Question : A pilot in an aeroplane at an altitude of 200 metres observes two points lying on either side of a river. If the angles of depression of the two points be $45^{\circ}$ and $60^{\circ}$, then the width of the river is:

Option 1: $(200+\frac{200}{\sqrt{3}})$ metres

Option 2: $(200-\frac{200}{{\sqrt3}})$ metres

Option 3: $400 {\sqrt3}$ metres

Option 4: $(\frac{400}{{\sqrt3}})$ metres

Question : In $\triangle ABC, \angle B = 60^\circ$ and $\angle C = 40^\circ$, AD and AE are respectively the bisectors of $\angle A$ and perpendicular on BC. Find the measure of $\angle EAD$.

Option 1: $11^\circ$

Option 2: $10^\circ$

Option 3: $12^\circ$

Option 4: $9^\circ$

Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?

Option 1: $8\sqrt{2}$ cm

Option 2: $4\sqrt{2}$ cm

Option 3: $8\sqrt{3}$ cm

Option 4: $4\sqrt{3}$ cm

Question : ABCD is a cyclic quadrilateral in which angle B is opposite to angle D. If $\angle \mathrm{B}=(\mathrm{x}+10)^{\circ}$ and $\angle \mathrm{D}=(2 \mathrm{x}+35)^{\circ}$, then what is the value of $\mathrm{x}$?

Option 1: 40$^{\circ}$

Option 2: 45$^{\circ}$

Option 3: 50$^{\circ}$

Option 4: 35$^{\circ}$

Question : Minor arc $BC$ subtends $\angle BAC$ and $\angle BDC$ at points $A$ and $D$, respectively, on the circumference of the major sector of the circle with centre $O$. What is the value (in degrees) of $(\angle ABC+\angle ACB)$, if $\angle BDC=73^{\circ}?$

Option 1: $117^{\circ}$

Option 2: $107^{\circ}$

Option 3: $103^{\circ}$

Option 4: $113^{\circ}$