TN 11th Model Question Paper Maths

HIGHER SECONDARY IST YEAR

MATHEMATICS
MODEL QUESTION PAPER
TIME:2 ½ HOURS www.tnschools.co.in Max.Marks:90
PART-I

All questions are compulsory.
Choose the correct answer.

1. Number of elements in a matrix of order 2x3 is
(a) 5 (b) 2 (c) 3 (d) 6

2. If A is a square matrix of order 4 then � is
(a) � (b)K2 (c)K3 (d)K4

3. If “G” is centroid of the triagle ABC and „O‟ is any other point then
� + � + � = is equal to
(a) � (b) �� (c) 3 �� (d)4 ��

4. If =2 − and = - then the magnitude of - is
(a) 1 (b)9 (c)3 (d) 3

5. A polygon has 44 diagonals, then the number of its sides is
(a) 11 (b)7 (c)8 (d)12
6.
3 +7 _ 10
� =
then A is
−1 ( −2) −2 −1
(a)13 (b)-13 (c)-10 (d) 10

7. The A.M., G.M., H.M., between two positive numbers a and b are
equal then
(a) a=b (b)ab=1 (c)a > b (d) a < b

8. If an = n2 3 –n then the third term is
1 1
(a) (b) 1 (c) (d) 3
9 3

9. If the pair of straight lines given by ax2+2hxy+by2=0 are perpendicular,
then
(a) ab=0 (b) a+b=0 (c) a-b=0 (d) a=0

10. The radius of the circle x2+y2-2x+4y-4=0 is
(a) 1 (b) 2 (c) 3 (d) 4

11. If cos �=0 then � is
�
(a)n  (b) (2n+1) (c)−  (d) -n 
2

12. If the terminal side is collinear with the initial side in the opposite
direction, then the angle included is
(a) 0 ° (b) 90° (c)180° (d)270°

13. The range of the function logex is
(a) (0, ∞) (b) (-∞, ∞) (c) (-∞, 0) (d) [0, ∞ )

14. The value of 3.5 is
(a) 2 (b) 3 (c) 4 (d) 5

15. ( ) is
1 1 1 1
(a) (b) (c) (d)
2 2 2

16.
lim 3
1+ is
→∞
(a) e (b) ex (c) e3 (d) ∞

17. log = is
1 (log )2
(a) +c (b) +C (c ) x log + + (d) x log − +
2

18. 2
sin 3 ( ) is

(a) e2x (2sin 3x - 3 cos 3x)+c (b) e2x (3sin 2x - 2 cos 2x)+c
13 13
2x
(c) e (2sin 3x + 3 cos 3x)+c (d) e2x (3cos 3x + 2 sin 3x)+c
13 13

19. If two events A and B are independent then P(A/B)= ------------
(a) P(A) (b) P(AՈB) (c) P(A)=P(B) (d) P(A)
P(B)
20. X speaks truth in 95 percent of cases and Y in 80 percent of cases.
The percentage of cases they likely to contradict each other in stating
same fact is
(a) 14% (b) 86% (c) 23% (d) 85.5%
PART - II
Answer any SEVEN questions. 7 x 2 = 14
Question 30 is compulsory.
2
21.
a1 b1 = a12+a22 a1 b1+ a2 b2
Prove that a2 b2 a1 b1+ a2 b2 b12 + b22

22. If ABC and A′B′C′ are two triangles and G, G′ be their corresponding
centroids, prove that ′+ ′+ ′=3 ��′

23. If 10Pr = 5040, find the value of r.

24. A point moves so that it is always at a distance of 6 units from the point
(1, -4). Find its locus.

25. Simplify : Cos (-870°)

26. If f,g : R R, defined by f(x)=x+1 and g(x)=x2 then find (fog) (3)

27. Find d2y if y=x3-6x2+7x+6
dx2

28. 2
Evaluate :

29. Three coins are tossed once. Find the probability of getting atleast two
heads.
30. 1 1 1
2 −1 + + …………
11 31 51
show that 2 +1 = 1 1
1+ + …………….
21 41

PART III

Answer any SEVEN questions. 7x3=21
Question 40 is compulsory.

31. Prove that the sum of the vectors directed from the vertices to the mid-
point opposite sides of a triangle is zero.

32. Find the co – efficient of x5 in the expansion of
1
+ 3 2

33. Find 5 geometric means between 576 and 9.

34. The slope of one of the straight lines ax2+2hxy+by2=0 is twice that of
the other, show that 8h2=9ab.

35. Show that : Sin20o Sin40° Sin 80° =
3
8

36. −1
Let f: RR be defined by f (x) = 3x+2 find and show that
−1 −1
fo = of=I.

37. Evaluate : Lim 1+ – 1−
x 0 Sin-1 x
38. Integrate : (3 + 4) 3 + 7 dx

39. Two cards are drawn from a pack of 52 cards in succession. Find the
probability that both are kings when,
(i) The first drawn card is replaced
(ii) The card is not replaced.

40. 3 −2
Find k so that A2 = KA – 2I where A =
4 −2

PART -IV

Answer all the question : 7x5=35
41. Using factor theorem prove that
(b+c)2 a2 a2
b2 (c+a)2 b2 =
2abc (a+b+c)3
c2 c2 (a+b)2

(Or)

Examine whether the vectors +3 + , 2 – - and 7 +5 are
coplanar.

42. If A + B = 45°, show that (1 + tanA) (1 + tanB) = 2 and hence deduce
1
the value of tan 22 °
2
(Or)

State and prove Napier‟s formulae.

43. Prove by Mathematical Induction
12+22+32+.........................................+n2 = n(n+1) (2n+1) ,for all n∈N
6
(Or)

+ +
If a,b,c are in H.P. Prove that + =2
− −

44. Find the equation of the circle passing through the points (1,1), (2,-1)
and (3,2).
(Or)
Find the co-ordinates of orthocentre of the triangle formed by the
straight lines x – y – 5 = 0, 2x – y – 8 = 0 and 3x – y – 9 = 0

2
45. If y = cos (sinx), Prove that + + 2
=0
2
(OR)

∆
For < 1 and for any rational index n, prove that

lim −
=na n-1 (aǂ 0)
→ −

46. 2
Evaluate the definite integral as limit of sum
1
2 +5

(OR)

Evaluate
3 +1
2 2 + +3

47. 1
If x is real, prove that the range of f(x) = x2-2x+4 is between [ , 3]
3
x2+2x+4
(OR)

In a bolt factory machines A1, A2, A3 manufacture respectively 25%,
35% and 40% of the total output of these 5, 4, 2 percent are defective
bolts. A bolt is drawn at random from the product and is found to be
defective. What is the probability that it was manufactured by machine
A2?

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