If `sinh^3x-cosh^3x=(k e^x-e^(kx))/(1-k)` then `k=` (i)`-1` (ii)`0` (iii)`-3` (iv) `2`

If sin h^(3)x-cos h^(3)x=(ke^(x)-e^(-kx))/(1-k) then k=

If (x^2+kx-3)=(x-3)(x+1) then k=

If sinh(x+y) cosh(x-y)=k (sinh2x+sinh2y) then k =

If cosh^(-1)(k)=log_(e)(3+2sqrt(2)) then k=

If ("coth"(x)+1)/("coth(x)-1)=e^(kx) then k =

If (3x)/((x-k)(x+1))=2/(x-k)+1/(x+1), " then "k=

Equation of pair of lines passing through origin and making an angle (pi)/(4) with the line 3x+2y+4=0 is (3x+2y)^(2)-k(2x-3y)^(2)=0 then k=(i)1 (ii) -1 (iii) 3 (iv) (1)/(3)

If Lt_(xto0) kx cosec x=Lt_(x to0)x" cosec "kx , then k is (i) -1,1 (ii) -2,2 (iii) -(1)/(2),(1)/(2) (iv) none of these

If sinh 9 - k sinh k = ( k + 1 ) sinh ""^3 k, then k =

Lt_(x to 0)(e^(x)+sinx-1)/(3x) is equal to (i) 1/3 (ii) -1/3 (iii) 2/3 (iv) -2/3