If ${}^{43}{C}_{r-6}{=}^{43}{C}_{3r+1},$ then the value of r is

Q. If ⁴³C_{r − 6} = ⁴³C_{3r + 1} , then the value of r is
(a) 12
(b) 8
(c) 6
(d) 10
(e) 14

Q.

If the mean of the following distribution is 6, find the value of 'p'.

Q. If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is

(a) 12
(b) 8
(c) 6
(d) 3

Q. If $\sum _{r=0}^n\left(\frac{r+2}{r+1}\right)C_r=\frac{2^8-1}{6}$, where $C_r={}^n{C}_r$, then the value of $n$ is

Q. If ${\int }_0^{a^2}\frac{1}{1+16x^2}dx=\frac{\pi }{16}$, then the value of a is