What should come in place of x in the following equation? x 128 = 162 x

Correct Answer: 42

Explanation:

$$\begin{gathered} G i v e n x × y = x + y + x y \\ H e r e x = 6 , y = 24 \\ T h e n , \\ x × y = 6 + 24 + 6 x 24 \\ 6 x 24 = 30 + 144 \\ = 30 + 12 \\ = 42 . \end{gathered}$$

Correct Answer: 3

Explanation:

Given    1 . 21 x 0 . 9 1 . 1 x 0 . 11

 

=  1 . 21 x 100 x 0 . 9 x 10 1 . 1 x 10 x 0 . 11 x 100

 

=  9

 

= 3.

Correct Answer: 676

Explanation:

L e t 28 x + 1426 = 3 × 718

 

Then  28 x = 2154 - 1426 

 

? 28 x = 728 ? x = 26

 

? x = 676

Correct Answer: 2

Explanation:

Given that  x = 2 + 2 2 3 + 2 1 3

 

So x - 2 =  2 2 3 + 2 1 3

 

Now cubing on both sides, we get

 

 

=>  x 3 - 8 - 6 x 2 + 12 x = 4 + 2 + 6 ( x - 2 )

 

Therefore,  x 3 - 6 x 2 + 6 x = - 6 + 8 = 2

 

 

Correct Answer: 87

Explanation:

4 b = 6 c ? b = 3 2 c a n d 3 a = 4 b ? a = 4 3 b = 4 3 ( 3 2 c ) = 2 c 

a + b + c = 27 29 ? 2 c + 3 2 c + c = 27 29 ? c = 6 29

 

  ? a 2 + b 2 + c 2 = ( a + b + b ) 2 - 2 ( a b + b c + c a ) 

 

= ( 27 29 ) 2 - 2 2 c × 3 2 c + 3 2 c × c + c × 2 c 

 

  = 729 × 29 - 2 × 13 2 c 2

= 87

Correct Answer: 6

Explanation:

0 . 204 × 42 0 . 07 × 3 . 4 = 8568 238 = 36 = 6

Correct Answer: 2

Explanation:

( 0 . 75 ) 3 1 - 0 . 75 + 0 . 75 + ( 0 . 75 ) 2 + 1 = ( 0 . 75 ) 3 + ( 1 - 0 . 75 ) ( 1 ) 2 + ( 0 . 75 ) 2 + 1 × 0 . 75 1 - 0 . 75 

 

 

=  ( 0 . 75 ) 3 + ( 1 ) 3 - ( 0 . 75 ) 3 1 - 0 . 75 = 1 0 . 25 = 4 = 2

Correct Answer: 4/3

Explanation:

By simplifying, we get 4/3

Correct Answer: 5sqrt{3}

Explanation:

Given Exp =  3 2 6 - 3 × 6 + 3 6 + 3 - 4 3 6 - 2 × 6 + 2 6 + 2 - 6 2 2 - 3

 

=  3 2 ( 6 + 3 ) 6 - 3 - 4 3 ( 6 + 2 ) 6 - 2 + 3 3 - 2 × 3 + 2 3 + 2

 

=  2 6 + 3 - 3 6 + 2 + 3 3 + 2

 

=  12 + 6 - 18 - 6 + 3 3 + 3 2

 

= 5 3 

Correct Answer: 81

Explanation:

729 = 9 x 9 x 9

=> Cube root of 729 = 9

 

Now, required square of 9 = 9 x 9 = 81.