surds and indices aptitude questions

6.

(256)^0.16 x (256)^0.09 = ?

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

Answer & Explanation

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)

= 4^4(1/4)

= 4¹

= 4

7.

The value of [(10)¹⁵⁰ ÷ (10)¹⁴⁶]

A.	1000	B.	10000
C.	100000	D.	10⁶

Answer & Explanation

Answer: Option B

Explanation:

(10)¹⁵⁰ ÷ (10)¹⁴⁶ =	10¹⁵⁰
	10¹⁴⁶

= 10^{150 – 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.	x^{a – b – c}	D.	None of these

Answer & Explanation

Answer: Option B

Explanation:

Given Exp. =

1

+

1

+

1

	1 +	x^b	+	x^c
		x^a		x^a

	1 +	x^a	+	x^c
		x^b		x^b

	1 +	x^b	+	x^a
		x^c		x^c

=	x^a	+	x^b	+	x^c
	(x^a + x^b + x^c)		(x^a + x^b + x^c)		(x^a + x^b + x^c)

=	(x^a + x^b + x^c)
	(x^a + x^b + x^c)

= 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 & Explanation

Answer: Option B

Explanation:

Let (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x.

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

	5^{(2 x 7.5)} x 5^2.5	= 5x
	5^{(3 x 1.5)}

	5¹⁵ x 5^2.5	= 5^x
	5^4.5

5^x = 5^{(15 + 2.5 – 4.5)}

5^x = 5¹³

x = 13.

10.

(0.04)^-1.5 = ?

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

Answer & Explanation

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.

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