MCQ
If n is the positive integer, then 23n - 7n - 1 is divisible by.
- A7
- B10
- C49
- D81
Solution:
Given: 23n - 7n - 1. It can also be written as 8n - 7n - 1
Let 8n - 7n - 1 = 0
So, 8n = 7n + 1
8n = (1 + 7)n
By applying binomial theorem, we get
8n - 1 - 7n = 49 (or) 23n - 7n - 1 = 49
Hence, 23n - 7n - 1 is divisible by 49.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Let Sn denote the sum of the cubes of the first n natural numbers and sn denote the sum of the first n natural numbers. Then $\sum\limits^\text{n}_{\text{r}=1}\frac{\text{S}_\text{r}}{\text{S}_\text{r}}$ equals to:
$\frac{\text{n}(\text{n}+1)(\text{n}+2)}{6}$
$\frac{\text{n}(\text{n}+1)}{2}$
$\frac{\text{n}^{2}+3\text{n}+2}{2}$
None of these.
The locus of the point of intersection of lines $\text{x} \cos \text{a} + \text{y} \sin \text{a = a}$ and $\text{x} \sin \text{a - y} \cos \text{a = b}$ (a is a variable):
The following information relates to a sample of size 60 $\sum\text{x}^2=18000$ and $\sum\text{x}=960,$ then the variance is: