71). \( \Large 7^{12}-4^{12} \) is exactly divisible by which of the following number?
| A). 34 |
| B). 33 |
| C). 36 |
| D). 35 |
|
72). If N, (N + 2) and (N + 4) are prime numbers, then the number of possible solutions for N are
| A). 1 |
| B). 2 |
| C). 3 |
| D). None of these |
|
73). The smallest positive prime (say p )) such that \( \Large 2^{p}-1 \) is not a prime is
| A). 5 |
| B). 11 |
| C). 17 |
| D). 29 |
|
74). If b is the largest square divisor of c and \( \Large a^{2} \) divides c, then which one of the following is correct? (where, a, b and c are integers)
| A). b divides a |
| B). a does not divide b |
| C). a divides b |
| D). a and b are coprime |
|
75). If n is a whole number greater than 1, then \( \Large n^{2}(n^{2}-1) \) is always divisible by
| A). 12 |
| B). 24 |
| C). 48 |
| D). 60 |
|
76). What is the sum of all positive integers lying between 200 and 400 that are multiples of 7?
| A). 8729 |
| B). 8700 |
| C). 8428 |
| D). 8278 |
|
77). Consider the following statements
I. To obtain prime numbers less than 121, we are to reject all the multiples of 2, 3, 5 and 7.
ll. Every composite number less than 121 is divisible by a prime number less than 11.
Which of the statements given above is/are correct?
| A). Only I |
| B). Only II |
| C). Both I and II |
| D). Neither I nor ll |
|
78). Consider the following statements
I. 7710312401 is divisible by 11.
II. 173 is a prime number.
Which of the statements given above is/are correct?
| A). Only l |
| B). Only II |
| C). Both I and II |
| D). Neither I nor ll |
|
79). If k is a positive integer, then every square integer is of the form
| A). Only 4k |
| B). 4k or 4k + 3 |
| C). 4k+1 or 4k+ 3 |
| D). 4k or 4k+1 |
|
80). Every prime number of the form 3k + 1 can be represented in the form 6m + 1 (where k, m are integers), when
| A). k is odd |
| B). k is even |
| C). k can be both odd and even |
| D). No such form is possible |
|
