(25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^?

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: Rs. 240

Explanation:

Let C's share = Rs. x

Then, B's share = Rs.	x	,   A's share = Rs.	❨	2	x	x	❩	= Rs.	x
	4			3		4			6

∴	x	+	x	+ x = 1360
	6		4

⟹	17x	= 1360
	12

⟹ x =	1360 x 12	= Rs. 960
	17

Hence, B's share = Rs.	❨	960	❩	= Rs. 240.
		4

Correct Answer: Rs. 2400

Explanation:

Let the price of a saree and a shirt be Rs. x and Rs. y respectively.

Then, 2x + 4y = 1600 .... (i)

    and x + 6y = 1600 .... (ii)

Divide equation (i) by 2, we get the below equation. 

=> x +  2y =  800. --- (iii)

Now subtract (iii) from (ii)

 x +  6y = 1600  (-)
 x +  2y =  800  
----------------
      4y =  800
----------------

Therefore, y = 200.

Now apply value of y in (iii)

=>  x + 2 x 200 = 800

=>  x + 400 = 800

Therefore x = 400

Solving (i) and (ii) we get x = 400, y = 200.

∴ Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.

Correct Answer: 62.5

Explanation:

Let the capacity of 1 bucket = x

Then, the capacity of tank = 25x.

New capacity of bucket =	2	x
	5

∴ Required number of buckets =	25x
	(2x/5)

=	❨ 25x	x	5	❩
			2x

=	125
	2

= 62.5

Correct Answer: 26

Explanation:

Let the number of hens be x and the number of cows be y

Then, x + y = 48 .... (i)

  and 2x + 4y = 140   ⟹   x + 2y = 70 .... (ii)

Solving (i) and (ii) we get: x = 26, y = 22.

∴ The required answer = 26.

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: 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: 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: 2

Explanation:

Given ❨	a	❩	x - 1	=	❨	b	❩	x - 3
	b					a

⟹

❨

a

❩

x - 1

=

❨

a

❩

-(x - 3)

=

❨

a

❩

(3 - x)

b

b

b

⟹ x - 1 = 3 - x

⟹ 2x = 4

⟹ x = 2.

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.