16
P
,
R
and
S
lie on a circle centre
O
as shown
above, while
Q
lies outside the circle. Find
<
PSO
.
A. 40
0
B. 45
0
C. 55
0
D. 35
0
21.
The shadow of a pole 5
.
3 m
high is 5m.
Find the angle of elevation of the sun.
A. 60
0
B. 75
0
C. 45
0
D. 30
0
22.
An arc of a circle of length 22cm subtends
an angle of 3x
0
at the centre of the circle.
Find the value of x if the diameter of the
circle is 14cm.
A. 180
0
B. 1
20
0
C. 60
0
D. 30
0
23.
(2, 0)
(0, 6)
(0, 0)
x
y
The shaded area in the diagram above is
represented by
A.
{(x, y): y + 3x <
-
6}
B. {(x, y): y
3x < 6}
C.
{(x, y): y
3x <
-
6}
D. {(x, y): y + 3x < 6}
24.
Find the values of x
where the curve
y = x
3
+ 2x
2
5x
6 crosses the x
-
axis.
A. 2,
-
1 and
3
B. 2, 1 and 3
C.
2,
-
1 and 3
D.
2, 1 and
3
25.
Find the sum to infinity of the series
...
,
,
,
18
1
6
1
2
1
A.
3
2
B. 1
C.
3
1
D.
4
3
26.
The length L of a simple pendulum varies
directly as the square of its period T. If a
pendulum with period 4sec. is 64cm long,
find the length of a pendulum whose period
is 9 sec.
A. 96cm
B.
36cm
C. 324cm
D. 144cm
27.
What are the integral values of x which
satisfy the inequality
1 < 3
2x
.
5.
A. 0, 1, 2
B.
1, 0, 1
C.
2, 1, 0,
-
1
D.
1, 0, 1, 2
28.
Find the remainder when
3x
3
+ 5x
2
11x + 4 is divided by x + 3.
A. 1
B.
4
C. 4
D.
1
29.
If the operation
*
on the set of integers is
defined by p
*
q =
,
pq
find the value of
4
*
(8
*
32).
A. 3 B. 16
C. 8
D. 4
30.
Given that the first and
fourth terms of a
G.P. are 6 and 162 respectively, find the
sum of the first three terms of the
progression.
A. 48 B. 78
C. 27
D. 8
31.
Factorize completely ac
2bc
a
2
+ 4b
2
.
A.
(a
2b)(c
a + 2b)
B. (a
2b)(c + a + 2b)
C.
(a
2b)(c + a
-
2b)
D. (a
2b)(c
a
-
2b)
32.
The inverse of the matrix
.
.
.
.
.
.
.
.
1
1
1
2
is
A.
.
.
.
.
.
.
.
.
.
.
2
1
1
1
B.
.
.
.
.
.
.
.
.
2
1
1
1
C.
.
.
.
.
.
.
.
.
.
2
1
1
1
D.
.
.
.
.
.
.
.
.
.
2
1
1
1
33.
y is inversely
proportional to x and y = 4
when x = ½ . Find x when y = 10.
A. 2 B. 10 C.
10
1
D.
5
1
34.
The nth terms of two sequences are Q
n
=
3.2
n
-
2
and U
m
= 3.2
2m
-
3
. Find the product of
Q
2
and U
2
.
A. 12 B. 18 C. 6 D. 3
35.
If P =
.
.
.
.
.
.
.
.
.
.
.
.
1
0
1
5
4
3
1
0
1
, then |P| is