28)) If `a^2+b^2=1, m^2 +n^2=1, then`

If a^(2)+b^(2)=1,m^(2)+n^(2)=1, then which of the following is true for all values of m,n,a,b

For the natural number m, n, if ( 1- y ) ^(m) (1 + y) ^( n) =1 + a _(1) y + a _(2) y ^(2) + ...+ a _( m + n) y ^( m +n) and a _(1) = a _(2) = 10, then the value of (m+n) is equal to :

Let A=[(l,m,n),(p,q,r),(1,1,1)] and B=A^(2) . If (l-m)^(2)+(p-q)^(2)=9, (m-n)^(2)+(q-r)^(2)=16, (n-l)^(2)+(r-p)^(2)=25 , then the value of |det(B)-140| is_______

The sides of a triangel are such that a/(1+m^2+n^2)=b/(m^2+n^2)=c/((1-m^2)(1+n^2)) , prove that A=2tan^-1 m/n, B=2tan^-1 (mn) and /_\ = (mnbc)/(m^2+n^2)

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

If (l_(1), m_(1), n_(1)) , (l_(2), m_(2), n_(2)) are D.C's of two lines, then (l_(1)m_(2)-l_(2)m_(1))^2+(m_(1)n_(2)-n_(1)m_(2))^2+(n_(1)l_(2)-n_(2)l_(1))^2+(l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2))^2=

If m = sqrtfrac(n)(n+1/2) and m = 1/2, then n =

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then (a^2)/8 is equal to (a) m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c) m_1^2+m_3^2-2m_2^2 (d) none of these