Let t be a positive integer and `|((2t-1),m^2-1,cos^2(m)),(mC_t,2^m,cos^2(m)),(1,m+1,cos(m^2))|` then the value of `sum_(t=0)^m Delta_t` is equal to

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Deltar = |[2r-1,.^mC_r,1],[m^2-1,2^m,m+1],[sin^2(m^2),sin^2m,sin(m^2)]| . Then the value of sum_(r=0)^m Deltar

Let m be a positive integer and Delta r=det[[m^(2)-1,*^(m)C_(r),1m^(2)-1,2^(m),m+1sin^(2)(m^(2)),sin^(2)m,sin(m^(2))]] of sum_(r=0)^(m)Delta r

Let m be a positive integer and Delta_(r)=|(2r-1,""^(m)C_(r),1),(m^(2)-1,2^(m),m+1),(sin^(2)(m^(2)),sin^(2)(m),sin^(2)(m+1))|(0lerlem) Then the value of sum_(r=0)^(m)Delta_(r ) is given by a)0 b) m^(2)-1 c) 2^(m) d) 2^(m)sin^(2)(2^(m))

If Delta_r= |[2r-1, mC_r,1],[m^2-1,2^m,m+1],[m^2+m+1,2^m+1,m+2]| , then sum_(r=0)^m Delta_r=

If m and n are positive integers and f(x)=int_(1)^(x)(t-a)^(2n)(t-b)^(2m+1)dt,a!=b then

If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -

Suppose m and n are positive integers and let S=sum_(k=0)^(n)(-1)^(k)(1)/(k+m+1)(nC_(k)) and T=sum_(k=0)^(m)(-1)^(k)1(k+n+1)(mC_(k)) then S-T is equal to