Correct Answer: (9, 6, 54)

Solution : Given:
(12, 8, 80); (16, 10, 131)

In the given sets, divide the second number by 2, then subtract the cube of the result from the square of the first number.
(12, 8, 80)→8 ÷ 2 = 4; {(12)² – (4)³} = {144 – 64} = 80
(16, 10, 131)→10 ÷ 2 = 5; {(16)² – (5)³} = {256 – 125} = 131
Let's check the given options –
First option: (11, 5, 55)→5 ÷ 2 = 2.5; {(11)² – (2.5)³} = {121 – 15.625} = 105.375 ≠ 55
Second option: (13, 4, 160)→4 ÷ 2 = 2; {(13)² – (2)³} = {169 – 8} = 161 ≠ 160
Third option: (14, 12, 126)→12 ÷ 2 = 6; {(14)² – (6)³} = {196 – 216} = –20 ≠ 126
Fourth option: (9, 6, 54)→6 ÷ 2 = 3; {(9)² – (3)³} = {81 – 27} = 54

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

Correct Answer: (15, 17, 47)

Solution : Given:
(17, 24, 58); (26, 37, 89)

Here, (17, 24, 58)→(17 × 2) + 24 = 34 + 24 = 58
(26, 37, 89)→(26 × 2) + 37 = 52 + 37 = 89

Let's check the options –
First option: (15, 17, 47)→(15 × 2) + 17 = 30 + 17 = 47
Second option: (41, 39, 125)→(41 × 2) + 39 = 82 + 39 = 121 ≠ 125
Third option: (10, 20, 44)→(10 × 2) + 20 = 20 + 20 = 40 ≠ 44
Fourth option: (21, 38, 96)→(21 × 2) + 38 = 42 + 38 = 80 ≠ 96

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: (17, 289, 4913)

Solution : Given:
(9, 81, 729); (14, 196, 2744)

Here, (9, 81, 729)→(9)² = 81; (9)³ = 729
(14, 196, 2744)→(14)² = 196; (14)³ = 2744

Let's check each option –
First option: (11, 212, 464)→(11)² = 121 ≠ 212; (11)³ = 1331 ≠ 464 
Second option: (17, 289, 4913)→(17)² = 289; (17)³ = 4913
Third option: (25, 625, 9375)→(25)² = 625; (25)³ = 15625 ≠ 9375 
Fourth option: (15, 375, 1125)→(15)² = 225 ≠ 375; (15)³ = 3375 ≠ 1125

So, only the second option follows the same pattern as followed by the given number pair. Hence, the second option is correct.

Correct Answer: Protection of plant Varieties and Farmers Right Authority 

Solution : The correct option is Protection of plant Varieties and Farmers Right Authority.

Plant variety protection and farmer rights are not addressed under Section 3(3) of the Environment (Protection) Act of 1986. Instead, the Protection of Plant Varieties and Farmers' Rights Act, 2001, is a separate area of law in India that deals with plant variety protection and farmer rights. It establishes a framework for the registration and protection of new plant varieties, as well as recognises farmers' rights in specific areas of plant breeding and seed usage.
 

Correct Answer: (12, 125, 7)

Solution : Given:
(9, 343, 2); (12, 729, 3)

Here, the pattern followed is as follows –
⇒ (9, 343, 2)→9 – 2 = 7 and 7³ = 343
⇒ (12, 729, 3)→12 – 3 = 9 and 9³ = 729

Let's check the options –
First option: (98, 49, 92)→98 – 92 = 6 and 6³ = 216 ≠ 49
Second option: (13, 4, 89)→89 – 13 = 76 and 76³ = 438976 ≠ 4
Third option: (12, 66, 20)→20 – 12 = 8 and 8³​​​​​​​ = 512 ≠ 66
Fourth option: (12, 125, 7)→12 – 7 = 5 and 5³​​​​​​​ = 125

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

Correct Answer: (16, 49, 9)

Solution : Given:
(13, 64, 5); (10, 1, 9)

In the given sets, subtract the third number from the first number and then find the square of the resultant number to get the second number.
(13, 64, 5)→13 – 5 = 8; 8² = 64
(10, 1, 9)→10 – 9 = 1; 1² = 1
Let's check the options –
First option: (15, 144, 9)→15 – 9 =6; 6² = 36 ≠ 144
Second option: (16, 256, 9)→16 – 9 = 7; 7² = 49 ≠ 256
Third option: (15, 306, 9)→15 – 9 = 6; 6² = 36 ≠ 306
Fourth option: (16, 49, 9)→16 – 9 = 7; 7² = 49

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

Correct Answer: 9 : 122 : 14

Solution : Given :
12 : 92 : 8; 16 : 92 : 6

Subtract 4 from the product of the first and the third numbers to obtain the second number.
⇒ 12 : 92 : 8→(12 × 8) – 4 = 96 – 4 = 92 
⇒ 16 : 92 : 6→(16 × 6) – 4 = 96 – 4 = 92

Let's check the options —
First option : 9 : 122 : 14→(9 × 14) – 4 = 126 – 4 = 122
Second option : 13 : 60 : 5→(13 × 5) – 4 = 65 – 4 = 61 ≠ 60
Third option : 15 : 184 : 12→(15 × 12) – 4 = 180 – 4 = 176 ≠ 184
Fourth option : 8 : 109 : 14→(8 × 14) – 4 = 112 – 4 = 108 ≠ 109

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: (13, 160)

Solution : Given:
(17, 280); (22, 475)

Here, (17, 280)→(17)² – 9 = 289 – 9 = 280
(22, 475)→(22)² – 9 = 484 – 9 = 475

Let's check the options –
First option: (21, 450)→(21)² – 9 = 441 – 9 = 432 ≠ 450
Second option: (26, 485)→(26)² – 9 = 676 – 9 = 667 ≠ 485
Third option: (13, 160)→(13)² – 9 = 169 – 9 = 160
Fourth option: (12, 137)→(12)² – 9 = 144 – 9 = 135 ≠ 137

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: 1965

Solution : The correct option is 1965.

Under the Food Corporations Act of 1964, the Food Corporation of India (FCI) was established on January 14, 1965. FCI's main goals are to help India's public distribution system and guarantee food security. Its duties include obtaining, storing, moving, distributing and selling food grains and other necessary food items all over the nation.

Correct Answer: Time Study

Solution : The correct answer is (a) Time Study

Time study involves analyzing and measuring the time required to perform a specific task or job accurately. It aims to determine the standard time needed to complete a job efficiently. In this scenario, XYZ Tech Solutions is using time study to set performance standards based on the time taken to complete tasks.

In summary, XYZ Tech Solutions using time study to set performance standards for each task aligns with the technique of "Time Study," which involves analyzing and measuring the time required to perform specific tasks accurately to determine standard time and improve efficiency.