If `Delta_(r)=|(2^(r)-1,2.3^(r)-1,4.5^(r)-1),(alpha,beta,gamma),(2^(n)-1,3^(n)-1,5^(n)-1)|` then find the value of `Delta`.

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))

Let Delta_(r)=|(r-1,n,6),((r-1)^(2),2n^(2),4n-2),((r-1)^(3),3n^(3),3n^(2)-3n)| Show that sum_((r=1)) ^(n) Delta_(r) is constant.

Find the value of r if 5P_r = 6P_(r-1)

If .^(n)C_(r - 1) = 28, .^(n)C_(r) = 56 and .^(n)C_(r + 1) = 70 , then the value of r is equal to

If Delta_(k) = |(1,n,n),(2k,n^(2)+n+1,n^(2)+n),(2k-1,n^(2),n^(2)+n+1)|and sum_(k=1)^(n)Delta_(k)=56. then n equals a)4 b)6 c)8 d)None of these

If 8! ((1)/(3!) + (5)/(4!) ) = ""^(9) P_(r) , then the value of r is

Let Delta_(1)=|(ap^(2),2ap,1),(aq^(2),2aq,1),(ar^(2),2ar,1)|andDelta_(2)=|(apq,a(p+q),1),(aqr,a(q+r),1),(arp,a(r+p),1)| then a) Delta_(1)= Delta_(2) b) Delta_(2)=2Delta_(1) c) Delta_(1) = 2Delta_(2) d) Delta_(1) +2Delta_(2) = 0