Surds And Indices

Question:
If 3(x – y) = 27 and 3(x + y) = 243, then x is equal to:

[A].

0

[B].

2

[C].

4

[D].

6

Answer: Option C

Explanation:

3x – y = 27 = 33       x – y = 3 ….(i)

3x + y = 243 = 35       x + y = 5 ….(ii)

On solving (i) and (ii), we get x = 4.

Question:
If m and n are whole numbers such that mn = 121, the value of (m – 1)n + 1 is:

[A].

1

[B].

10

[C].

121

[D].

1000

Answer: Option D

Explanation:

We know that 112 = 121.

Putting m = 11 and n = 2, we get:

(m – 1)n + 1 = (11 – 1)(2 + 1) = 103 = 1000.

Question:
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:

[A].

1.45

[B].

1.88

[C].

2.9

[D].

3.7

Answer: Option C

Explanation:

xz = y2       10(0.48z) = 10(2 x 0.70) = 101.40

0.48z = 1.40

z =	140	=	35	= 2.9 (approx.)
	48		12

Question:
If 5a = 3125, then the value of 5(a – 3) is:

[A].

25

[B].

125

[C].

625

[D].

1625

Answer: Option A

Explanation:

5a = 3125       5a = 55

a = 5.

5(a – 3) = 5(5 – 3) = 52 = 25.

Question: (25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
[A].

8.5

[B].

13

[C].

16

[D].

17.5

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.

Question: (17)3.5 x (17)? = 178
[A].

2.29

[B].

2.75

[C].

4.25

[D].

4.5

Answer: Option D

Explanation:

Let (17)3.5 x (17)x = 178.

Then, (17)3.5 + x = 178.

3.5 + x = 8

x = (8 – 3.5)

x = 4.5

Question:
(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.

Question:
(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

Question: 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.