# Recent questions tagged gate2015-me-3

1
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 $20cm^{2},$ then the area of triangle $PQR$ in $cm^{2}$ is ______
2
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? X and Y are not independent Y and Z are dependent Y and Z are independent X and Z are independent
3
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: $−4\leq x\leq 5$ and $6 \leq y \leq16.$ How many different triangles could be constructed with these properties? $110$ $1,100$ $9,900$ $10,000$
4
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: No manager is a leader. All leaders are executives. Conclusions: No manager is an executive. No executive is a manager. Only conclusion I follows. Only conclusion II follows. Neither conclusion I nor II follows. Both conclusions I and II follow.
5
Select the appropriate option in place of underlined part of the sentence. Increased productivity necessary reflects greater efforts made by the employees. Increase in productivity necessary Increase productivity is necessary Increase in productivity necessarily No improvement required
6
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches? $20$ $10$ $8$ $5$
7
Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, then the third statement is: True False Uncertain Data insufficient