ST. BRITTO’S MATRICULATION HIGHER SECONDARY SCHOOL
ADAMBAKKAM – 88
PRE-HALF YEARLY EXAMINATIONS - I
MATHEMATICS
STD : X
2015
TIME:2 ½ HR
MARKS : 100
I. Choose the correct answer:15 x 1 = 15
1 . Matrix A = [aij]m x n is a square matrix if
(a) m < n
(b) m > n
(c) m = 1
(d) m = n
8 4
2 1
2 . If
= 4
then the value of x is
𝑥 8
1 2
(a) 1
(b) 2
(c) ¼
(d) 4
3. A is of order m x n and B is of order p x q, addition of A and B is possible only if
(a) m = p
(b) n = q
(c) n = p
(d) m = p, n = q
4. In ∆ ABC, DE is || to BC, meeting AB and AC at D and E. If AD = 3cm, DB = 2cm and
AE = 2.7 cm, then AC is equal to
(a) 6.5cm
(b) 4.5cm
(c) 3.5cm
(d) 5.5cm
5. The sides of two similar triangles are in the ratio 2 : 3 ,then their areas are in the ratio
(a) 9 : 4
(b) 4 : 9
(c) 2 : 3
(d) 3 : 2
6. The perimeter of two similar triangle ∆ ABC and ∆ DEF are 36cm and 24 cm
respectively.If DE = 10cm, then AB is
(a) 12cm
(b) 20cm
(c) 15cm
(d) 18cm
7. The CSA of a right circular cylinder of radius 1cm and height 1cm is equal to
(a) πcm2
(b) 2πcm2
(c) 3πcm2
(d) 2cm2
8. If the radius of a sphere is 2cm, then the CSA of the sphere is equal to
(a) 8πcm2
(b) 16cm2
(c) 12cm2
(d) 165cm2
2
9. If the surface area of a sphere is 100π cm , then its radius is equal to
(a) 25cm
(b) 100cm
(c) 5cm
(d) 10cm
10. The range of first 10 prime numbers 2,3,5,7,11,13,19,23,29 is
(a) 28
(b) 26
(c) 29
(d) 27
11. For any collection of n items, Σ (x – x) =
(a) Σx
(b) x
(c) nx
(d) 0
12. For a collection of 11 items, Σx = 132, then the arithmetic mean is
(a) 11
(b)12
(c) 14
(d) 13
13. Varience of the 10,10,10,10,10 is
(a) 10
(b) √10
(c) 5
(d) 0
14. If S is the sample space of a random experiment then p(s) =
(a) 0
(b) 1/8
(c) ½
(d) 1
15. The probability that a non- leap year will have 53 Sundays and 53 Monday is
(a) 1/7
(b) 2/7
(c) 3/7
(d) 0
II
Answer any 10 only:10 x 2 = 20
16. Construct 2 x 2 matric A – [aij] whose elements are given by aij = ( 2i – j)
1 2
3
17. If A = 2 4 −5 then verify that (AT)T = A
3 −5 6
3 2
8 −1
18. If A =
and B =
find the matrix c, if C = 2A + B
5 1
4 3
19. E and F are points on the sides PQ and PR respectively of a ∆ PQR. For PE = 4cm,
QE =4.5cm, PF = 8cm, RF = 9cm.
20. AB and CD are two chords of a circle which intersects each other internally at p, if
CP = 4cm, AP = 8cm, PB = 2cm , then find PD.
21. If the CSA of a solid hemisphere is 2772sqcm,then find the total surface area.
22. Volume of a solid cylinder is 62.37cu.cm. find the radius of its height is 4.5cm.
23. The outer and the inner radii of a hollow sphere are 12cm and 10cm. find its volume.
24. Find the standard deviation of the first 10 natural numbers.
25. If the coefficient of variation of a collection of data is 57 and its SD is 6.84,then find
The mean.
26. If A is an event of a random experiment such that P(A) : P(A) = 7 : 12 then find P(A)
27. The coins are tossed together. What is the probability of getting at most one hand.
28. A box contains 4 green, 5 blue and 3 red balls. A ball is drawn at random. Find the
Probability that the selected ball is (i) red in colour (ii) not green in colour.
2
29. If A and B are two events such that P(A) = ¼, P(B) = 5 and P(AUB) = ½, then find
P(A∩ 𝐵)
30. The radii of two right circular cylinders are in the ratio 3 : 2 and their heights are in
the ratio 5 : 3, find the ratio of their C.S.A.
(OR)
𝑦
6−2𝑥
Solve
x 31+4𝑦
3𝑥
Page-2III
Answer the following questions: ( any 9 only)
31. Find X and Y if 2X + 3Y = 2 3 and 3X + 2Y = 2
4 0
-1
32. If A ==
1
2
−1
3
9 x 5 = 45
-2
5
then show that A2 – 4A + 5I = 0
1
−4
−1 6
and B =
, then prove that (A + B)2 ≠ A2 + 2AB + B2.
−2 3
3 −2
34. A circle touches ∆ at P, AB and AC produced at Q and R respectively.Prove that
AQ = AR = ½ (perimeter of ∆ ABC)
35. A point O in the interior of a rectangle ABCD is joined to each of the vertices A,B,C
and D. Prove that OA2 + OC2 = OB2 + OD2
36. State and prove the BPT (thales) theorem.
37. The outer curved surface area of a holl. cylinder is 540 π sq.cm.Its internal iameter
Is 16 cm and height is 15 cm find the Total surface area .
38. The radius and height of a right cone are in the ratio 2 : 3 find the slant height if its
volume is 100.48cu.cm. (take π = 3.14)
39. A capsule is the shape of cylinder with two hemispheres stuck to each to its ends. If
The length of the entire capsule is 14mm and the diameter of the capsule is 5mm, find
its surface area.
40. An iron right circular cone of diameter 8cm and height 12cm is melted and recast into
spherical lead shots of radius 4mm. how many lead shots can be made?
41. Following are the runs scored by two batsman in 5 cricket matches.who is more
Consistant In scoring runs.
Batsman A
38
47
34
18
33
Batsman B
37
35
41
27
35
42. Given ∑x = 99, n= 9 and ∑(x – 10)2 = 79.Find ∑x2 and ∑(x – x)2
43. Three coins are tossed simultaneously. Find the probability of getting (i) at least one
had (ii) exactly two tails (iii) at least two hands.
44. A card us drawn at random from a well-shuffled deck of 52 cards. Find the
probability that It will be a spade or a king.
33. If A =
45. A bag contains 50 bolts and 150 nuts.Half of the bolts and half of the nuts are rusted.If an
Item is chosen at random,find the probability that it is rusted or that it it is a bolt.
(OR)
4 1 2
2 0 4
1 2 −3
If A =
1 −2 3 , B = 6 2 8 and C = 5 0
2
0 3 2
2 4 6
1 −1 1
then verify that A + (B+C) = (A + B) + C
IV
Answer any 2 for the following question:2 x 10 = 20
46(a) Draw the two tangents from a point which is 10cm away from a centre of a circle
of radius 6cm. also measure th lengths f th tangents.
(OR)
(b) Construct ∆ ABC in which the base BC = 5cm, A = 45o and the median from
A to BC is 4cm.
47 (a) Solve graphically
x2 -3 x – 10 = 0
(b) Draw the graph of y = x2 - x – 8 and hence find the roots of x2 –2 x – 15 = 0
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