Aptitude - Surds and Indices

Answer: Option B

Explanation:

Given Expression	= (243)(n/5) x 32n + 1 9n x 3n - 1
	= (35)(n/5) x 32n + 1 (32)n x 3n - 1
	= (35 x (n/5) x 32n + 1) (32n x 3n - 1)
	= 3n x 32n + 1 32n x 3n - 1
	= 3(n + 2n + 1) 3(2n + n - 1)
	= 33n + 1 33n - 1
	= 3(3n + 1 - 3n + 1)   = 32   = 9.

Answer: Option B

Explanation:

1	+	1	=	1  +  1 1 + an am 1 + am an
1 + a(n - m)		1 + a(m - n)

=	am	+	an
	(am + an)		(am + an)

=	(am + an)
	(am + an)

   = 1.

Answer: Option E

Explanation:

We know that 11² = 121.

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

(m - 1)^{n + 1} = (11 - 1)^{(2 + 1)} = 10³ = 1000.

Answer: Option B

Explanation:

Given Exp.	= x(b - c)(b + c - a) . x(c - a)(c + a - b) . x(a - b)(a + b - c)
	= x(b - c)(b + c) - a(b - c)  .  x(c - a)(c + a) - b(c - a)    .  x(a - b)(a + b) - c(a - b)
	= x(b2 - c2 + c2 - a2 + a2 - b2)  .   x-a(b - c) - b(c - a) - c(a - b)
	= (x0 x x0)
	= (1 x 1) = 1.

Answer: Option E

Explanation:

	x	-	1		2	= x +	1	- 2
			x				x

= (3 + 22) +	1	- 2
	(3 + 22)

= (3 + 22) +	1	x	(3 - 22)	- 2
	(3 + 22)		(3 - 22)

   = (3 + 22) + (3 - 22) - 2

   = 4.

		x	-	1		= 2.
				x