If	❨	a	❩	x - 1	=	❨	b	❩	x - 3	, then the value of x is:
		b					a

Correct Answer: 2.9

Explanation:

x ^z = y ²    ⟺    10 ^(0.48z) = 10 ^{(2 x 0.70)} = 10 ^1.40

⟹ 0.48z = 1.40

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

Correct Answer: 1000

Explanation:

We know that 11 ² = 121.

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

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

Correct Answer: 1

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.

Correct Answer: 13

Explanation:

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

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

⟹ 5^x = 5^{(15 + 2.5 - 4.5)}

⟹ 5^x = 5¹³

∴ x = 13.

Correct Answer: 4

Explanation:

3 ^{x - y} = 27 = 3 ³    ⟺    x - y = 3 ....(i)

3^{x + y} = 243 = 3⁵    ⟺    x + y = 5 ....(ii)

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

Correct Answer: 9

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.

Correct Answer: 1

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.

Correct Answer: 10000

Explanation:

(10)150 ÷ (10)146 =	10150
	10146

   = 10^{150 - 146}

   = 10⁴

   = 10000.

Correct Answer: 25

Explanation:

5 ^a = 3125    ⟺    5 ^a = 5 ⁵

⟹ a = 5.

∴ 5^{(a - 3)} = 5^{(5 - 3)} = 5² = 25.

Correct Answer: 1

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.