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*In Short:*

^{11}C_{2} = \(\frac{11!}{2! \times (11 – 2)!}\) = 55

*Explanation:*

In the example of (a + b)^{n}, the (r + 1)^{th} term, denoted by t_{r + 1}, is given by

t_{r + 1} = ^{n}C_{r} . a^{n-r} . b^{r}

Letting a = 1, b = x and n = 11, we get

t_{r + 1} = ^{11}C_{r} . 1^{11-r} . x^{r}

As, we need the cofficient of x^{2}, we have to take r = 2

^{11}C_{2} = \(\frac{11!}{2! \times (11 – 2)!}\) = 55

The coefficient of x^{2} in (1 + x)^{11} is 55.

**Representaton of Relation using Matrix:**

Let A = {a_{1}, a_{2}, …….., a_{m}} and B = {b_{1}, b_{2}, ………, b_{n}) are finite sets containing m and n elements respectively and set R be a relation from A to B then R can be represented by the *mn* matrix.

M_{R} = [m_{ij}] where m_{ij} = \(\left\{\begin{matrix}1 \enspace if \enspace (a_i, b_j) \enspace ∈ \enspace R \\ 0 \enspace if \enspace (a_i, b_j) \enspace ∉ \enspace R\end{matrix}\right.\)

The matrix M_{R} is called matrix of R.

*Example:*

Let A = {1, 3, 4}, R = {(1, 1), (1, 3), (3, 3), (4, 4)}

M_{R} = \(\begin{bmatrix}1 & 1 & 0\\ 0 & 1& 0\\ 0 & 0 & 1\end{bmatrix}\)

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