100+ Surds and Indices Questions for Bank Exams Pdf - 1

Ans: C

8^-25 - 8^-26 = $$({1/8^25 – {1/8^26})$$ = $${(8 - 1)}/ {8}^26$$ = 7 × 8^-26.

Ans: D

2^{n + 4} - 2^{n + 2} = 3

⇔ 2^{n + 2} (2² - 1) = 3

⇔ 2^{n + 2 = 1 = 20}

⇔ n + 2 = 0

⇔ n = - 2.

Ans: B

21^? × 21^6.5 = 21^12.4

{∴ a^m × aⁿ = a^{m + n}}

⇒ 21^{? + 6.5} = 21^12.4

⇒ ? + 6.5 = 12.4

⇒ ? = 12.4 – 6.5 = 5.9.

Ans: A

$${16 × 32} / {9 × 27 × 81}$$

= $${2^4 × 2^5} / {3^2 × 3^3 × 3^4}$$

= $${2}^(4 + 5) / {3}^(2 + 3 + 4)$$

= $${2}^9/{3}^9$$

= $$({2}/{3})^9$$.

Ans: A

$${5.4 ÷ 3 × 16 ÷ 2}/ {18 ÷ 5 × 6 ÷ 3}$$

= $${5.4 /3 × 16/2} / {18/5 × 6/3}$$

= $${1.8 × 8} / {3.6 × 2}$$ = 2.