Question : If $2A=3B$, then what is the value of $\frac{A+B}{A}$?
Option 1: $\frac{5}{4}$
Option 2: $\frac{2}{3}$
Option 3: $\frac{5}{2}$
Option 4: $\frac{5}{3}$
Correct Answer: $\frac{5}{3}$
Solution : Given: $2A=3B$ ⇒ $\frac{A}{B}=\frac{3}{2}$ Let, $A=3k,B=2k$ $\frac{A+B}{A}=\frac{3k+2k}{3k}=\frac{5}{3}$ Hence, the correct answer is $\frac{5}{3}$.
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Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:
Option 1: $\frac{2}{3 \sqrt{3}}$
Option 2: $\frac{3}{2 \sqrt{3}}$
Option 3: $\frac{5}{2 \sqrt{3}}$
Option 4: $\frac{5}{3 \sqrt{3}}$
Question : If $A+\frac{1}{1+\frac{1}{2+\frac{1}{3}}}=\frac{9}{10}$, then the value of A is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{10}$
Option 3: $\frac{2}{5}$
Option 4: $\frac{1}{10}$
Question : If $3A=5B$, what is the value of $\frac{A+B}{B}$?
Option 1: $\frac{8}{3}$
Option 2: $\frac{8}{5}$
Option 3: $\frac{5}{8}$
Question : If $a-\frac{1}{a}=4$, then the value of $a+\frac{1}{a}$ is:
Option 1: $5 \sqrt{5}$
Option 2: $4 \sqrt{5}$
Option 3: $2 \sqrt{5}$
Option 4: $3 \sqrt{5}$
Question : If $\alpha$ is an acute angle and $2\sin \alpha+15\cos^2\alpha=7$, then the value of $\cot \alpha$ is:
Option 1: $\frac{4}{3}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{5}{4}$
Option 4: $\frac{3}{4}$
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