Correct Answer: (17, 9, 157)

Solution : Given:
(22, 9, 198)

Here, the pattern followed is as follows –
(22, 9, 198)→22 × 9 = 198
Let's check the options –
First option: (19, 7, 133)→19 × 7 = 133
Second option: (26, 5, 130)→26 × 5 = 130
Third option: (28, 7, 196)→28 × 7 = 196
Fourth option: (17, 9, 157)→17 × 9 = 153 ≠ 157

So, only the fourth option does not follow the pattern of the given set of numbers. Hence, the fourth option is correct.

Correct Answer: (13, 12, 38)

Solution : Given:
(10, 22, 42); (15, 14, 44)

Multiply the first number by 2 and, then add the resultant to the second number, to get the third number –
(10, 22, 42); (10 × 2) + 22 = 20 + 22 = 42
(15, 14, 44); (15 × 2) + 14 = 30 + 14 = 44

Let's check the options –
First option: (9, 22, 38); (9 × 2) + 22 = 18 + 22 = 40 ≠ 38
Second option: (12, 12, 24); (12 × 2) + 12 = 24 + 12 = 36 ≠ 24 
Third option: (13, 12, 38); (13 × 2) + 12 = 26 + 12 = 38
Fourth option: (6, 3, 17); (6 × 2) + 3 = 12 + 3 = 15 ≠ 17

So, only the third option follows the same relation as the given set of numbers. Hence, the third option is correct.

Correct Answer: bbb

Solution : Given: 

a_bba_bba_bb

Let's check the given options –

First option: aab

The series becomes aabbaabbabbb

There is no pattern in the above series.

Second option: abb

The series becomes aabbabbbabbb

There is no pattern in the above series.

Third option: bbb

The series becomes  abbbabbbabbb

The pattern in the series becomes abbb / abbb / abbb

Fourth option: bba

The series becomes  abbbabbbaabb

There is no pattern in the above series.

Hence, the third option is correct.

Correct Answer: (7, 22, 3)

Solution : Given:
(4, 25, 6); (8, 25, 3)

Here, (4, 25, 6)→(4 × 6) + 1 = 24 + 1 = 25
(8, 25, 3)→(8 × 3) + 1 = 24 + 1 = 25

Let's check the options –
First option: (3, 81, 6)→(3 × 6) + 1 = 18 + 1 = 19 ≠ 81
Second option: (7, 22, 3)→(7 × 3) + 1 = 21 + 1 = 22
Third option: (12, 96, 8)→(12 × 8) + 1 = 96 + 1 = 97 ≠ 96
Fourth option: (14, 55, 4)→(14 × 4) + 1 = 56 + 1 = 57 ≠ 55

So, only the second option follows the same pattern as followed by the given set of numbers. Hence, the second option is correct.

Correct Answer: (75, 69, 216)

Solution : Given:
(67, 63, 64); (24, 17, 343)

Cube the difference between the first number and the second number, to obtain the third number in the given set of numbers –
⇒ (67, 63, 64)→(67 – 63)³ = 4³ = 64
⇒ (24, 17, 343)→(24 – 17)³ = 7³ = 343

Let's check the options –
First option: (75, 69, 216)→(75 – 69)³ = 6³​​​​​​​ = 216
Second option: (27, 22, 120)→(27 – 22)³ = 5³​​​​​​​ = 125 ≠ 120
Third option: (46, 41, 40)→(46 – 41)³ = 5³​​​​​​​ = 125 ≠ 40
Fourth option: (97, 88, 81)→(97 – 88)³ = 9³​​​​​​​ = 729 ≠ 81

So, only the first option follows the same pattern as followed by the given set of numbers. Hence, the first option is correct. 

Correct Answer: (18, 15, 81)

Solution : Given:
(23, 25, 16); (21, 17, 256)

Here, (23, 25, 16)→(25 – 23)⁴ = (2)⁴ = 16
(21, 17, 256)→(21 – 17)⁴ = (4)⁴ = 256

Let's check the options –
First option: (14, 19, 125)→(19 – 14)⁴ = (5)⁴ = 625 ≠ 125
Second option: (27, 23, 64)→(27 – 23)⁴ = (4)⁴ = 256 ≠ 64
Third option: (18, 15, 81)→(18 – 15)⁴ = (3)⁴ = 81
Fourth option: (11, 9, 12)→(11 – 9)⁴ = (2)⁴ = 16 ≠ 12

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.

Correct Answer: (72, 36, 108)

Solution : Given:
(34, 17, 51); (46, 23, 69)

Multiply the second number by 2 to obtain the first number and multiply the second number by 3 to obtain the third number in the given set of numbers –
(34, 17, 51)→17 × 2 = 34; 17 × 3 = 51
(46, 23, 69)→23 × 2 = 46; 23 × 3 = 69

Let's check the options –
First option: (68, 34, 204)→34 × 2 = 68; 34 × 3 = 102 ≠ 204
Second option: (54, 27, 108)→27 × 2 = 54; 27 × 3 = 81 ≠ 108
Third option: (72, 36, 108)→36 × 2 = 72; 36 × 3 = 108
Fourth option: (44, 22, 88)→22 × 2 = 44; 22 × 3 = 66 ≠ 88

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct. 

Correct Answer: (65, 71, 77)

Solution : Given:
(9, 15, 21); (31, 37, 43)

Add 6 to the first and second numbers, to get the second and third numbers respectively.
(9, 15, 21)→9 + 6 = 15; 15 + 6 = 21
(31, 37, 43)→31 + 6 = 37; 37 + 6 = 43

Let's check the options –
First option: (32, 38, 43)→32 + 6 = 38; 38 + 6 = 44 ≠ 43
Second option: (45, 51, 56)→45 + 6 = 51; 51 + 6 = 57 ≠ 56
Third option: (65, 71, 77)→65 + 6 = 71; 71 + 6 = 77
Fourth option: (23, 28, 39)→23 + 6 = 29 ≠ 28; 28 + 6 = 34 ≠ 39

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.

Correct Answer: (16, 43, 22)

Solution : Given:
(11, 33, 17); (18, 44, 21)

Like, (11, 33, 17)→11 + 17 + 5 = 33
(18, 44, 21)→18 + 21 + 5 = 44

Let's check the options –
First option: (7, 32, 19)→7 + 19 + 5 = 31 ≠ 32
Second option: (12, 40, 18)→12 + 18 + 5  = 35 ≠ 40
Third option: (16, 43, 22)→16 + 22 + 5 = 43
Fourth option: (15, 34, 19)→15 + 19 + 5 = 31 ≠ 34

So, only the third option follows the same pattern as followed by the given set of numbers. Hence, the third option is correct.

Correct Answer: (4, 7, 33)

Solution : Given:
(7, 11, 72); (5, 8, 39)

Here, (7, 11, 72)→(11 – 7) × (11 + 7) = 4 × 18 = 72
(5, 8, 39)→(8 – 5) × (8 + 5) = 3 × 13 = 39

Now, let's check the given options –
First option: (4, 7, 33)→(7 – 4) × (7 + 4) = 3 × 11 = 33
Second option: (2, 3, 1)→(3 – 2) × (3 + 2) = 1 × 5 = 5 ≠ 1
Third option: (5, 2, 23)→(2 – 5) × (2 + 5) = –3 × 7 = –21 ≠ 23
Fourth option: (5, 6, 13)→(6 – 5) × (6 + 5) = 1 × 11 = 11 ≠ 13

So, only the first option follows the same pattern as followed by the given set of numbers. Hence, the first option is correct.