**QUESTION: 1**

Two circles with centers A and B respectively intersect at two points C and D. Given that A, B, C, D lie on a circle of radius 3 and circle A has radius 2, what is the radius of circle B?

Level: Moderate

**OPTIONS**

- 4
- 5
- $4\sqrt{2}$
- $3\sqrt{2}$

**QUESTION: 2**

Amit is chasing Anant in his car on Mumbai-Pune Expressway. He observes that when he is just 100 m away from a dark tunnel, Anant has already entered the tunnel and covered some distance inside. When Amit just emerges from the tunnel, he can see Anant 80 m ahead of him. Amit is driving at a speed 12.5% faster than the speed at which Anant is driving. What fraction of the length of the tunnel Anant must have covered, when Amit was 100 m away from the tunnel?

Level: Difficult

**OPTIONS**

- more than 1/9th
- more than 1/9th but less than 8/9th
- more than 8/9th
- less than 1/9th

**QUESTION: 3**

If $x^{3}+a x^{2}+b x+3$ and $x^{3}+b x^{2}+a x+2$ intersect at exactly one point, which lies on x axis, in the X -Y plane, what is the value of (a+b)?

Level: Difficult

**OPTIONS**

- -7
- -8
- -2
- 0

**QUESTION: 4**

A family of comprising 6 members can do a task in 12 days. The time taken to complete the same work by 3 out of the 6 members is twice of the time taken by 2 other members of the family, and thrice of the time taken by the 6th member. If these three groups work alternatively for 6 days, then in how many days can the group containing two members working alone complete the remaining work?

Level: Easy

**QUESTION: 5**

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

Level: Easy

**OPTIONS**

- -4
- -12
- 12
- None of these