If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
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 expression 3 2n + 2 - 8n - 9 is divisible by 64 for all ______.
n ∈ N, n < 2
n ∈ N n ≥ 2
n ∈ N, n > 2
The number 101 x 102 x 103 x 104 x ..... x 107 is divisible by ______.
4000
4050
5040
5050
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 value of ( 1 x 2 x 3 ) + ( 2 x 3 x 4 ) + ( 3 x 4 x 5 ) + ..... + n terms is ______.
By the method of mathematic induction, the inequality 2n + 7 ≤ ( n + 3 ) 2 is true ?
For all n ∈ N
For all n < 1
Only when n is odd
Only when n is even
The total number of proper divisors of 38808 is _______.
80
70
60
50
If x 3 > ( x2 + x + 2 ), then ?
x < 2
x ≥ 2
x > 2
x ≤ 2
If n is a positive integer, then n ( n2 - 1 ) ( n2 - 4 ) is divisible by _______.
4 x 5 x 6
5 x 6 x 7
2 x 4 x 6
3 x 4 x 5
