If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by
x2
x3
x5
x7
The total number of proper divisors of 38808 is
80
70
60
50
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 3 > ( x2 + x + 2 ), then
x < 2
x ≥ 2
x > 2
x ≤ 2
If x > -1, then the statement ( 1 + x ) n > 1 + nx is true for
All n < 1
All n > 1
All n ∈ N
All n > 1 provided x ≠ 0
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 ≥ 3
n ∈ I
n < 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
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
P (n) = P (n + 1 ) for all natural numbers n, then P (n) is true ?
For all n
For all n > 1
For all n > m
Nothing can be said
