Question : Let ABC be a right-angled triangle where $\angle \mathrm{A}=90^{\circ}$ and $\angle \mathrm{C}=45^{\circ}$. Find the value of $\sec \mathrm{C}+\sin \mathrm{C} \sec \mathrm{C}$.

Option 1: $1$

Option 2: $1-\sqrt{2}$

Option 3: $1+\sqrt{2}$

Option 4: $\sqrt{2}-1$

Question : In a right-angled triangle $\mathrm{XYZ}$, if $\mathrm{X}=60^{\circ}$ and $\mathrm{Y}=30^{\circ}$, then find the value of $\sin (\mathrm{X}-\mathrm{Y})$.

Option 1: $\frac{3}{5}$

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

Option 3: $\frac{3}{4}$

Option 4: $\frac{2}{3}$

Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=5 \mathrm{x}-60^{\circ}, \angle \mathrm{B}=2 \mathrm{x}+40^{\circ}, \angle \mathrm{C}=3 \mathrm{x}-80^{\circ}$. Find $\angle \mathrm{A}$.

Option 1:  $75^{\circ}$

Option 2: $90^{\circ}$

Option 3: $80^{\circ}$

Option 4: $60^{\circ}$

Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $45^{\circ}$

Option 4: $90^{\circ}$

Question : In $\triangle \mathrm{PQR}, \angle \mathrm{P}=46^{\circ}$ and $\angle \mathrm{R}=64^{\circ}$.If $\triangle \mathrm{PQR}$ is similar to $\triangle \mathrm{ABC}$ and in correspondence, then what is the value of $\angle \mathrm{B}$?

Option 1: 70°

Option 2: 90°

Option 3: 100°

Option 4: 110°