Question : If $\triangle$DEF is right-angled at E, DE = 15, and $\angle$DFE = 60° then, what is the value of EF?

Option 1: $5\sqrt3$

Option 2: $5$

Option 3: $15$

Option 4: $30$

Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?

Option 1: DF = 5 cm, $\angle$E = 60°

Option 2: DE = 5 cm, $\angle$F = 60°

Option 3:  DE = 5 cm, $\angle$D = 60°

Option 4: DE = 5 cm, $\angle$E = 60°

Question : If $\triangle ABC$ is right-angled at B, AB = 30 units and $\angle ACB=60°$, what is the value of AC?

Option 1: $20$ units

Option 2: $20\sqrt3$ units

Option 3: $40$ units

Option 4: $60$ units

Question : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?

Option 1: $12\sqrt{3}$

Option 2: $12\sqrt2$

Option 3: $12$

Option 4: $24$

Question : In $\triangle ABC, DE \parallel BC$ in such a way that $A-D-B$ and $A-E-C$ are equal. If $ \angle A C B=40°$, then $\angle D A E+\angle ADE =$ ___________.

Option 1: 240°

Option 2: 120°

Option 3: 140°

Option 4: 230°

Question : In $\triangle A B C, \mathrm{BD} \perp \mathrm{AC}$ at $\mathrm{D}$. $\mathrm{E}$ is a point on $\mathrm{BC}$ such that $\angle B E A=x^{\circ}$. If $\angle E A C=46^{\circ}$ and $\angle E B D=60^{\circ}$, then the value of $x$ is:

Option 1: 72°

Option 2: 78°

Option 3: 68°

Option 4: 76°