A student needs to enroll for a minimum of 60 credits. A student cannot enroll for more than 70 credits. The credits are divided amongst project and three distinct sets of courses namely, core courses, specialization courses, and elective courses. It is compulsory for a student to enroll for exactly 15 credits of core courses and exactly 20 credits of project. In addition, a student has to enroll for a minimum of 10 credits of specialization courses. The maximum credits of elective courses that a student can enroll for is $\_\_\_\_$

If $P e^x=Q e^{-x}$ for all real values of $x$, which one of the following statements is true?

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$ ?

The average marks obtained by a class in an examination were calculated as 30.8 . However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42 . After correcting the marks, the average becomes 31.4. How many students does the class have?