Event A : The sun will rise from east tomorrow.

Event B : It will rain on Monday.

Event C : February month has 29 days in a leap year.

Which of the above event(s) has probability equal to 1 ?

1. all events A, B and C

2. both events A and B

3. both events B and C

4. both events A and C

The three vertices of a scalene triangle are always equidistant from a fixed point. The point is :

1. Orthocenter of the triangle

2. Incenter of the triangle

3. Circumcenter of the triangle

4. Centroid of the triangle

An observer at point E, which is at a certain distance from the lamp post AB, finds the angle of elevation of top of lamp post from positions C, D and E as α, β and γ. It is given that B, C, D and E are along a straight line.

Which of the following conditions is satisfied ?

1. tan α > tan β

2. tan β < tan γ

3. tan γ > tan α

4. tan α < tan β

(i) Shares of company A, paying 12%, ₹ 100 shares are at ₹ 80.

(ii) Shares of company B, paying 12%, ₹ 100 shares are at ₹ 100.

(iii) Shares of company C, paying 12%, ₹ 100 shares are at ₹ 120.

Shares of which company are at premium ?

1. Company A

2. Company B

3. Company C

4. Company A and C