Let `px^4+qx^3+rx^2+sx+t=|{:(x^2+3x,x-1,x+3),(x+1,-2,x-4),(x-3,x+4,3x):}|` be an identity where p,q,r,s and t are constants, then the value of s is equal to

If px^4+qx^3+rx^2+sx+t=|(x^2+3x,x-1,x+3),(x+1,2-x,x-3),(x-3,x+4,3x)| then t is equal to

If px^(4)+qx^(3)+rx^(2)+sx+t=|{:(x^(2)+3x,x-1,x+3),(x^(2)+1,2-x,x-3),(x^(2)-3,x+4,3x):}| then t is equal to

|[x^2+3,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4,3x]|=px^4+Qx^3+rx^2+sx+t

If p x^4\ \ q x^3+r x^2+s x+t=|x^2+3xx-1x+3x+1 2-xx-3x-3x+4 3x|t h e n\ is equal to- a. b. c. d. none

If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}| , where p is a constant, then (d^(3))/(dx^(3))(f(x)) , is

Suppose |{:(1+x,x,x^2),(x,1+x,x^2),(x^2,x,1+x):}|=Px^5+Qx^4+Rx^3+Mx^2+Nx+Z be an identify in x AA ,P,Q,R,M,N,Z independent of x, then

If x^(2)-2x-1 is a factor of px^(3)+qx^(2)+1 , (where p , q are integers) then find the value of p +q.

If |(x^2+x, x-1, x+1), (x, 2x, 3x-1), (4x+1, x-2, x+2)|= px^4 +qx^3+rx^2+sx+t be n identity in x and omega be an imaginary cube root of unity, (a+bomega+comega^2)/(c+aomega+bomega^2)+(a+bomega+comega^2)/(b+comega+aomega^2)= (A) p (B) 2p (C) -2p (D) -p