Indices and Surds
Question
Q1.
Find m so that (3/4)3 x (9/16) = (3/4)2m + 3
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(3/4)3 x (3/4)2 = (3/4)2m + 3
(3/4)5 = (3/4)2m + 3
5 = 2m + 3
2 = 2m
m = 1
Solution
Q2.
32.31.5.3x = (9)3, find x.
Solution.
32+1.5+x =(32)3
33.5+x = 36
3.5 + x = 6
x = 6 - 3.5 = 2.5
Solution
Q3.
x = 2m , y = 2m+1. find the value of 2x/y
(a) 2 (b) 1 (c) 3 (d) 4
Solution.
2.2m/2m+1 = 2m+1/2m+1 = 1
Solution
Q4.
If 2√80 = 17.89, find the value of 10√5.
Solution.
2√80
2 × 4√5
8√5 = 17.89
√5 = 2.24
10√5 = 10 × 2.24 = 22.4
Solution
Q5.
If x = (3)1/2 + 1/(3)1/2 -1 and y = 1/x so, find (x+y/x-y)2 .
Solution.
(x+y/x-y) = 2/(3)1/2
(x+y/x-y)2 = 4/3
Solution
Q6.
Find remainder when 4y6 - 5y3 - 3 is divided by y3 - 2
Solution.
y3 = x, then x - 2
f(x)= 4x2 - 5x - 3
put, x = 2
f(2)= 4(2)2 - 5(2) - 3
= 3
Solution
Q7.
xm= yn= zp and y4 = x2z3 find n.
Solution.
xm= yn= zp = k (say)
x = k1/m, y = k1/n, z = k1/p
Now, y4 = x2z3
k4/n = k2/m.k3/p
4/n = 2/m + 3/p
4/n = (2p +3m)/mp
n = 4mp/(2p + 3m)
Solution
Q8.
x = 6n, ends with the digit zero, if n is .
Solution.
x = 6n = (3 x 2)n,
→ The only prime factor is 2 , 5 does not occur.
Solution
Q9.
The value of(256)0.16 x (256)0.09 is :.
(a)256.25 (b)64 (c)16 (d)4
Solution.
(256)16/100 x (256)9/100
= (256)25/100
= (256)1/4
= (44)1/4
=(4)4 x 1/4 = 4
Solution
Q10.
Find the value of
a2 + b2 + c2 / bc + ca + ab
, if a + b + c = 0
(a) -2 (b) -3 (c) 2 (d) 3
Solution.
(a) -2
(a + b + c)2 = a2 + b2 + c2 + 2(ab + ac + bc)
Solution
