If a and b are nataural numbers such that a2 - b2 is a prime number, then _____.
a2 - b2 = 1
a2 - b2 = 2
a2 - b2 = a - b
a2 - b2 = a + b
The total number of proper divisors of 38808 is _______.
80
70
60
50
A student was asked to prove a statement P (n) by method of induction. He proved that P (3 ) is true such that
P (n) = P (n + 1 ) for all ______.
n ∈ N
n ≥ 3
n ∈ I
n < 3
The sum of all positive divisors of 960 is _____.
3048
2688
2248
1880
The unit digit in the number 7126 is ______.
1
3
9
5
If log2 7 = x, then x is ________.
An irrational number
A rational number such that 0 < x < 2
A prime number of the form 7n + 2
A rational number such that 2 < x < 3
The statement P (n ): ( 1 x 1! ) + (2 x 2! ) + (3 x 3! ) + .... + ( n x n !) = ( n + 1 )! - 1' is _____.
True for all values of n > 1
Not true for any value of n
True for all values of n ∈ N
None of these
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
The number 101 x 102 x 103 x 104 x ..... x 107 is divisible by ______.
4000
4050
5040
5050
The expression 3 2n + 2 - 8n - 9 is divisible by 64 for all ______.
n ∈ N, n < 2
n ∈ N n ≥ 2
n ∈ N, n > 2