Question-1 The statement P (n ): ( 1 x 1! ) + (2 x 2! ) + (3 x 3! ) + .... + ( n x n !) = ( n + 1 )! - 1' is _____.

Question-2 If n > 1 and x ≠ 0. then expression ( 1 + x)^{n} - nx -1 is divisible by _________.

Question-3 If equation (5 + 2 √6)^{n} = i + f, Where i ∈ N, 0 < f < 1, then value of ( i + f ) ( 1 - f) is ______.

Question-4 The solution of the inequality is.

Question-5 The unit digit in the number 7^{126} is ______.

Question-6 The total number of proper divisors of 38808 is _______.

Question-7 If log_{2} 7 = x, then x is ________.

Question-8 The value of ( 1 x 2 x 3 ) + ( 2 x 3 x 4 ) + ( 3 x 4 x 5 ) + ..... + n terms is ______.

Question-9 The remainder, when number 5^{99} is dividend by 13, is ______.

Question-10 By the method of mathematic induction, the inequality 2n + 7 ≤ ( n + 3 ) ^{2} is true ?