9 16 23 30 37 44 51

This is an alternating addition series, with a random number, 21, interpolated as every third number. The addition series alternates between adding 3 and adding 4. The number 21 appears after each number arrived at by adding 3.

This is an alternating subtraction series with the interpolation of a random number, 5, as every third number. In the subtraction series, 3 is subtracted, then 4, then 3, and so on.

Clearly, India needs to have military force to defend itself against the threat of other military powers in the world. So, none of the arguments holds strong.

The Public Distribution System is indeed necessary to provide basic amenities to the economically backward sections of population. So, argument I is vague. Also, if the Objectives of a system are not fulfilled because of corruption, then getting rid of the system is no solution. Instead, efforts should be made to end corruption and extend its benefits to the people for whom it is meant. So, argument II also does not hold,

Clearly, higher education is not the cause of unemployment. In fact, it has created greater job opportunities. So, argument II is vague. Also, higher education promotes the country's development. So, argument I holds.

This is a simple addition series, which begins with 2 and adds 6.

In this alternating repetition series, a random number, 33, is interpolated every third number into a simple addition series, in which each number increases by 2.

This is an alternating addition series with a random number, 4, interpolated as every third number. In the main series, 1 is added, then 2 is added, then 1, then 2, and so on.

This is an alternating subtraction series with repetition. There are two different patterns here. In the first, a number repeats itself; then 3 is added to that number to arrive at the next number, which also repeats. This gives the series 17, 17, 20, 20, 23, and so on. Every third number follows a second pattern, in which 3 is subtracted from each number to arrive at the next: 34, 31, 28.

This is an alternating addition and subtraction series. In the first pattern, 2 is added to each number to arrive at the next; in the alternate pattern, 6 is subtracted from each number to arrive at the next.