Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:

1) Both p and q may be prime numbers.

2) Both p and q may be composite numbers

3) one of p and q may be prime and the other composite.

Which of the above statements are correct?

A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?

Consider the following for real numbers α, β, γ and δ ?

1) sec α = 1/4

2) tan β = 20

3) cosec γ = 1/2

4) cos δ = 2

How many of the above statements are not possible?

There are two parallel streets each directed north to south. A person in the first street travelling from south to north wishes to take the second street which is on his right side. At some place, he makes a 150 deg turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60 deg and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets?

For the inequation x^2–7x + 12 > 0, which one of the following is correct ?

Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?

In the following passage some of the words have been left out. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.

Modern man is imprisoned by his time-table and his routine. His life is all care and _____. He does not have _____ for anything but his duties and occupation for _____ money. Men, in all _____ may have been prone to this disease and; indeed, we in India may not have been _____ by it to the extent that people in western countries have been.

we in India may not have been _____ by it to the extent that people in western countries have been.

In the following passage some of the words have been left out. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.

Modern man is imprisoned by his time-table and his routine. His life is all care and _____. He does not have _____ for anything but his duties and occupation for _____ money. Men, in all _____ may have been prone to this disease and; indeed, we in India may not have been _____ by it to the extent that people in western countries have been.

Men, in all _____ may have been prone to this disease and; indeed,