Q1.
Find the value of
4x0 - 1 /x0 - 2
(a) -3 (b) -2 (c) 3 (d) 1
Solution.
x
0 = 1
4(1) - 1/1 - 2
= 3/-1 = -3
Solution
Q2.
Find the value
(243)n/5 . 32n + 1/9n . 3n -1
(a) 12 (b) 2 (c) 3 (d) 9
Solution.
(35)n/5 . 32n + 1/32n . 3n -1
=
3n . 32n + 1/33n -1
=
33n + 1/33n -1
= 3
3n + 1 . 3
-3n + 1 = 3
2 = 9
Solution
Q3.
If 2x - 2(x -1) = 8, find xx
(a) 144 (b) 196 (c) 256 (d) 306
Solution.
2x - 2x/2 = 8
2x (1 - 1/2) = 8
2x = 16
2x = 24
x = 4
Solution
Q4.
If xy = 25, find the value of (x - 1)y
(a) 3 (b) 4 (c) 2 (d) 8
Solution.
52 = 25
x = 5, y = 2
(5 - 1)2 - 1
41 = 4
Solution
Q5.
If 2x + 4 - 2x + 2 = 6 , find x
(a) -2 (b) -1 (c) 1 (d) 2
Solution.
2x (24 - 22) = 3
2x (12) = 6
2x = 1/2
2x = 2-1
x = -1
Solution
Q6.
If ax = b, by = c , cz = a, find the value of (xyz)2
(a) 4 (b) 1 (c) 2 (d) 3
Solution.
cz = a,
byz = a
axyz = a
xyz = 1
Solution
Q7.
If 2x = 3y = 6-z, then find the value of(1/x + 1/y + 1/z)2
(a) 3 (b) 1 (c) 0 (d) 4
Solution.
(c) 0
Solution
Q8.
If a = x1/3 + x-1/3, find a3 - 3a
(a) (x2 + 1)/x (b) (x - 1)/x
(c) x (d) 1
Solution.
(a) (x2 + 1)/x
a3 = (x1/3 + x-1/3)3
∴ (a + b)3 = a3 + b3 + 3ab(a + b)
Solution
Q9.
If (100)9 ÷ 1015 = x, find x .
(a) 1 (b) 10 (c) 1000 (d) 100
Solution.
1018 ÷ 1015 = 103 = 1000
Solution
Q10.
If (a/b)x - 1 = (b/a)x - 3, find x
(a) 9 (b) 8 (c) 2 (d) 4
Solution.
(a/b)x - 1 = (a/b)3 - x
x - 1 = 3 - x
2x = 4
x = -2
Solution
