Correct Answer: 280.875

Explanation:

Given Exp. = 8988 x	1	x	1	=	2247	= 280.875
	8		4		8

Correct Answer: 273258

Explanation:

5358 x 51	= 5358 x (50 + 1)
	= 5358 x 50 + 5358 x 1
	= 267900 + 5358
	= 273258.

Correct Answer: 270

Explanation:

Let the smaller number be x . Then larger number = ( x + 1365).

∴ x + 1365 = 6x + 15

⟹ 5x = 1350

⟹ x = 270

∴Smaller number = 270.

Correct Answer: 1951609

Explanation:

1397 x 1397	= (1397)2
	= (1400 - 3)2
	= (1400)2 + (3)2 - (2 x 1400 x 3)
	= 1960000 + 9 - 8400
	= 1960009 - 8400
	= 1951609.

Correct Answer: 2704

Explanation:

Given Exp.	= [(a + b)2 - 4ab], where a = 476 and b = 424
	= [(476 + 424)2 - 4 x 476 x 424]
	= [(900)2 - 807296]
	= 810000 - 807296
	= 2704.

Correct Answer: 140

Explanation:

20 x x = (64 + 36)(64 - 36) = 100 x 28

⟹      x =	100 x 28	= 140
	20

Correct Answer: 6 and 12 both

Explanation:

(6 n ² + 6 n ) = 6 n ( n + 1), which is always divisible by 6 and 12 both, since n ( n + 1) is always even.

Correct Answer: 8

Explanation:

( x ⁿ - 1) will be divisibly by ( x + 1) only when n is even.

(49¹⁵ - 1) = {(7²)¹⁵ - 1} = (7³⁰ - 1), which is divisible by (7 +1), i.e., 8.

Correct Answer: 2

Explanation:

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

Correct Answer: 9240

Explanation:

On dividing we get, 

 88) 9217 (104
        88
        ----
          417
          352
          ----
          65
          ----
  
 Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65.
                            = 9217 + 23
                            = 9240.