If area of pentagon PQRST be 7 ,where P(-1,-1),Q(2,0),R(3,1),S(2,2) and T(-1,t),t>0, then the value of t is

Find t if the area of the pentagon ABCDE be 45/2 where a=(1,3), B=(-2,5), C=(-3,-1) D=(0,-2) and E=(2,t).

Let x=2(t+(1)/(t)) and y=2(t-(1)/(t)),t!=0. Then,the value of (dy)/(dx) at t=2 is

Let S(t) be the area of the Delta OAB with O(0,0,0),A(2,2,1) and B(t,1,t+1) The value of the definite integral int_(1)^(e)(S(t))^(2)Intdt, is equal to ((e^(3)+a)/(b^(2))) where a,b in N, find (a+b).

Let T_(r) be the r^(th) term of a sequence, for r=1,2,3,......... If 3T_(r+1)=T_(r) and T_(7)=(1)/(243) then the value of sum_(r=1)^(oo)(T_(r).T_(r+1)) is :

"Let "plambda^(4) + qlambda^(3) +rlambda^(2) + slambda +t =|{:(lambda^(2)+3lambda,lambda-1, lambda+3),(lambda+1, -2lambda, lambda-4),(lambda-3, lambda+4, 3lambda):}| be an identity in lambda , where p,q,r,s and t are constants. Then, the value of t is..... .

If a circle cuts a rectangular hyperbola xy=1 in four points P,Q,R,S and the parameters of these four points be t_(1),t_(2),t_(3) and t_(4) respectively and -20t_(1)t_(2)t_(3)t_(4)=k , then value of k equals

If t-1 and -t-1,t in R are the roots of (a+2)x^(2)+2ax-1=0, then complete set of values of 'a' is