I. E irodav

In Figure, D E || A C and D F || A E . Prove that (E F)/(B F)=(E C)/(B E) .

If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1))

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) or, (dy)/(dx)+e^(y-x)=0

If E_(1) and E_(2) are two events such that P(E_(1))=1//4 , P(E_(2)//E_(1))=1//2 and P(E_(1)//E_(2))=1//4 , then

If E' denote the complement of an event E , what is the value of P(E')+P( E )?

If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)+e^(y-x)=0

If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

An electron and a photon possess the same de Broglie wavelength. If E_e and E_ph are, respectively, the energies of electron and photon while v and c are their respective velocities, then (E_e)/(E_(ph)) is equal to