IIMB 2001 (QA) PYQs

In the given diagram $\triangle ABC$ is a right-angled triangle, $\angle ABC=90\degree$ , $BD ⊥ AC$. If $AB:AC=3:5$ and area of $\triangle ABD$ is $90$ cm$^2$, then the area of $\triangle ABC$(in cm$^2$) is

In the figure given below: $QM, PN, RT$ are the altitudes of an isosceles triangle and $PQ = QR = 15$ cm and $PR = 18$ cm. Find the ratio of $QT:QO$

In $\triangle A B C, \angle A=66^{\circ} .$ $AB$ and $A C$ are produced to points $D$ and $E$ , respectively. If the bisectors of angle $CBD$ and angle $B C E$ meet at the point $O$, then $\angle B O C$ is equal to: