Cat 2009 Quant Test 77

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Quant Test 77

1. If N is a natural number having total number of divisors 18, which of the following can’t be the number of divisors of N2 ?

j 35 k l m n j 51 k l m n j 75 k l m n j 65 k l m n j 55 k l m n i Skip this question j k l m n

2. A circle is drawn with centre O and OB as radius, where OB is one of the sides of a parallelogram ABOD. The circle cuts AB and DO at the points N and M respectively. If the radius of the circle is 3 units, AN = 1 unit and NB = 4 units, then which of the following is/are correct?

j Area of quadilateral ANMD = 3/2 * sqrt5 square units k l m n j Area of ABOD = 5 sqrt5 square units k l m n j Area of ΔBON = 3 sqrt5 square units k l m n j BD = 5 units k l m n j DM = 1 unit k l m n i Skip this question j k l m n Directions for Questions from 3 to 4: Answer the questions on the basis of the information given below. PQR is an equilateral triangle as shown in the figure given below. Let S be a point on QR. A semicircle is drawn having SR as diameter such that PQ is a tangent to the semicircle at the point T. Given that the center of the semicircle is at point O and the radius of the semicircle is 1 unit.

3. Given that the semicircle cuts PR at the point U. What is the ratio of length of the line segment PU to the radius of the semicircle?

j 1: (2 –sqrt(3)) k l m n j 2 : sqrt(3) k l m n j 3 : ( sqrt(3) +1) k l m n j 1: ( sqrt(3) −1) k l m n j None of these k l m n i Skip this question j k l m n

4. What is the value of PT/TQ ?

j 2( sqrt(3) −1) k l m n j sqrt(2) k l m n

j 3( sqrt(2) −1) k l m n j 2 sqrt(3) −1 k l m n j sqrt(3) +1 k l m n i Skip this question j k l m n

5. Mr. Ganguly, the captain, after winning the match distributed few toffees to every other player of his team. The first player received 50 toffees and then one tenth of the remaining toffees available with Mr. Ganguly. The second player received 100 toffees and then one tenth of the remaining toffees available with the captain. The third player received 150 toffees and then one tenth of the remaining toffees available with the captain. The same was true for the toffees received by the subsequent players. After distributing the toffees Mr. Ganguly found that every other player of his team got the same number of toffees. How many players are there in the team including the captain?

j 9 k l m n j 10 k l m n j 11 k l m n j 12 k l m n j Cannot be determined k l m n i Skip this question j k l m n

6. Given that a5 + b5 + c5 = 91849, where a, b, c are distinct digits. What is the remainder when a six-digit number 2a5b1c is divided by 11?

j 4 k l m n j 6 k l m n j 2 k l m n j 1 k l m n j 0 k l m n i Skip this question j k l m n

7. The number of factors of the number N = 46 + 68 is

j 18 k l m n j 36 k l m n j 54 k l m n j 72 k l m n j None of these k l m n i Skip this question j k l m n

8. Richa has three types of boxes large, medium and small. She plays a game in which she placed 9 large boxes on the table. She puts 5 medium boxes each, in few of the large boxes then she puts 5 small boxes each, in few of the medium boxes. If the number of boxes that have been left empty in the game is 41, then how many boxes were used in the game by Richa?

j 72 k l m n j 49 k l m n j 63 k l m n j 56 k l m n j 102 k l m n i Skip this question j k l m n

9. If f(x) = 2x2 + (ab2 + ac2 – 2abc)x + abc and the minimum value of f(x) is at x = –54, then the what is the minimum value of (a + 2b – 2c)? (Given that a > b > c)

j 18 k l m n j 10 k l m n j 12 k l m n j 20 k l m n

j – 20 k l m n i Skip this question j k l m n

10. The sum of the digits of the number (132 × 102000 – 56879 + 12345) is

j 15996 k l m n j 16896 k l m n j 19996 k l m n j 14896 k l m n j 17996 k l m n i Skip this question j k l m n

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