1.
If 22n - 1 =
 1 8n -3
, then the value of n is:
• A.
3
• C.
0
• B.
2
• D.
- 2
• Report
Explanation :

22n - 1 =
 1 8n - 3
22n - 1 =
 1 (23)n -3
=
 1 23(n -3)
=
 1 2(3n - 9)
= 2(9 - 3n)

2n - 1 = 9 - 3n

5n = 10

n = 2

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2.
(2.4 x 103) ÷ (8 x 10-2) = ?
• A.
3 x 10-5
• C.
3 x 105
• B.
3 x 104
• D.
30
• Report
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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3.
(18)3.5 ÷ (27)3.5 x 63.5 = 2? :
• A.
3.5
• C.
6
• E.
None of these
• B.
4.5
• D.
7
• Report
Explanation :

(18)3.5 ÷ (27)3.5 x 63.5 = 2x

(18)3.5 x
 1 (27)3.5
x 63.5 = 2x

(32 x 2)3.5 x
 1 (33)3.5
x (2 x 3)3.5 = 2x

3(2 x 3.5) x 23.5 x
 1 3(3 x 3.5)
x 23.5 x 33.5 = 2x

37 x 23.5 x
 1 310.5
x 23.5 x 33.5 = 2x

27 x 2x

x = 7

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4.
Number of prime factors in
 612 x (35)28 x (15)16 (14)12 x (21)11
is :
• A.
56
• C.
112
• B.
66
• D.
None of these
• Report
Explanation :

 612 x (35)28 x (15)16 (14)12 x (21)11
=
 (2 x 3)12 x (5 x 7)28 x (3 x 5)16 (2 x 7)12 x (3 x 7)11

=
 212 x 312 x 528 x 728x 316 x 516 212 x 712 x 311 x 711

 = 2(12 - 12) x 3(12 + 16 - 11) x 5(28 + 16) x 7(28 - 12 - 11)

 = 20 x 317 x 544 x 7-5

=
 317 x 544 75

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

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5.
If 2n - 1 + 2n + 1 = 320, then n is equal to:
• A.
6
• C.
5
• B.
8
• D.
7
• Report
Explanation :

2n - 1 + 2n + 1 = 320

2n - 1 (1 + 22) = 320

5 x 2n - 1 = 320

2n - 1 =
 320 5
= 64 = 26

n - 1 = 6

n = 7

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