Combinatorics

In an objective type examination, 120 objective type questions are there; each with 4 options P, Q, R and S. A candidate can choose either one of these options or can leave the question unanswered. How many different ways exist for answering this question paper?

The number of functions $f$ from $A={0,1,2}$ into $B={0,1,2,3,4,5,6,7}$ such that $f(i) \le f(j)$ for $i
1 $8C_3$
2 $8C_3 + 2(8C_2)$
3 $10C_3$
4 None of these
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NIMCET Previous Year PYQ NIMCET NIMCET 2008 PYQ

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Solution

Number of non-decreasing functions = combinations with repetition $= \binom{8+3-1}{3}=\binom{10}{3}$

Twelve villages in a district are divided into 3 zones with 4 villages per zone. The telephone department intends to connect villages so that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?

From 50 students: 37 passed Math, 24 Physics, 43 Chemistry. At most 19 passed Math & Physics, at most 29 passed Math & Chemistry, at most 20 passed Physics & Chemistry. Intersection of all 3 is $x$. Find maximum possible value of $x$.

A set contains $(2n+1)$ elements. If the number of subsets that contain at most $n$ elements is $4096$, then the value of $n$ is:

If $\displaystyle \sum_{K=0}^{2n}(-1)^K\binom{2n}{K}^2 = A$, find $\displaystyle \sum_{K=0}^{2n}(-1)^K(K-2n)\binom{2n}{K}^2$.