For all p, such that `1<=p<=100` if `n(A_p)=p+2` and `A_1subA_2subA_3sub......subA_(100)` and `nnn_(p=1)^(100)A_p=A` then `n(A)=`

Find all cubic polnomials p(x) such that (x-1)^(2) is a factor of p(x)+2 and (x+1)^(2) is a factor of p(x)-2 .

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals

Let P be a matrix of order 3 x 3 such that all the entries in P are from the set {-1,0,1} . Then, the maximum possible value of the determinant of P is _____

Let p_(1),p_(2),p_(3) be primes with p_(2)!=p_(3), such that 4+p_(1)p_(2) and 4+p_(1)p_(3) are perfect squares.Find all possible values of p_(1),p_(2),p_(3)

If x is real , show that each of the following expressions is capable of assuming all real values: p^2/(1-x)-q^2/(1+x)

Let p and q be real numbers such that the function f(x)={{:(p^(2)+qx","xge1),(-5px^(2)-6","xlt1):} is derivable for all x in R . Then sum of all possible values of p is

Let p and q be real numbers such that the function f(x)={{:(p^(2)+qx","xge1),(-5px^(2)-6","xlt1):} is derivable for all x in R . Then sum of all possible values of p is

Let P be a matrix of order 3xx3 such that all the entries in P are from the set {-1,\ 0,\ 1} . Then, the maximum possible value of the determinant of P is ______.