### Mathematics - Mathematical Induction and Its Application

#### Question - 1

P(n) is the statement "n2-n+41(n $\epsilon$ N),is a prime".Then which of the following is not true?

• A P(1)
• B P(2)
• C P(3)
• D P(4)

#### Question - 2

For all n $\epsilon$ ,$\frac { { n }^{ 7 } }{ 7 } +\frac { { n }^{ 5 } }{ 5 } +\frac { 2{ n }^{ 3 } }{ 3 } -\frac { { n }^{ } }{ 105 }$ ,is

• A a positive integer
• B a negative integer
• C 0
• D a rational number

#### Question - 3

$p^{n+1}+(p+1)^{2n-1}\ \ \ (n\epsilon N)$ ,is divisible by

• A p
• B p2
• C p2+p+1
• D p2+p

#### Question - 4

n(n2-1) is divisible by 24, when n is

• A even
• B odd
• C any integer
• D None of these

#### Question - 5

The smallest positive integer for which the inequality $n!<\left( \frac { n+1 }{ 2 } \right)$ is true,is

• A 1
• B 2
• C 3
• D 4

#### Question - 6

The greatest positive integer which divides (n+1)(n+2)(n+3)...(n+k) for all n $\epsilon$ N. is

• A k
• B k!
• C (k+1)!
• D (k+2)!

#### Question - 7

The number 2.7n+3.5n-5(n $\epsilon$ N) is divisible by

• A 24
• B 36
• C 48
• D None of these

#### Question - 8

The number np - n ( n?$\epsilon$? N, P is a prime number ) is a divisible by

• A n
• B n2
• C p
• D p2

#### Question - 9

x(xn-1-nan-1) + an(n-1) is a divisible by (x-a)k for all n>1,then k equals

• A 4
• B 3
• C 2
• D None of these

#### Question - 10

Which one of the following is true for all n $\epsilon$ N?

• A 1+3+5+....+(2n-1) = n2
• B 1+3+5+...+(2n-1) = n
• C 1+3+5+....+(2n-1) = n3
• D None of the above