GATE IN 2015 Question Paper (01-Feb-2015) (Shift 2)

Select the appropriate option in place of underlined part of the sentence.

Increased productivity necessary reflects greater efforts made by the employees.

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows:

Statements :

I. No manager is a leader.

II. All leaders are executives.

Conclusions :

I. No manager is an executive.

II. No executive is a manager.

In the given figure angle Q is a right angle, PS:QS = 3:1, RT:QT = 5:2 and PU:UR = 1:1. If area of triangle QTS is 20 cm², then the area of triangle PQR in cm² is ______.

Right triangle PQR is to be constructed in the xy – plane so that the right angle is at P and line PR is parallel to the x-axis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: –4 ≤ x ≤ 5 and 6 ≤ y ≤ 16. How many different triangles could be constructed with these properties?

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?