GATE Questions

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Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively.

Now, required time after which they met for the first time = LCM of (16, 24 & 36) min

Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.

Given teacher drinks 9 ltr
Let number of boys be 'A'.
Let number of girls be 'B'.
Boy drinks 7 ltr and girl drinks 4 ltr
After class total water consumed = 42 ltr
Then,
9 + 7A + 4B = 42
=> 7A + 4B = 33
By trial and error method,
The only integers which satisfy the equation is A = 3 and B = 3
Therefore, number of girls in the class = 3.

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.

A clipboard is a temporary storage area for items that the user wants to cut or copy from one place to another.

For example, in a word processor application, the user might want to cut text from one part of a document and paste it in another part of the document or somewhere else, it is temporarily stored in clipboard.

Let rate = R% and time = R years.

Then, (1200 x R x R) / 100 = 432

=> R = 6.

The statement mentions that chances of heart ailments are greatly reduced by a regular half-hour exercise. So, a follows. However, it talks of only reducing the probability which does not mean that persons involved in sedentary jobs shall definitely suffer from heart ailments. So, b does not follow.

Hence, concusion a only follows the given statement.

$$\begin{gathered} Given 3.2% of 500 × 2. 4% of ? = 312 \\ Then, \\ 3.2 x 500100 x 2.4 x ?100 = 312 \\ 16 x 2.4x?100 = 312 \\ 9.6 x ?25 = 312 \\ 9.6 x ? = 7800 \\ ? = 78009.6 \\ ? = 812.5 \end{gathered}$$

Given in the question that, there are 7 boys and 6 girls. 

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

$$\begin{gathered} 6C3 x 7C2 + 6C4 x 7C1 + 6C5 \\ = 6x5x43x2x1 x 7x62x1 + 6x5x4x34x3x2x1 x 7 + 6x5x4x3x25x4x3x2x1 \\ = 420 + 105 + 6 \\ = 531. \end{gathered}$$