Fill up factors :

`l^2 - 1/l^2 = ----`

Factorize (l+m)^(2)-4lm

Write the greatest common factor in each of the term. l ^(2) m ^(2) n, l m ^(2) n ^(2) , l ^(2) mn ^(2)

In a series L_R circuit X_L = R and power factor of the circuit is P_1 . When capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P_2 . Calculate P_1/P_2

Let lim_(x to 0) ("sin" 2X)/(tan ((x)/(2))) = L, and lim_(x to 0) (e^(2x) - 1)/(x) = L_(2) then the value of L_(1)L_(2) is

Let L be the set of all straight lines in plane. l_(1) and l_(2) are two lines in the set. R_(1), R_(2) and R_(3) are defined relations. (i) l_(1)R_(1)l_(2) : l_(1) is parallel to l_(2) (ii) l_(1)R_(2)l_(2) : l_(1) is perpendicular to l_(2) (iii) l_(1) R_(3)l_(2) : l_(1) intersects l_(2) Then which of the following is true ?

If c is small in comparision with l then ((l)/(l+c))^((1)/(2))+((l)/(l-c))^((1)/(2))=

Show that the matris [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] is orthogonal, if l_(1)^(2) + m_(1)^(2) + n_(1)^(2) = Sigmal_(1)^(2) = 1 = Sigma l_(2)^(2) = Sigma_(3) ^(2) and l_(1) l_(2) + m_(1)m_(2) + n_(1) n_(2) = Sigma l_(1)l_(2) =0 = Sigma l_(2)l_(3) = Sigma l_(3) l_(1).