Kannur University 2006 MATHEMATICS - Question Paper

11 81-E (NS)
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51. 2 circles of radii 6·9 cm and 2·8 cm touch every other externally. Then the distance
ranging from their centres is
(A) 3·45 cm (B) 1·4 cm
(C) 4·1 cm (D) 9·7 cm.
52. 3 circles with centres A, B and C touch every other as shown in the figure. If the
radii of these cirles are eight cm, three cm and two cm respectively, then the perimeter of
? ABC is
B
C
A •
•
•
(A) 13 cm (B) 16 cm
(C) three cm (D) 26 cm.
53. For a circle of radius five cm, 2 tangents PA and PB are drawn from a point P. If
PA = 12 cm and ? PAB = 60°, then the length of AB is
(A) 10 cm (B) 12 cm
(C) 2·5 cm (D) six cm.
54. The formula used to obtain the total surface area of a cone is
(A) 2pr ( r + h ) (B) pr ( r + h )
(C) pr ( r + l ) (D)
13
pr two h.
55. The circumference of a hollow cylindrical pipe is 14 cm and the height is 20 cm. The
lateral surface area of the pipe is
(A) 280 sq.cm (B) 1760 sq.cm
(C) 880 sq.cm (D) 140 sq.cm.
56. The total surface area of a sphere with diameter 14 cm is
(A) 2464 sq.cm (B) 154 sq.cm
(C) 88 sq.cm (D) 616 sq.cm.
81-E (NS) 12
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57. The height of water level in a circular well is seven m and its diameter is 10 m. quantity of
water stored in the well is
(A) 550 cubic m
(B) 70 cubic m
(C) 35 cubic m
(D) 110 cubic m.
58. The number of edges in an octahedron is
(A) eight (B) 6
(C) 12 (D) 14.
59. The provided graph is not traversable because
P
U
Q
R
T
S
V
(A) all the nodes are even nodes
(B) all the nodes are odd nodes
(C) only 2 odd nodes are there
(D) there are more than 2 odd nodes.
60. The number of arcs in the graph for the provided matrix
? ? ? ?
? ? ? ?
0 one 2
1 0 3
2 three 0
is
(A) 12 (B) 6
(C) three (D) 5.

PART – B
61. provided X = { x : x, is a prime number less than 12 } ,
Y = { x : x, is an even number less than 12 }
Z = { x : x, is an odd number less than 12 }
Prove that for the above sets, intersection of sets is associative. 2
81-E (NS) 14
?
62. If A = ?
?
?
? ? ?
1 0
2 3
obtain AA l . 2
63. How many three digit numbers can be formed using the digits 2, 3, 4, five and six without
repetition ? How many of these are even numbers ? 2
OR
A box contains five blue and four red marbles. In how many ways can four marbles be drawn
so as to include two red marbles ?
81-E (NS) 16
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64. If x + y + z = 0, then prove that
x 2
yz +
y 2
xz +
z 2
xy = 3. 2
OR
If a + b + c = 2s, then prove that a two – b two – c two + 2bc = four ( s – b ) ( s – c ).
65. Simplify : 2
2
3 – 2
+
3
3 + 2
.
66. Sailor Shivu, covered a distance of eight km in one hr 40 minutes downstream and returns
to the starting point. If the speed of the stream is two km/hr, obtain the speed of the
boat in still water. 2
67. Draw the graph of y = x two . 2
68. 21 lead marbles of even size are recast to form a big sphere. obtain the quantity of the
big sphere if the radius of every marble is two cm. 2
21 81-E (NS)
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69. compute the area of the field shown in the diagram ( measurements are in metres ).
2
C
A
D E
B
Q
P
50
60
40
55
70
65
?
70. Verify Euler’s formula for a triangle based prism. 2
71. provided series four + 12 + 36 + …… , obtain S three : S six . 3
OR
In an A.P. if T n = 4n + 3, obtain S 15 .
72. The H.C.F. and L.C.M. of 2 algebraic expressions are ( a – three ) and
( a three – 5a two – 2a + 24 ) respectively. If 1 of the expressions is ( a two – 7a + 12 ) ,
obtain the other expression. 3
73. In a circle of radius 2·5 cm draw 2 radii such that the angle ranging from them is 60°.
Draw 2 tangents at the ends of the radii. 3
74. 2 circles of radii 3·5 cm and 1·5 cm, have their centres nine cm apart. Draw a
transverse common tangent to the circles and measure the length. 3
75. The distribution of ages ( in years ) of 20 persons in a locality is recorded as follows :
Age ( in years ) 30 – 34 35 – 39 40 – 44 45 – 49 50 – 54
Number of persons two five six five 2
compute (i) the avg. (ii) standard deviation of the distribution of the above data.
76. State the Pythagoras theorem and prove it. 4

Earning:   Approval pending.