MCQ
For two independent events $A$ and $B , P ( A + B )$ is equal to :
- A$P ( A )+ P ( B )- P ( AB )$
- B$P ( A )+ P ( N )- P ( A ) \cdot P ( B )$
- C$P ( A )+ P ( B )+ P ( AB )$
- ✓$P ( A )+ P ( B )$
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If the middle term of $\Big(\frac{1}{\text{x}}+\text{x}\sin\text{x}\Big)^{10}$ is equal to $7\frac{7}{8},$ then value of x is:
$2\text{n}\pi+\frac{\pi}{6}.$
$\text{n}\pi+\frac{\pi}{6}.$
$\text{n}\pi+(-1)^\text{n}\frac{\pi}{6}.$
$\text{n}\pi+(-1)^\text{n}\frac{\pi}{3}.$
Hint: $\text{T}_6=\ ^{10}\text{C}_5\frac{1}{\text{x}^5}.\text{x}^5\ \sin^5\text{x}=\frac{63}{8}\Rightarrow\sin^5\text{x}=\frac{1}{2^5}\sin\frac{1}{2}$
$\Rightarrow\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{6}$
What is the approximate radius of the circle whose equation is $\text{(x}-\sqrt{3)}^2+(\text{y}+2)^2=11?$