[( 3.242 x 14 ) / 100] =?

Correct Answer: 7.43673

Explanation:

For the product of 3.5413 x 2.1
Consider 35413 x 21 = 743673
Total decimal places = 4 + 1
? 3.5413 x 2.1=7.43673

Correct Answer: 60.658

Explanation:

51.300 + 7.078 + 1.380 + 0.900 = 60.658

Correct Answer: 2b/a

Explanation:

Given in question,
x + a/x = b
? ( x² + a )/x = b
? x² + a = bx .........................(i)
? bx - x² = a .........................(ii)
Now Given in question,
( x² + bx + a ) / ( bx² - x³ )
? ( x² + a + bx ) / ( bx² - x³ )
Put the value of x² + a from equation (i) in above equation,
? ( bx + bx )/(bx² - x³)
= (2bx)/( bx² - x³ )
= (2bx)/x( bx - x² )
= 2b/(bx - x²)
Put the value of bx - x² from equation (ii) in above equation, we will get
= 2b/a

Correct Answer: 52

Explanation:

Given, x = ( ?3 + 1) / ( ?3 - 1 )
y = ( ?3 - 1 ) / ( ?3 + 1 )
Then , x + y = { ( ?3 + 1) / ( ?3 - 1 ) } + { ( ?3 - 1 ) / ( ?3 + 1 ) }
? x + y = { (?3 + 1)² + (?3 - 1)² } / (?3 - 1) (?3 + 1)
? x + y = ( 3 + 1 +2?3 + 3 + 1 - 2?3 ) / ( 3 - 1 )
? x + y = 8/2
? x + y = 4 --------------------(1)
Now xy = ( ?3 - 1 / ?3 + 1 ) x ( ?3 + 1 / ?3 - 1 )
xy = (3 - 1) / (3 - 1) = 2/2 = 1------------------(2)
Given in question,
? x²/y + y²/x
= ( x³ + y³ )/xy ------------------- (3)
Apply the algebra formula, A³ + B³ = (A + B)³ - 3AB(A + B)
= (x + y)³ - 3xy(x + y)/xy
Put the value of x + y from (1) and xy from (2) in Equation (3), we will get
= (4)³ - 3 x 1 x (4)/1
= 64 - 3 x 1 x 4
= 64 - 12
= 52

Correct Answer: -2

Explanation:

Given that,
a = (?2 - 1)^1/3
By cubing the both side of the given equation.
a³ = ?2 - 1
Then 1/a³ = 1/?2 - 1
Now multiply and divide the above equation by ?2 + 1
? 1/a³ = ( ?2 + 1 ) / ( ?2 + 1 ) x 1/(?2 - 1 )
? 1/a³ = ( ?2 + 1 ) x 1 / ( ?2 + 1 ) x (?2 - 1 ) [ Use the formula (A + B)(A - B) = A² - B² ]
? 1/a³ = ( ?2 + 1 ) / ( 2 - 1 )
? 1/a³ = ?2 + 1
According to the question
( a - a^-1 )³ + 3 ( a - a^-1 )
= (a - 1/a)³ + 3(a - 1/a) Use the formula [ ( A - B)³ = A³ - B³ + 3AB(A - B) ]
= a³ - 1/a³ - 3 a x 1/a (a -1/a) + 3(a - 1/a)
= a³ - 1/a³ - 3 (a -1/a) + 3(a - 1/a)
= a³ - 1/a³
Pu the value of a³ and 1/a³
= ?2 -1 - ( ?2 + 1 )
= ?2 -1 - ?2 - 1
= -2

Correct Answer: 0.09724

Explanation:

9.724 ÷ 100 = 0.09724
Shift decimal two palaces to the left. i.e 100

Correct Answer: 0.0310324250

Explanation:

Here 5 x 25 x 6301 x 394=310324250
Total decimal places = (2+3+5) = 10
? 5 x 0.25 x 6.301 x 0.00394 = 0.0310324250

Correct Answer: .0005

Explanation:

Let 0.8y = 0.0004
Then,y = 0.0004 / 0.8
= 0.004 / 8
= .0005

Correct Answer: 0.00072

Explanation:

? 9 x 8=72
? 0.09 x 0.008 = 0.00072 (Five place of decimal )

Correct Answer: 300

Explanation:

Let k % of 10.8=32.4
⇒ (k x 10.8) / 100 = 32.4
⇒ k = (32.4 x 100 )/10.8
= 300