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
If x 3 > ( x2 + x + 2 ), then ?
x < 2
x ≥ 2
x > 2
x ≤ 2
The unit digit in the number 7126 is ______.
1
3
9
5
If n > 1 and x ≠ 0. then expression ( 1 + x)n - nx -1 is divisible by _________.
x2
x3
x5
x7
If equation (5 + 2 √6)n = i + f, Where i ∈ N, 0 < f < 1, then value of ( i + f ) ( 1 - f) is ______.
0
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
The solution of the inequality is.
( 2/3, 8 )
( -2, 8/3 )
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
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 remainder, when number 599 is dividend by 13, is ______.
2
8
12
32
