एक गुणोत्तर श्रेढ़ी में यदि `T_l=l` तथा `T_m=m` तो सिद्ध कीजिये कि इसका n वा पद `(l^(n-m)/m^(n-l))^(1/(l-m))` होगा

(x^l /x^m)^n.(x^m/x^n)^l. (x^n/x^l)^m=

(log x)/(l+m-2n)=(log y)/(m+n-2l)=(log z)/(n+l-2m)

If a=x^(m+n)\ y^l,\ b=x^(n+l)\ y^m and c=x^(l+m)y^n , prove that a^(m-n)\ b^(n-l)\ c^(l-m\ )=1

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

Workout the following divisions : 54mnl (l+m) (m + n) (u +l) ÷ (81 mn ( l+ m)(n+l))

(a^n/a^m)^(m+n)xx(a^l/a^n)^(n+l)xx(a^m/a^l)^(l+m) =_____

Explain giving reasons which of the following sets of quantum number are not possible (a ) n=0, l =0 m_(l) = 0, m_(s ) =+ (1)/(2) ( b) n=1 , l = 0 m_(l) = 0, m_(s ) = - (1)/(2) ( c) n=1 , l = 1, m_(l ) = 0, m_(s ) = + (1)/(2) (d ) n= 2, l = 1, m_(l ) = 0, m_(s ) = (1) /(2) ( e) n=3, l = 3, m_(l) = 3, m_(s ) = + (1)/(2) (f ) n=3, l = 1, m_(l) = 0, m_(s) l = + (1)/(2)

Differential coefficient of (x^((l + m)/(m - n)))^(1/(n-1)).(x^((m +n)/(n -1)))^(1/(l - m)).(x^((n + 1)/(l - m)))^(1/(m -n)) w.r.t x is

Subtract: 3l(l-4m+5n) ,4l(10n-3m+2l)