1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If $$z_1$$ and $$z_2$$ be nth root of unity which subtend a right angled at the origin. Then, $$n$$ must be of the form

A
$$4 K+1$$
B
$$4 k$$
C
$$4 k+2$$
D
$$4 k+3$$
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

A tower $$T_1$$ of the height $$60 \mathrm{~m}$$ is located exactly opposite to a tower $$T_2$$ of height $$80 \mathrm{~m}$$ on a straight road. From the top of $$T_1$$, if the angle of depression of the foot of $$T_2$$ is twice the angle of elevation of the top of $$T_2$$, then the width (in $$\mathrm{m}$$) of the road between the feet of the towers $$T_1$$ and $$T_2$$ is

A
$$20 \sqrt{3}$$
B
$$10 \sqrt{3}$$
C
$$10 \sqrt{2}$$
D
$$20 \sqrt{2}$$
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

Water is being filled at the rate of $$1 \mathrm{~cm}^3 / \mathrm{s}$$ in a right circular conical vessel (vertex downwards) of height $$35 \mathrm{~cm}$$ and diameter $$14 \mathrm{~cm}$$. When the height of the water levels is $$10 \mathrm{~cm}$$, the rate (in $$\mathrm{cm}^2 / \mathrm{sec}$$) at which the wet conical surface area of the vessel increases is

A
$$\frac{\sqrt{26}}{10}$$
B
5
C
$$\frac{\sqrt{21}}{5}$$
D
$$\frac{\sqrt{26}}{5}$$
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

Let $$\frac{\sin A}{\sin B}=\frac{\sin (A-C)}{\sin (C-B)}$$, where $$A, B$$ and $$C$$ are angles of a $$\triangle A B C$$. If the lengths of the sides opposite these angles are $$a, b$$ and $$c$$ respectively, then

A
$$b^2-a^2=a^2+c^2$$
B
$$b^2, c^2, a^2$$ are in AP
C
$$c^2, a^2, b^2$$ are in AP
D
$$a^2, b^2, c^2$$ are in AP
EXAM MAP