P (n) = P (n + 1 ) for all natural numbers n, then P (n) is ture ?
For all n
For all n > 1
For all n > m
Nothing can be said
If x > y > 0 where a > 1, then ?
log ax > log ay
logax < logay
logax ≥ logay
log ax = log ay
A student was asked to prove a statement P (n) by method of induction. He proved that P (3 ) is true such thatP (n) = P (n + 1 ) for all ______.
n ∈ N
n ≥ 3
n ∈ I
n < 3
The value of ( 1 x 2 x 3 ) + ( 2 x 3 x 4 ) + ( 3 x 4 x 5 ) + ..... + n terms is ______.
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 solution of the inequality is.
( 2/3, 8 )
( -2, 8/3 )
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
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
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
