Aptitude - Surds and Indices

Exercise :: Surds and Indices - General Questions

6. 

(256)0.16 x (256)0.09 = ?

A. 4
B. 16
C. 64
D. 256.25

Answer: Option A

Explanation:

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)

   = (256)0.25

   = (256)(25/100)

   = (256)(1/4)

   = (44)(1/4)

   = 44(1/4)

   = 41

   = 4


7. 

The value of [(10)150 ÷ (10)146]

A. 1000
B. 10000
C. 100000
D. 106

Answer: Option B

Explanation:

(10)150 ÷ (10)146 = 10150
10146

   = 10150 - 146

   = 104

   = 10000.


8. 

1  + 1 + 1 = ?
1 + x(b - a) + x(c - a) 1 + x(a - b) + x(c - b) 1 + x(b - c) + x(a - c)

A. 0
B. 1
C. xa - b - c
D. None of these

Answer: Option B

Explanation:

Given Exp. =
1  +  1  +  1
1 + xb + xc
xa xa
1 + xa + xc
xb xb
1 + xb + xa
xc xc

   = xa + xb + xc
(xa + xb + xc) (xa + xb + xc) (xa + xb + xc)

   = (xa + xb + xc)
(xa + xb + xc)

   = 1.


9. 

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

A. 8.5
B. 13
C. 16
D. 17.5
E. None of these

Answer: Option B

Explanation:

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.

Then, (52)7.5 x (5)2.5 = 5x
(53)1.5

5(2 x 7.5) x 52.5 = 5x
5(3 x 1.5)

515 x 52.5 = 5x
54.5

5x = 5(15 + 2.5 - 4.5)

5x = 513

x = 13.


10. 

(0.04)-1.5 = ?

A. 25
B. 125
C. 250
D. 625

Answer: Option B

Explanation:

(0.04)-1.5 = 4 -1.5
100

   = 1 -(3/2)
25

   = (25)(3/2)

   = (52)(3/2)

   = (5)2 x (3/2)

   = 53

   = 125.