Delhi Police Constable Exam Model Paper 2

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Question : 79 of 100

Marks: +1, -0

What value should come in place of question mark (?) in the following equation?

27 ^{3/2} × 9^{ 5/2} × 3 ^{–6} = 9^{ ?}

$3/4$
$7/4$
$7/2$
$3/2$

Solution:

27^{3/2 }× 9^ {5/2 }× 3^{-6 }= 9^{?}

⇒

(3^3)^{3/2} × (3^2)^{5/2} × 3^{–6} = 3^{2 × ?}

∵ (a^m)^n = a^{mn}

⇒

(3)^{9/2} × (3)^5 × 3^{–6 }= 3^{2 × ?}

∵ a^m × a^n = a^{(m + n)}

⇒ (3)^{(9/2) + 5 {– 6} = 3^{2 × ?}

⇒

(3)^{7/2} = 3^{2 × ?}

⇒

7/2 = 2 × ?

∴ ? = 7/4

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