CL Mock CAT Discussion 3

I am writing Mock test and want to share my approach to the questions and wish if you can also share your method of solving the questions, it will be of great help to all of us.

I am writing Mock test and want to share my approach to the questions and wish if you can also share your method of solving the questions, it will be of great help to all of us.

1. Let P = {n! + 1, n! + 2, ..., n! + n} such that 'n' is a natural number greater than 42. At the most, how many elements in set P can be prime numbers?

(a) 0 (b) 1 (c) 2 (d) More than 22.

2. If log( x + 16/x) > 1, then what is the range of x?

(a) 2 8 (d) 0 83.

3. The vertices of a triangle ABC are (1, 2), (–3, 2) and (–3, –1). Find the coordinates of the incentre ofthe triangle.

(a) (–2, 1) (b) (–2, –1) (c) (2, –1) (d) None of these.

4.Three runners – A, B and C – start from a point on a circular track simultaneously. A and B run in clockwise direction whereas C runs in anti-clockwise direction. When A and C meet for the first time, B is diametrically opposite to them. If A is the fastest among them, the ratio of the speeds of A, B and C can be

(a) 5 : 2 : 1 (b) 4 : 2 : 1 (c) 5 : 2 : 2 (d) 5 : 2 : 35.

5. Three beakers – A, B and C – contain 100 ml of pure water, 100 ml of pure milk and 100 ml of pure alcohol respectively. To start with, 25 ml of the contents of beaker A is poured into beaker B. After mixing, 25 ml of the contents of beaker B is poured into beaker C, following which, 25 ml of the resultant mixture is poured into beaker A. What is the ratio of the final quantity of alcohol in beaker A to that of milk in beaker C?

(a) 3 : 2 (b) 2 : 3 (c) 5 : 4 (d) 4 : 5