If `x^(2)-63x-64=0` and p and n are integers such that `p^(n)=x`, which of the following CANNOT be a value for p?

P a n d Q are two positive integers such that P Q = 64 . Which of the following cannot be the value of P + Q ? 16 (b) 20 (c) 35 (c) 65

If .^(n)P_(r)=x.^(n-1)P_(r-1) , then which of the following is the value of x?

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

If f(x) =(p-x^n)^(1/n) , p >0 and n is a positive integer then f[f(x)] is equal to

If f'(x)=(x-a)^(2n)(x-b)^(2p+1) , when n and p are positive integers, then :

If f(x)=(p-x^(n))^((1)/(n)),p>0 and n is a positive integer then f[f(x)] is equal to

If n is a natural number and we define a polynomial p_(a)(x) of degree n such that cos n theta=p_(n)(cos theta), then The value of p_(n+1)(x)+p_(n-1)(x)=

Let P(x) be a polynomial such that p(x)-p'(x)= x^(n) , where n is a positive integer. Then P(0) equals-

If a is defined by f (x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n) where n is a non negative integer and a_(0),a_(1),a_(2),…….,a_(n) are real numbers and a_(0) ne 0, then f is called a polynomial function of degree n. For polynomials we can define the following theorem (i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a). (ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0. The factor of the polynomial x^(3)+3x^(2)+4x+12 is