Correct Answer: (13, 7, 218)

Solution : Given: 
(9, 3, 90); (5, 4, 41)

Add the squares of the first two numbers to obtain the third number —
⇒ (9, 3, 90)→9² + 3² = 81 + 9 = 90
⇒ (5, 4, 41)→5² + 4² = 25 + 16 = 41

Let's check the options —
First option: (13, 7, 218)→13² + 7² = 169 + 49 = 218
Second option: (7, 8,117)→7² + 8² = 49 + 64 = 113 ≠ 117
Third option: (11, 8,182)→11² + 8² = 121 + 64 = 185 ≠ 182
Fourth option: (4,12,162)→4² + 12² = 16 + 144 = 160 ≠ 162

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: (9, 81, 729)

Solution : Given:
(7, 49, 343); (8, 64, 512)

The second number is the square of the first number and the third number is the cube of the first number –
(7, 49, 343)→(7)² = 49; (7)³ = 343
(8, 64, 512)→(8)² = 64; (8)³ = 512

Let's check the options – 
First option: (6, 36, 206)→(6)² = 36; (6)³ = 216 ≠ 206
Second option: (5, 25, 225)→(5)² = 25; (5)³ = 125 ≠ 225
Third option: (11, 121, 1221)→(11)² = 121; (11)³ = 1331 ≠ 1221
Fourth option: (9, 81, 729)→(9)² = 81; (9)³ = 729

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

Correct Answer: (5, 14, 29)

Solution : Given:
(9, 26, 53); (8, 23, 47)

In the given sets, subtract the second number from the third number and divide the resultant by 3 to get the first number.
(9, 26, 53)→53 – 26 = 27; 27 ÷ 3 = 9
(8, 23, 47)→47 – 23 = 24; 24 ÷ 3 = 8
Let's check the options –
First option: (5, 14, 29)→29 – 14 = 15; 15 ÷ 3 = 5
Second option: (6, 17, 36)→36 – 17 = 19; 19 ÷ 3 = 6.3 ≠ 6
Third option: (11, 32, 56)→56 – 32 = 24; 24 ÷ 3 = 8 ≠ 11
Fourth option: (7, 20, 42)→42 – 20 = 22; 22 ÷ 3 = 7.3 ≠ 7

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, 6, 110)

Solution : Given:
(8, 6, 50); (24, 4, 98)

Here, (8, 6, 50)→(8 × 6) + 2 = 48 + 2 = 50
(24, 4, 98)→(24 × 4) + 2 = 96 + 2 = 98

Let's check the options –
First option: (2, 48, 100)→(2 × 48) + 2 = 96 + 2 = 98 ≠ 100
Second option: (12, 8, 100)→(12 × 8) + 2 = 96 + 2 = 98 ≠ 100
Third option: (32, 3, 144)→(32 × 3) + 2 = 96 + 2 = 98 ≠ 144
Fourth option: (18, 6, 110)→(18 × 6) + 2 = 108 + 2 = 110

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: Andhra Pradesh  
 

Solution : The linguistic movement in Andhra Pradesh set a precedent for the reorganization of states on linguistic lines in India, as it led to the formation of the first state based on language, inspiring similar demands in other regions.

Correct Answer: (6, 9, 162)

Solution : Given:
(9, 7,189); (4,13,156)

The product of the first and second numbers is multiplied by 3, to get the third number –
⇒ (9, 7,189)→(9 × 7) × 3 = 189
⇒ (4, 13,156)→(4 × 13) × 3 = 156

Let's check each option –
First option: (5, 9,160)→(5 × 9) × 3 = 135 ≠ 160
Second option: (6, 9,162)→(6 × 9) × 3 = 162
Third option: (8, 5,125)→(8 × 5) × 3 = 120 ≠ 125
Fourth option: (7, 8,188)→(7 × 8) × 3 = 168 ≠ 188

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

Correct Answer: (12, 24, 8)

Solution : Given:
(8, 12, 6); (9, 18, 8)

In the above-given sets, the pattern followed is as follows –
(8, 12, 6)→8 × 6 = 48; 48 ÷ 4 = 12
(9, 18, 8)→9 × 8 = 72; 72 ÷ 4 = 18
Now, let's check the given options –
First option: (4, 12, 6)→4 × 6 = 24; 24 ÷ 4 = 6 ≠ 12
Second option: (12, 24, 8)→12 × 8 = 96; 96 ÷ 4 = 24
Third option: (7, 24, 4)→7 × 4 = 28; 28 ÷ 4 = 7 ≠ 24
Fourth option: (9, 10, 11)→9 × 11 = 99; 99 ÷ 4 = 24.75 ≠ 10

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: 60 years

Solution : The correct answer is (c) 60 years

The retirement age of government employees can vary slightly depending on the specific rules and regulations of different government departments or services. However, the standard retirement age for most government employees in India is 60 years. This applies to employees in various sectors such as central government, state government, public sector undertakings, and autonomous bodies. It's important to note that there may be exceptions or variations in retirement age for certain positions or categories of employees.

Correct Answer: (11, 36, 5)

Solution : Given:
(9, 16, 5); (7, 9, 4)

Here, (9, 16, 5)→(9 – 5)² = (4)² = 16
(7, 9, 4)→(7 – 4)² = (3)² = 9

Let's check the options –
First option: (14, 64, 7)→(14 – 7)² = (7)² = 49 ≠ 64
Second option: (14, 100, 5)→(14 – 5)² = (9)² = 81 ≠ 100
Third option: (11, 36, 5)→(11 – 5)² = (6)² = 36
Fourth option: (12, 66, 4)→(12 – 4)² = (8)² = 64 ≠ 66

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, 31, 3)

Solution : Given:
(2, 28, 4); (3, 22, 2)

The logic here is – (The first number × 4) + (The third number × 5) = The second number
(2, 28, 4)→(2 × 4) + (4 × 5) = 8 + 20 = 28
(3, 22, 2)→(3 × 4) + (2 × 5) = 12 + 10 = 22

Let's check the options –
First option: (6, 29, 3)→(6 × 4) + (3 × 5) = 24 + 15 = 39 ≠ 29
Second option: (1, 10, 5)→(1 × 4) + (5 × 5) = 4 + 25 = 29 ≠ 10
Third option: (7, 32, 2)→(7 × 4) + (2 × 5) = 28 + 10 = 38 ≠ 32
Fourth option: (4, 31, 3)→(4 × 4) + (3 × 5) = 16 + 15 = 31

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