IF `(1+x)^p=3+ 8/3+80/3^3+240/3^4+…….oo, then (1+x)^p=`

If 1+2x +3x^2+4x^3 +…..oo ge 4 then

If x =3 + (4)/(2!) + (8)/(3!) + (16)/(4!) + .....oo then 1/x =

A random variate X takes the values 0, 1, 2, 3 and its mean is 1.3. If P(X= 3) = 2P(X= 1) and P(X= 2) = 0.3 , then P(X= 0) is equal to

If 3+1/4(3+p)+1/(4^2)(3+2p)+... + oo=8 , then p

If P_(1) = 1 - (w)/2 + (w^2)/4 - (w^3)/(8) + ……… oo and P_(2) = (1 - omega^2)/2 { where w is non-real root of equation x^3 = 1 } , then P_(1)P_(2) is equal to

Assertion (A) : x + x^(2)/(1!) + x^(3) /(2!) + (x^4)/(3!) + .....+ oo = f(x) Then the series f(1), f(2) ,f(3) ,f(4) ... Are in G.P . Reason (R) : In the above series f'(x) = e^(x) (x+1)

1 + ""^2C_1x + ""^3C_2 x^2+ ""^4C_3 x^3 + ….. to oo terms can be summed up if

If p_1 and p_2 be the lengths of perpendiculars from the origin on the tangent and normal to the curve x^(2/3)+y^(2/3)= a^(2/3) respectively, then 4p_1^2 +p_2^2 =

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

If P(A) = 3/8 , P(B) = 1/3 and P(AcapB)=1/4 then P(barAcapbarB) equals