Permutations

Let

In a word EXAMINATION has therfore 7 letters can be chosen in following ways Case I when 2 alike of one kind and 2 alike of second kind of is
.
Number of words
Case II when 2 alike of one kind and 2 different ie,

Number of words
Case III when all are different. ie, .
Number of words
Hence, total number of words

Step 1: Understand the arrangement condition.
Since the books on each subject must remain together, we can treat the entire set of Math books and the set of Physics books as individual "blocks".
Thus, we have 2 "blocks" (one for Math and one for Physics).
Step 2: Calculate the number of ways to arrange the blocks.
These 2 blocks can be arranged in ways.
This is because we can place the Math block first or the Physics block first.
Step 3: Calculate the number of arrangements within each block.
The 5 Math books can be arranged in ways within their block.
The 3 Physics books can be arranged in ways within their block.

Step 4: Total number of arrangements.
The total number of arrangements is:
Step 5: Conclusion. Therefore, the total number of arrangements is 1440, which is option (a).