If `(1-p)(1+3x+9x^2+27x^3+81x^4+243x^5)=1-p^6, p ne 1` then the value of `p/x` is

If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value of p/xi s 1/3 b. 3 c. 1/2 d. 2

If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], then the value of (p+q) is_______>

X is a discrete random variable which takes the values of 0,1,2 and P (X=0) = (144)/(169) P(X=1) = (1)/(169) then the value of P(X=2) is ………. .

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If lim_(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1 , then the value of p is___________.

Let f(x)=[(1-sinpix)/(1+cos2pix), x<1/2 and p , x=1/2 and sqrt(2x-1)/(sqrt(4+sqrt(2x-1))-2) .Determine the value of p, if possible, so that the function is continuous at x = 1/2 .

If p_(1)^(x_(1))timesp_(2)^(x_(2))timesp_(3)^(x_(3))timesp_(4)^(x_(4))=11340 where p_(1), p_(2), p_(3), p_(4) are primes in ascending order and x_(1), x_(2), x_(3), x_(4) are integers, find the value of p_(1), p_(2), p_(3), p_(4) and x_(1), x_(2), x_(3), x_(4) .

Polynomial P(x) is divided by (x-3) , the remainder if 6.If P(x) is divided by (x^2-9) , then the remainder is g(x) . Then the value of g(2) is ___________.

If the events A and B are mutually exclusive events such that P(A) = (3x + 1)/(3) and P(B) = (1 - x)/(4) , then the set of possible real values of x lies in the interval

Let P(x) = x^10+ a_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^2 be a polynomial with real coefficients. If P(1) and P(2)=5 , then the minimum-number of distinct real zeroes of P(x) is