If x > -1, then the statement ( 1 + x ) n > 1 + nx is ture for ________.
All n < 1
All n > 1
All n ∈ N
All n > 1 provided x ≠ 0
The number 101 x 102 x 103 x 104 x ..... x 107 is divisible by ______.
4000
4050
5040
5050
All possible two - factor products are from the digits 1,2,3,4, ...., 200. The number of factors out of the total obtained, which are multiples of 5, is _______.
8040
7180
6150
4040
The value of ( 1 x 2 x 3 ) + ( 2 x 3 x 4 ) + ( 3 x 4 x 5 ) + ..... + n terms is ______.
If Pm stands for mPm' then the value of 1 + P1 + 2P2 + 3P3 + ..... + nPn is ______.
n!
n2
( n + 1 )!
( n - 1 ) !
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
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
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
If x 3 > ( x2 + x + 2 ), then ?
x < 2
x ≥ 2
x > 2
x ≤ 2