`" If "_(" X ")" is "B(x,n,(1)/(3)),P(x>=1)>0.8" ,the least value of "n`

For X ~ B(n , P) and P(X=x) = ""^(8)C_(x) (1//2)^(x) (1//2)^(8-x) then state values of n and P

f(x)=e^(x)-e^(-x)-2sin x-(2)/(3)x^(3). Then the least value of n for which (d^(n))/(dx^(n))f(x)|_(x=0) is nonzero is 5(b)6(c)7(d)8

If (e^(x))/(1-x) = B_(0) +B_(1)x+B_(2)x^(2)+...+B_(n)x^(n)+... , then the value of B_(n) - B_(n-1) is

Let X be the number of successes in 'n' independent Bernoulli trials with probability of success p=(3)/(4) , the least value of 'n' so that P(x ge 1) ge 0.9375 is

If lim_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p , then p is equal to

If cos x*cos2x*cos4x*cos8x for x=(2 pi)/(3) is a rational number (p)/(q) where p,q in N .then the least value of (p+q) is

If (1 + x + x^(2) + x^(3))^(n)= a_(0) + a_(1)x + a_(2)x^(2) + a_(3) x^(3) +...+ a_(3n) x^(3n) , then the value of a_(0) + a_(4) +a_(8) + a_(12)+….. is