Dehli Police Constable Model Paper 2 (HM)

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Question : 79 of 100

Marks: +1, -0

निम्नलिखित समीकरण में प्रश्न चिन्ह (?) के स्थान पर क्या मान आना चाहिए।

27^{3/2} × 9^{5/2 } × 3^{–6}

= 9?

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

Solution:

⇒

(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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