the co ordinates of the ortho centre of the triangle whose vertices are the points(-2,-1) (6,-1) and (2,5)

45. If x= sin t y = sin pt Show that (1-x2) y2-xy1+p

2y=0

(OR)

Prove that 0

lim 1Sin

46. (OR)

Evaluate 2

3 5

2 3

xdx

x x

47. If x is real , prove that 2 5 9

x

x x is lies between

11

11and

(OR)

A problem in Mathematics is given to three students whose chance of solving it are ½ 1/3 and ¼ (i) What

is the probability that the problem is solved (ii) what is the probability that exactly one of them will solve it.

Send your Answer scripts to the following address: Mr. G NARASIMHAN, (Retired Headmaster) No 40/28 BUDDHAR STREET, East Tambaram, Chennai 59, Cell Number: 9884588989

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