Simplify the following: `4m^2+3n^2-(6m^2+7n^2)`

Simplify in following. 4m^2 + 3n^2 - (6m^2 + 7n^2)

Simplify the following : (4m + 5n)^2 + (5m + 4n)^2

simplify the expression: (7m – 8n)^2 + (7m + 8n)^2

Let's write the value of (m^2 + n^2) (m^3 + n^3) by calculation if m + n = 5 and mn = 6.

Explain, given reasons, which of the following sets of quantum numbers are not possible. (1) n=0,l=0,m_(l)=0,m_(S)+(1)/(2) (2) n=1,l=0,m_(l)=0,m_(S)=-(1)/(2) (3) n=1,l=1,m_(l)=0,m_(S)=+(1)/(2) (4) n=2, l=1, m_(1)=0,m_(S)=-(1)/(2) (5) n=3, l=3, m_(l)=-3,m_(S)=+(1)/(2) (6) n=4, l=1, m_(l)=0,m_(S)=+(1)/(2) .

If m^2+m^('2)+2mn'cos theta =1 n^2+n^('2)+2"nn"' cos theta=1 and mn +m'n'+(mn'+m'n)cos theta=0 then show that m^2+n^2=m^('2) +n^('2) =cosec^2 theta .

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot

Simplify : (2^n.6^(m+1).10^(m-n).15^(m+n-2))/(4^m.3^(m+n).25^(m-1)) .