अंकों 1, 2, 3 और 4 से, इन अंकों में से किसी अंक को बिना दोहराए, बनी उन सभी 4-अंकों की संख्याओं का, जो 2000 से कम हैं, योगफल क्या है ?

Correct Answer: (A) 7998

For a 4-digit number formed from digits 1, 2, 3, and 4 to be strictly less than 2000, its thousands digit must be 1. The remaining positions are filled by distinct permutations of $\{2, 3, 4\}$, yielding $3! = 6$ such numbers: 1234, 1243, 1324, 1342, 1423, and 1432. The thousands digits sum to $6$$\times$ 1000 = 6000. In each of the hundreds, tens, and units places, each of the digits 2, 3, and 4 appears $6/3 = 2$ times (summing to $2$$\times$ (2 + 3 + 4) = 18). Thus, the total sum is $6000 + 18$$\times$ 100 + 18 $\times$ 10 + 18 $\times$ 1 = 6000 + 1800 + 180 + 18 = 7998.