CAT Previous Paper 2008 Test Online

1. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq cm) of the intersecting region?

2. The integers 1, 2, ………..40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a +b -1 is written. What will be the number left on the board at the end?

3. Find the sum √1+1/1² + ½²  +  √1 + ½² + 1/3² + ……. + √1 + 1/2007² + 1/2008²

4. The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is:

5. The consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?

6. Consider a square ABCD with midpoints E, F, G, H, of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

7. Which of the following cannot be true?

8. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

9. What are the last two digits of 7²⁰⁰⁸?

10. As navigators, calendar makers, and other ________ of the night sky accumulated evidence to the contrary, ancient astronomers were forced to __________ that certain bodies might moves in circles about points, which in turn moved in circles about the earth.

11. If the roots of the equation x³ – ax² + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b?

12. Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

13. Let f(x) be a function satisfying f(x) f(y) = f(xy) for all real x, y. If f(2) = 4 then what is the value of f (1/2)?

14. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?

15. Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq.cm) of the cylinder.

16. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?

17. Let f(x) = ax² + bx + c, where a, b and c are certain constants and a not equal 0. It is known that f(5) = -3f(2) and that 3 is a root of f(x) = 0.
What is the other root of f(x) = 0?

18. The genocides in Bosnia and Rwanda, apart from being mis-described in the most sinister and _______ manner as ‘ethnic cleansing’, were also blamed, in further hand-washing rhetoric on something dark and interior to _________ and perpetrators alike.

19. What is the number of distinct terms in the expansion of (a + b + c)²⁰?

20. . Let f(x) = ax² + bx + c, where a, b and c are certain constants and a not equal 0. It is known that f(5) = -3f(2) and that 3 is a root of f(x) = 0.
What is the value of a + b + c?

21. The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Neelam rides her bicycle from her house at A to her club C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is:

22. Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to each a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to:

23. number of common terms in the two sequences 17, 21, 25, ……….417, and 16, 21, 26, …… 466 is:

24. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

25. Suppose, the seed of any positive integers n is defined as follows:
seed(n) = n, if n < 10
= seed(s(n)), otherwise,
where s(n) indicates the sum of digits of n.
For example,
seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc.
How many positive integers n, such that n < 500; will have seed(n) = 9?