Evaluate` ((a^mxxb^n)^pxx(a^pxxb^m)^n)/(axxb)^p`

If a,b and c are three mutually perpendicular vectors, then the projection of the vectors l(a)/(|a|)+m(b)/(|b|)+n((axxb))/(|axxb|) along the angle bisector of the vectors a and b is

Evaluate |{:(""^(m)C_(1),""^(m)C_(2),""^(m)C_(3)),(""^(n)C_(1),""^(n)C_(2),""^(n)C_(3)),(""^(p)C_(1),""^(p)C_(2), ""^(p)C_(3)):}|

If quad ((sin^(m)x)/(sin^(n)x))^(m+n)((sin^(n)x)/(sin^(p)x))^(n+p)((sin^(p)x)/(sin^(m)x))^(p+) then f(x) is equal to

Find the value of sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p)) And hence,find the value of lim_(n rarr oo)(1)/(3^(n))sum_(p=1)^(n)(sum_(m=p)^(n)C_(m)^(m)C_(p))

if the straight line x cos alpha+y sin alpha=p touches the curve x^(m)y^(n)=a^(m+n) prove that p^(m+n)m^(m)n^(n)=(m+n)^(m+n)a^(m+n)sin^(n)alpha cos^(m)alpha

Find the value of ( a^( m^2 - n^2 ))^ (( m^2 + mn + n^2 )/( m + n )) times ( a^( n^2 - p^2 ))^ (( n^2 + np + p^2 )/( n + p ))times ( a^( p^2 - m^2 ))^ (( p^2 + mp + m^2 )/( p + m )) is ( a ) 0 ( b ) 1 ( c ) a^3 ( d ) a

If (2^(m+n))/(2^(n-m))=16,(3^(p))/(3^(n))=81 and a=2^(1//10) then (a^(2m+n-p))/((a^(m-2n+2p))^(-1))=

If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p)) then (dy)/(dx) at e^m^n^p is equal to: e^(m n p) (b) e^(m n//p) (c) e^(n p//m) (d) none

The set A and B has 3 common elements . If n(A) =5 and n(B)=4, then find n(AxxB) and x{(AxxB)nn (BxxA)}