JIPMAT (QA) PYQs

If $\sin (θ) - \cos (θ) = 0$, the value of sin⁴ (θ) + cos⁴ (θ) is:

In $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{BC}=5 \ \mathrm{cm}, \mathrm{AC}-\mathrm{AB}=1 \mathrm{~cm}$, then $\frac{1+\sin (\mathrm{C})}{1+\cos (\mathrm{C})}$ is

Given below are two statement:

Statement I: If $\sin (\theta)=\frac{5}{13}$, then the value of $\tan (\theta)=\frac{5}{12}$

Statement II: if $\cot (\theta)=\frac{12}{5}$, then the value of $\sin (\theta)=\frac{5}{12}$

In the light of the above statements, choose the correct answer form the question below: