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If n is a positive integer, then n ( n^{2} - 1 ) ( n^{2} - 4 ) is divisible by _______.

(A)

4 x 5 x 6

(B)

5 x 6 x 7

(C)

2 x 4 x 6

(D)

3 x 4 x 5

Question-4

P (n) = P (n + 1 ) for all natural number n, then P (n) is ture ?

(A)

For all n

(B)

For all n > 1

(C)

For all n > m

(D)

Nothing can be said

Question-5

The sum of all positive divisors of 960 is _____.

(A)

3048

(B)

2688

(C)

2248

(D)

1880

Question-6

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 _______.

(A)

8040

(B)

7180

(C)

6150

(D)

4040

Question-7

If x ^{3} > ( x^{2} + x + 2 ), then ?

(A)

x < 2

(B)

x ≥ 2

(C)

x > 2

(D)

x ≤ 2

Question-8

If x > -1, then the statement ( 1 + x )^{ n} > 1 + nx is ture for ________.

(A)

All n < 1

(B)

All n > 1

(C)

All n ∈ N

(D)

All n > 1 provided x ≠ 0

Question-9

The solution of the inequality 2x^{2} + x - 15 ≥ 0 is _______.

(A)

(B)

(C)

(D)

Question-10

By the mathematical induction, the expression 11^{n+2} + 12^{2n + 1} is divisible by _______.

(A)

133

(B)

124

(C)

114

(D)

113

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