By the method of mathematical 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 expression 3 2n + 2 - 8n - 9 is divisible by 64 for all ______.
n ∈ N
n ∈ N, n < 2
n ∈ N n ≥ 2
n ∈ N, n > 2
If x > y > 0 where a > 1, then ?
log ax > log ay
logax < logay
logax ≥ logay
log ax = log ay
If Pm stands for mPm' then the value of 1 + P1 + 2P2 + 3P3 + ..... + nPn is ______.
n!
n2
( n + 1 )!
( n - 1 ) !
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
By the mathematical induction, the expression 11n+2 + 122n + 1 is divisible by _______.
133
124
114
113
The solution of the inequality 2x2 + x - 15 ≥ 0 is _______.
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 equation (5 + 2 √6)n = i + f, Where i ∈ N, 0 < f < 1, then value of ( i + f ) ( 1 - f) is ______.
0
1
72n
22n
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
