MCQ
Value of $\sum^{\infty}_{\text{k}=1}\sum^{\text{k}}_{\text{r}=0}\frac{1}{3^{\text{k}}}\big({^\text{k}}\text{C}_{\text{r}}\big)$ is:
- A$2$
- B$\frac{2}{3}$
- C$\frac{1}{3}$
- D$\text{None of these}$
Solution:
$\sum\frac{1}{3^{\text{k}}}{^\text{k}}\text{C}_{\text{r}}$
$=\frac{1}{3^{\text{k}}}\sum{^\text{k}}\text{C}_{\text{r}}$
$=\frac{2^{\text{k}}}{3^{\text{k}}}$
This is a G.P
Therefore, the sum of the series will be
$\text{S}=\frac{\frac{2}{3}}{1-\frac{20}{3}}=2$
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Distance of the point (3, 4, 5) from the origin (0, 0, 0) is:
$\sqrt{50}$
$3$
$4$
$5$
$1$
$\frac{1}{2}$
$\frac{1}{\sqrt{\text{2}}}$
$0$
$\sin\text{x}+\text{i}\cos2\text{x}$ and $\cos\text{x}-\text{i}\sin2\text{x}$ are conjugate to each other for:
$\text{x}=\text{n}\pi$
$\text{x}=\Big(\text{n}+\frac{1}{2}\Big)\frac{\pi}{2}$
$\text{x}=0$
no value of x
The equation of a straight line that passes through the point (3, 4) and perpendicular to the line 3x + 2y + 5 = 0 is: