If "PATNA" is written as "ANTAP", how is "RAJASTHAN" written?

Correct — B.
Rule: write the word backwards: the last letter comes first, the first letter goes last.

PATNA → A N T A P = ANTAP
RAJASTHAN → N A H T S A J A R

That reads NAHTSAJAR → option (b).

Why the others are wrong

• (a)
  NAHSTAJAR — NAHSTAJAR has S before T. Read backwards, RAJASTHAN reaches T (letter 6) before S (letter 5), so the fourth and fifth letters of the code are T, S.
• (c)
  NAHTSRAJA — NAHTSRAJA reverses only STHAN and then copies RAJA forwards. Reversal turns the whole word round, so RAJA must flip too, ending the code in AJAR.
• (d)
  NAHTSAJRA — NAHTSAJRA swaps the last two letters. RAJASTHAN begins R, A, so written backwards it must end A, R: the code closes on JAR, not JRA.

A reversal code keeps every letter and changes only the order: letter 1 goes to the end, letter 2 to second-last, and so on. Test it on the given pair first: P-A-T-N-A read from the right is A-N-T-A-P.

Nothing moves along the alphabet, so the code holds exactly the letters of RAJASTHAN: three As and one each of R, J, S, T, H, N. All four options pass that test, so only the order separates them.

Key facts

• Reversal of a nine-letter word takes positions 9-8-7-6-5-4-3-2-1.
• A pure rearrangement keeps every letter, so all four options here are anagrams of RAJASTHAN.
• Check the ends first: the code must start with the word's last letter (N) and end with its first two letters backwards (A, R).

Common traps

• Reversing only the second chunk (STHAN → NAHTS) and copying RAJA forwards, which gives NAHTSRAJA
• Swapping neighbouring letters while reading a long word backwards: T and S in the middle, A and R at the end

No directly related past PYQ was found.