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SURDS AND INDICES PROBLEMS

Aptitude

SURDS AND INDICES -> IMPORTANT FACTS AND FORMULAE

1. LAWS OF INDICES :
  (i) am * an = am + n
  (ii)  am / an = am - n
  (iii)  (am)n = amn
  (iv)  (ab)n = anbn
  (v)  (a/b)n = an/ bn
  (vi)  a0 = 1
2. SURDS : Let a be rational number and n be a positive integer such
that a(1/n) = n√a
3 LAWS OF SURDS :
  (i)  n√a = a (1/n)
  (ii)  n√ab = n√a x n√b
  (iii)  n√a/b = n√a / n√b
  (iv)  (n√a)n = a

SURDS AND INDICES -> EXAMPLES

1. What is the quotient when (x-1 - 1) is divided by (x - 1)?
  Sol. x-1 - 1 / x-1 - (1/x)-1 / x-1 = (1-x)/x =(1-x)/x * 1/(x-1) = -1/x.
Hence, the required quotient is - 1/x
2. If 2x-1 + 2x+1 = 1280, then find the value of x
  Sol. 2x-1 + 2x+1 = 1280 ⇔ 2x-1(1+2x) = 1280
⇔ 2x-1 = 1280/5 = 256 = 28 ⇔ x-1 = 8 ⇔ x = 9.
Hence, x = 9.
3. If [1/5]3y = 0.008, then find the value of (0.25)y
  Sol. [1/5]3y = 0.008 = 8/1000 = 1/125 = [1/5]3 ⇔ 3y = 3 ⇔ y = 1.
∴ (0.25)y = (0.25)1 = 0.25.
Hence, the required distance is 6 km.

SURDS AND INDICES -> EXERCISE

10. If m and n are whole numbers such that mn = 121, then the value of (m-1)n+1 is:
 
  • A. 10
  • B. 100
  • C. 121
  • D. 1000
Ans: D.
Sol.
We know that 112 =121. Putting m = 11 and n = 2, we get :
(m - 1)n+1 = (11 - 1)(2+1) 103 = 1000.
 
11. If 2x = 3√32, then x is equal to :
 
  • A. 3/5
  • B. 5/3
  • C. 15
  • D. 25
Ans: B.
Sol.
2x = 3√32 ⇔ 2x = (32)1/3 = (25)1/3 = 25/3 ⇔ x = 5/3.
 
 
12. The value of (8-25 -8-26) is
 
  • A. 7 * 8-25
  • B. 7 * 8-26
  • C. 8 * 8-25
  • D. 8 * 8-26
Ans: B.
Sol.
8-25 -8-26 = [1/8-25 - 1/8-26] = 7 * 8-26.