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This mock test of Practice Test: Number Series- 1 for UPSC helps you for every UPSC entrance exam.
This contains 10 Multiple Choice Questions for UPSC Practice Test: Number Series- 1 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

17, 19, 23, 29, 31, 37, _____

Solution:

The given numbers are consecutive prime numbers in increasing order starting with 17.

Hence, the next number in the series is 41.

QUESTION: 2

225, 196, 169, _____, 121, 100, 81

Solution:

The given numbers are squares of consecutive natural numbers in decreasing order starting with 15,

**i.e.**, the numbers 225, 196, 169, ____, 100, 81 can be written as 15^{2}, 14^{2}, 13^{2} , ____, 11^{2} , 10^{2} , 9^{2}.

Hence, the missing number is 12^{2} = 144.

QUESTION: 3

54, 66, 82, 102, 126, _____

Solution:

1st term = 54

2nd term = 54 + 12 = 66

3rd term = 66 + 16=82

4th term = 82 + 20 =102

5th term = 102 + 24 = 126...

The difference is increasing by 4, starting with 12.

So, the next difference is 24 + 4 = 28.

Hence, the next number is 126 + 28 = 154.

QUESTION: 4

97, 83, 73, 67, 59, _____

Solution:

**List of Prime** **Numbers** **from** **1** **to 100:**

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,...

The given numbers are alternate prime numbers in decreasing order, starting with 97.

Hence, the next number in the series is 47.

QUESTION: 5

8, 16, 48, 96, 288, 576, _____

Solution:

1st term = 8

2nd term = 8 x 2 = 16

3rd term = 16 x 3 = 48

4th term = 48 x 2 = 96

5th term = 96 x 3 = 288

6th term = 288 x 2 = 576...

⇒ For every term at even position, the previous term is multiplied by 2.

⇒ For every term at odd position, the previous term is multiplied by 3.

So the missing term is: 576 × 3 = 1728

QUESTION: 6

75, 291, 416, 480, 507, ____

Solution:

1st term = 75

2nd term = 75 + 216 = 75 + 6^{3} = 291

3rd term = 291 + 125 = 291 + 5^{3} = 416

4th term = 416 + 64 = 416 + 4^{3} = 480

5th term = 480 + 27 = 480 + 3^{3} = 507...

The differences are cubes of consecutive natural numbers in decreasing order from 6.

So, the missing term = 507 + 8 = 507 + 2^{3} = 515

QUESTION: 7

225, 224, _____, 222, 221

Solution:

The given numbers are consecutive natural numbers in decreasing order starting with 225. Hence, the missing number is 223.

QUESTION: 8

5, 13, 41, 85, 257, _____

Solution:

1st term = 5

2nd term = 5 × 2 + 3 = 13

3rd term = 13 × 3 + 2 = 41

4th term = 41 × 2 + 3 = 85

5th term = 85 × 3 + 2 =257...

⇒ For every term at even position, the previous term is multiplied by 2 and 3 is added.

⇒ For every term at odd position, the previous term is multiplied by 3 and 2 is added.

So the missing term is: 257 × 2 + 3 = 517

QUESTION: 9

123 , 129, 141, _________, 159, 165

Solution:

The common difference between consecutive terms is 6, 12, 6, 12 & so on. So, the term next to 141 is 141 + 6 = 147

QUESTION: 10

0, 5, 22, 57, 116, _________

Solution:

The 1st to 5th terms are 0, 5, 22, 57, 116.

These terms are 1 – 1, 8 – 3, 27 – 5, 64 – 7, 125 – 9.

**i.e. **1^{3} – 1, 2^{3} – 3, 3^{3} – 5, 4^{3} – 7, 5^{3} – 9

So, the nth term of the series: n^{3} – (2n – 1).

So, the 6th term of the series is 6^{3} – (2 × 6 –1) = 216 – 11 = 205.

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