In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $$80$$ units, it takes $$100$$ cycles for failure. When the load is halved, it takes $$10000$$ cycles for failure. The load for which the failure will happen in $$5000$$ cycles is ________.

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5:4. There are 40 males in Electrical Engineering. What is the difference between numbers of female students in the Civil department and the female students in the Mechanical department?

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.

Q No	Marks	Answered Correctly	Answered Wrongly	Not Attempted
1	2	21	17	6
2	3	15	27	2
3	1	11	29	4
4	2	23	18	3
5	5	31	12	1

What is the average of the marks obtained by the class in the examination?

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p, and c respectively. Of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Following relations are drawn in m, p, c :

$$\left( I \right)\,p + m + c = {{27} \over {20}}$$

$$\left( {II} \right)\,p + m + c = {{13} \over {20}}$$

$$\left( {III} \right)\,\left( p \right) \times \left( m \right) \times \left( c \right) = {1 \over {10}}$$