Complex Numbers(p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Find k if following functions are continuous at the points indicated against them.

\begin{aligned}
& \mathrm{f}(\mathrm{x})=(1+k x)^{\frac{1}{x}}, \text { for } \mathrm{x} \neq 0 \\
& =e^{\frac{3}{2}}, \text { for } \mathrm{x}=0, \text { at } \mathrm{x}=0
\end{aligned}

Thane is the 20th station from C.S.T. If a passenger can purchase a ticket from any station to any other station, how many different tickets must be available at the booking window?

A hundred students appeared for two examinations. 60 passed the first, 50 passed the second, and 30 passed in both. Find the probability that students selected at random: failed in both examinations.

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

Insert two numbers between 1 and -27 so that the resulting sequence is a G.P.

Differentiate the following functions w.r.t. x. : \begin{equation}
\frac{1}{e^x+1}
\end{equation}

The letters of the word LOGARTHM are arranged at random. Find the probability that: Vowels are always together.