https://youtu.be/BEuk1P0EylQ

Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only real root of P'(x) =0 . If P(-1) lt P(1), then in the interval [-1,1]

P(x) is a non-zero polynomial such that P(0)=0 and P(x^3)=x^4P(x),P'(1)=7 and int_0^1P(x)=1.5 then int_0^1P(x) P'(x) dx =

The value of p and q(p!=0,q!=0) for which p ,q are the roots of the equation x^2+p x+q=0 are (a) p=1,q=-2 (b) p=-1,q=-2 (c) p=-1,q=2 (d) p=1,q=2

If p _(1) =0 and p _(2) =0 be two non-parallel planes, then the equation p_(1) + lamda p _(2) =0, lamda in R represents the family of all planes through the line of intersection of the planes p _(1) =0 and p _(2) =0 except the plane :

If E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(2))=0.2 and P(E_(1)nnE_(2))=0.1, then find: (i) P(barE_(1)nnE_(2)) (ii) P(E_(1)nnbarE_(2))

If alpha , beta are the roots of the quadratic equation (p^2 + p + 1) x^2 + (p - 1) x + p^2 = 0 such that unity lies between the roots then the set of values of p is (i) O/ (ii) p in (-infty,-1) cup (0,infty) (iii) p in (-1,infty) (iv) (-1,1)

If E and F are independent events such that 0 lt P(E) lt 1 and 0 lt P(F) lt 1 , then

If A and B are two events suc that P(A) gt 0 and P(A)+P(B) gt 1, then P(B//A)ge1-(P(B'))/(P(A))

If one root is square of the other root of the equation x^2+p x+q=0, then the relation between pa n dq is p^3-q(3p-1)+q^2=0 p^3-q(3p+1)+q^2=0 p^3+q(3p-1)+q^2=0 p^3+q(3p+1)+q^2=0

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1