View in English View in Hindi (16)^{9} / (16)^{4} * (16)^{3} = (16)^{?}

A) 6.75

B) 8

C) 10

D) 12

Correct Answer : 8

Explanation : (16)^{9} / (16)^{4} * (16)^{3}
=>(16)^{9-4} * (16)^{3}
=>(16)^{5} * (16)^{3}
=>(16)^{5+3}
=>(16)^{8}

? = ∛103823

A) 49

B) 51

C) 45

D) 47

Correct Answer : 47

Explanation : (^{n} √a )^{n} = a
(a^{m} )^{n} = a^{mn}

? = ∛103823
? = ∛(47) ^{3}
? = [(47)^{3} ]^{1/3}
? = 47^{3 x 1/3}
? = 47

If x^{m } . y^{n} = 7889, where x and y are prime numbers, the value of x + y is ?

A) 30

B) 60

C) 100

D) 120

Correct Answer : 30

Explanation : x^{m} .y^{n} = 7889
x^{m} .y^{n} = 7^{3} × 23^{1}
hence, x and y are 7 and 23
thus x + y = 30

Which of the following is the greatest?

A) 3333^{33}

B) 333^{333}

C) 33^{3333}

D) 3^{33333}

Correct Answer : 3^{33333}

Explanation : 3^{33333} is the greatest number.

Determine a possible value of x from the equation 5^{x-2 } X 2^{3x/(x+1)} = 4 ?

A) 1

B) 2

C) 0

D) 4

Correct Answer : 2

Explanation : 5^{x- 2} X 2^{3x/(x + 1)} = 4
5^{x- 2} X 2^{3x/(x + 1)} = 5^{0} * 2^{2}
Equation the indicates of equal bases,
x - 2 = 0 and 3x/(x + 1) = 2
From both these questions
x = 2

If 0.42 * 100^{K} = 42, then what is the value of K?

A) 4

B) 2

C) 1

D) 3

Correct Answer : 1

Explanation : 0.42 * 100^{K} = 42
(42/100) * 100^{K} = 42
100^{K} = (42*100)/42
100^{K} = 100
100^{K} = 100^{1}
K=1

What is the value of (443+547)^{2} + (443-547)^{2} / (443*443) + (547*547) ?

A) 0

B) 1

C) 2

D) 3

Correct Answer : 2

Explanation : (443+547)^{2} + (443-547)^{2} / (443*443) + (547*547)
= (443^{2 } + 547^{2 } + 2*443*547) + (443^{2 } + 547^{2 } - 2*443*547) / (443^{2} + 547^{2} )
= 2*(443^{2 } + 547^{2 } ) / (443^{2} + 547^{2} )
= 2