Instructions

For the following questions answer them individually

Question 21

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?

Question 22

Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch 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 60Ā° to AB. Also, C is located between south and southwest of A with AC at 30Ā° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

Question 23

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is 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?

Question 24

Find the sum $$\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}} +....+ \sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$$

Question 25

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 surfaces resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder.

Instructions

Directions for the following three questions: Answer the following questions based on the statements given below:

(i) There are three houses on each side of the road.

(ii) These six houses are labeled as P, Q, R, S, T and U.

(iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.

(iv) The houses are of different heights.

(v) T, the tallest house, is exactly opposite to the Red coloured house.

(vi) The shortest house is exactly opposite to the Green coloured house.

(vii) U, the Orange coloured house, is located between P and S.

(viii) R, the Yellow coloured house, is exactly opposite to P.

(ix) Q, the Green coloured house, is exactly opposite to U.

(x) P, the White coloured house, is taller than R, but shorter than S and Q.

Instructions

Directions for the next three questions:

Answer the following questions based on the information given below: Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer of each unit of data is known as ARDT. In the diagram below, the revenue received form data transfer as percentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.

The X axis represents the ARDT values and the Y axis represents the % of revenue from data transfer as a percentage of the total revenue.

Question 29

It was found that the volume of data transfer in India is the same as that of Singapore. Then which of the following statements is true?

Question 30

It is expected that by 2010, revenue from data transfer as a percentage of total revenue will triple for India and double for Sweden. Assume that in 2010, the total revenue in India is twice that of Sweden and that the volume of data transfer is the same in both the countries. What is the percentage increase of ARDT in India if there is no change in ARDT in Sweden?

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