41. The answer key to a hypothetical MCQ (Multiple Choice Questions) based exam (every question having four options a, b, c and d) followed the pattern a, b, c, d, a, a, b, b, c, c, d, d, a, a, a, b, b, b and so on… (answer to 1st question being a, to 2nd being b and so on as per the pattern given above). If the paper had 120 questions in total, what should have been the answer to the last question ?

42. Alan’s bag had a three-digit numeric lock. He set the password such that it was a palindrome and hence easy to remember. But he is not able to recall it precisely at the moment. But, he does remember the following with certainty
I. The middle digit was an even prime.
II. The sum of digits was divisible by 7 or 9.
III. The sum of squares of digits was less than 100.
Which of the following digits when entered, might open Alan’s bag ?

43. A bug and a housefly are resting at one corner of a cubical room with 3 m long sides. Both of them see a prey located at the diagonally opposite corner of the room at the same time and immediately start running/flying towards it. While the bug has to move on the floor or the walls and cannot fly, there is no such restriction for the housefly. Based on this information, and the assumption that they take up the shortest possible routes, which of the following statements is definitely correct ?

44. How many pairs of letters are there in these words which have as many letters between them in the word as in the alphabet ?

45. What is the value of ‘a’ ?
Statement I : a² + 6a + 9 = 0
Statement II : a > 0