Correct Answer: (4, 12, 16)

Solution : Given:
(2, 6, 8); (117, 351, 468)

In the given set of numbers, multiply the first number by three to obtain the second number and multiply the first number by four to obtain the third number.
(2, 6, 8)→2 × 3 = 6; 2 × 4 = 8
(117, 351, 468)→117 × 3 = 351; 117 × 4 = 468
Let's check each option –
First option: (6, 19, 25)→6 × 3 = 18 ≠ 19; 6 × 4 = 24 ≠ 25
Second option: (4, 12, 16)→4 × 3 = 12; 4 × 4 = 16
Third option: (5, 12, 25)→5 × 3 = 15 ≠ 12; 5 × 4 = 20 ≠ 25
Fourth option: (7, 14, 23)→7 × 3 = 21 ≠ 14; 7 × 4 = 28 ≠ 23

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: (21, 9, 60)

Solution : Given:
(26, 14, 170); (31, 7, 18)

In the given sets, add the first and the third numbers. The resultant is the square of the second number.
(26, 14, 170)→26 + 170 = 196; (14)² = 196
(31, 7, 18)→31 + 18 = 49; (7)² = 49
Now, let's check the given options –
First option: (11, 5, 17)→11 + 17 = 28; (5)² = 25 ≠ 28
Second option: (34, 10, 72)→34 + 72 = 106; (10)² = 100 ≠ 106
Third option: (21, 9, 60)→21 + 60 = 81; (9)² = 81
Fourth option: (14, 6, 24)→14 + 24 = 38; (6)² = 36 ≠ 38

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: Rural

Solution : The correct answer is Rural.

The "R" in NABARD stands for "rural." NABARD, which stands for the National Bank for Agriculture and Rural Development, is an apex financial institution in India that focuses on providing credit and other facilities for the development of agriculture and rural sectors in the country.

Correct Answer: (21, 189, 12)

Solution : Given:
(14, 112, 6); (17, 204, 5)

Like, (14, 112, 6)→(14 – 6) × 14 = 8 × 14 = 112
(17, 204, 5)→(17 – 5) × 17 = 12 × 17 = 204

Let's check the options –
First option: (21, 189, 12)→(21 – 12) × 21 = 9 × 21 = 189
Second option: (24, 145, 18)→(24 – 18) × 24 = 6 × 24 = 144 ≠ 145
Third option: (9, 89, 3)→(9 – 3) × 9 = 6 × 9 = 54 ≠ 89
Fourth option: (15, 135, 7)→(15 – 7) × 15 = 8 × 15 = 120 ≠ 135

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: (1, 2, 16)

Solution : Given:
(6, 2, 96); (5, 6, 240)

Like, (6, 2, 96)→(6 × 2) × 8 = 96
(5, 6, 240)→(5 × 6) × 8 = 240

Let's check the options –
First option: (4, 1, 6)→(4 × 1) × 8 = 32 ≠ 6
Second option: (12, 6, 45)→(12 × 6) × 8 = 576 ≠ 45
Third option: (1, 2, 16)→(1 × 2) × 8 = 16
Fourth option: (8, 3, 28)→(8 × 3) × 8 = 192 ≠28

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: (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.