41. If a2 + b2 + c2 = 1, what is the maximum value of abc ?
42. Which is not a prime number ?
43. If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the followings is also a multiple of 11 ?
44. If the symbol [x] denotes the greatest integer less than or equal to x, then the value of :
$$\left[ {\frac{1}{4}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{1}{{50}}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{2}{{50}}} \right]$$ $$ + $$ $$....$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{{49}}{{50}}} \right]$$
$$\left[ {\frac{1}{4}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{1}{{50}}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{2}{{50}}} \right]$$ $$ + $$ $$....$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{{49}}{{50}}} \right]$$
45. If (12n + 1) is divisible by 13, then n is :
46. By how many of the following numbers is 212 - 1 divisible ?
2, 3, 5, 7, 10, 11, 13, 14
2, 3, 5, 7, 10, 11, 13, 14
47. The least number of five digit is exactly divisible by 88 is :
48. The difference between the squares of any two consecutive integers is equal to :
49. The smallest 6-digit number exactly divisible by 111 is :
50. Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeros will the product end ?
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