Question 1181549
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There are too many questions in the post, so I will answer the first question, ONLY.


<pre>
Use the "inclusion-exclusion principle".


The number of students in the union is the sum of the students in three subsets (English, Hindi and Sanskrit) 
separately MINUS numbers of elements in in-pair intersections PLUS the number of students in the triple
intersection (thus you have an "alternate sum", for clarity)


    18 + 23 + 24 - 13 - 12 - 11 + 6 = 35.


<U>ANSWER</U>.  35 students took admission in class XI.
</pre>

Solved.


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On inclusion-exclusion principle, &nbsp;see this Wikipedia article


https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle



To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;see the lessons


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/misc/Counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Advanced-probs-counting-elements-in-sub-sets-of-a-given-finite-set.lesson>Advanced problems on counting elements in sub-sets of a given finite set</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Challenging-problems-on-counting-elements-in-subsets-of-a-given-finite-set.lesson>Challenging problems on counting elements in subsets of a given finite set</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Selected-problems-on-counting-elements-in-subsets-of-a-given-finite-set.lesson>Selected problems on counting elements in subsets of a given finite set</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Inclusion-Exclusion-principle.lesson>Inclusion-Exclusion principle problems</A> 


in this site.



Happy learning (!)