Question : If $ab=21$ and $\frac{(a+b)^{2}}{(a-b)^{2}}=\frac{25}{4}$, then the value of $a^{2}+b^{2}+3ab$ is:

Option 1: 115

Option 2: 121

Option 3: 125

Option 4: 127

Question : If $\tan A=\frac{3}{8}$, then the value of $\frac{3 \sin A+2 \cos A}{3 \sin A-2 \cos A}$ is:

Option 1: $-\frac{13}{25}$

Option 2: $-\frac{25}{7}$

Option 3: $\frac{25}{8}$

Option 4: $\frac{13}{21}$

Question : $\frac{1}{\sqrt a}-\frac{1}{\sqrt b}=0$, then the value of $\frac{1}{a}+\frac{1}{ b}$ is:

Option 1: $\frac{1}{\sqrt{ab}}$

Option 2: $\sqrt{ab}$

Option 3: $\frac{2}{\sqrt{ab}}$

Option 4: $\frac{1}{2\sqrt{ab}}$

Question : If $\frac{a^{2} - bc}{a^{2}+bc}+\frac{b^{2}-ca}{b^{2}+ca}+\frac{c^{2}-ab}{c^{2}+ab}=1$, then the value of $\frac{a^{2}}{a^{2}+bc}+\frac{b^{2}}{b^{2}+ac}+\frac{c^{2}}{c^{2}+ab}$ is:

Option 1: 0

Option 2: 1

Option 3: –1

Option 4: 2

Question : If $\sin A = \frac{4}{5}$, then what is the value of $\sin^2 A$?

Option 1: $\frac{26}{25}$

Option 2: $\frac{36}{25}$

Option 3: $\frac{48}{25}$

Option 4: $\frac{16}{25}$

Question : If $\frac{2+a}{a}+\frac{2+b}{b}+\frac{2+c}{c}=4$, then the value of $\frac{ab+bc+ca}{abc}$ is:

Option 1: $2$

Option 2: $1$

Option 3: $0$

Option 4: $\frac{1}{2}$