" If "(a+be^(y))/(a-be^(y))=(b+ce^(y))/(b-ce^(y))=(c+de^(y))/(c-de^(y))," then "a,b,c,d" are in "

a^(x) = b^(y) = c^(z) = d^(t) and a,b,c,d are in G.P. , then x,y,z,t are in :

If (a+b)/(c+d)=(x)/(y) , then y=_____

If a^(x) = b^(y) = c^(z) = d^(t) and a ,b ,c d are in G.P . Then x, y, z, t are in

If a ,\ b ,\ c >0\ a n d\ x ,\ y ,\ z in R , then the determinant |\ \ (a^x+a^x)^2(a^x-a^(-x))^2 1(b^y+b^(-y))^2(b^y-b^(-y))^2 1(c^z+c^(-z))^2(c^z-c^(-z))^2 1| is equal to- a. a^x b^y c^x b. a^(-x)b^(-y)c^(-z)\ c. a^(2x)b^(2y)c^(2x) d. zero

y=ae^x+be^(2x)+ce^(3x) , a,b,c are arbitrary constants.

The solution of (dy)/(dx)=(1)/(2x-y^(2)) is given by , (A) y=Ce^(-2x)+(1)/(4)x^(2)+(1)/(2)x+(1)/(4)," 4"(1)/(2)," (B) "x=Ce^(-y)+(1)/(4)y^(2)+(1)/(4)y+(1)/(2)," (C) "x=Ce^(y)+(1)/(4)y^(2)+y+(1)/(2)," (D) "x=Ce^(2y)+(1)/(2)y^(2)+(1)/(2)y+(1)/(4)

If (a)/(y+z-x)=(b)/(z+x-y)=©/(x+y-z) then show that (x)/(b+c)=(y)/(c+a)=(z)/(a+b)

Let Delta(y)=|{:(y+a,y+b,y+a-c),(y+b,y+c,y-1),(y+c,y+d,y-b+d):}| and, int_(0)^(2) Delta(y)dy=-16 , where a,b,c,d are in A.P., then the common difference of the A.P. is equal to