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Important Formulas
Surds and Indices

Home
General Aptitude
Surds and Indices

2^{2n - 1}

8^{n -3}

, then the value of n is:

A.
3
C.
0

B.
2
D.
- 2

Answer & Explanation
Report

Answer : [B]
Explanation :

2^{2n - 1}=

8^{n - 3}

2^{2n - 1} =

(2³)^{n -3}

2³⁽^{n -3)}

2⁽³^{n - 9)}

= 2^{(9 - 3n)}

2n - 1 = 9 - 3n

5n = 10

n = 2

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Name

(2.4 x 10³) ÷ (8 x 10^-2) = ?

A.
3 x 10^-5
C.
3 x 10⁵

B.
3 x 10⁴
D.
30

Answer & Explanation
Report

Answer : [B]
Explanation :

(2.4 x 10³) ÷ (8 x 10^-2) =

2.4 x 10³

8 x 10^-2

24 x 10²

8 x 10^-2

= (3 x 10⁴)

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Name

(18)^3.5 ÷ (27)^3.5x 6^3.5 = 2^? :

A.
3.5
C.
6
E.
None of these

B.
4.5
D.
7

Answer & Explanation
Report

Answer : [D]
Explanation :

(18)^3.5 ÷ (27)^3.5x 6^3.5 = 2^x

(18)^3.5 x

(27)^3.5

x 6^3.5 = 2^x

(3² x 2)^3.5 x

(3³)^3.5

x (2 x 3)^3.5 = 2^x

3^{(2 x 3.5)} x 2^3.5 x

3^{(3 x 3.5)}

x 2^3.5 x 3^3.5 = 2^x

3⁷ x 2^3.5 x

3^10.5

x 2^3.5 x 3^3.5 = 2^x

2⁷ x 2^x

x = 7

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Name

Number of prime factors in

6¹² x (35)²⁸x (15)¹⁶

(14)¹²x (21)¹¹

is :

A.
56
C.
112

B.
66
D.
None of these

Answer & Explanation
Report

Answer : [B]
Explanation :

6¹² x (35)²⁸x (15)¹⁶

(14)¹²x (21)¹¹

(2 x 3)¹² x (5 x 7)²⁸x (3 x 5)¹⁶

(2 x 7)¹²x (3 x 7)¹¹

2¹² x 3¹²x 5²⁸ x 7²⁸x 3¹⁶ x 5¹⁶

2¹²x 7¹² x 3¹¹ x 7¹¹

2^{(12 - 12)} x 3^{(12 + 16 - 11)}x 5^{(28 + 16)} x 7^{(28 - 12 - 11)}

2⁰ x 3¹⁷x 5⁴⁴x 7^-5

3¹⁷ x 5⁴⁴

7⁵

Number of prime factors = 17 + 44 + 5 = 66.

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Name

If 2^{n - 1} + 2^{n + 1} = 320, then n is equal to:

A.
6
C.
5

B.
8
D.
7

Answer & Explanation
Report

Answer : [D]
Explanation :

2^{n - 1} + 2^{n + 1} = 320

2^{n - 1}(1 + 2²) = 320

5 x 2^{n - 1} = 320

2^{n - 1}=

320

= 64 = 2⁶

n - 1 = 6

n = 7

Report

Name

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