Question
Obtain the values using binomial expansion: $(\sqrt{5}+$ $\sqrt{3})^{4}+(\sqrt{5}-\sqrt{3})^{4}$
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Answer
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The frequency distribution of sale of notebooks from a stationery shop in the month of June for the year $2014$ is as follows. Find coefficient of skewness using Karl Pearson’s method.
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→Obtain domain, co-domain and range for the following functions :
$(1)$ $f: \mathrm{A} \rightarrow \mathrm{B}, \mathrm{A}=\{-1,0,1\}, \mathrm{B}=\{1,2,3,4,5,6,7\}, f(x)=2 x+5, x \in \mathrm{A}$
$(2)$ $g: \mathrm{A} \rightarrow \mathrm{N}, \mathrm{A}=\{-1,2,3,4\}, g(x)=3 x+5, x \in \mathrm{A}$
$(3)$ $h: \mathrm{P} \rightarrow \mathrm{S}, \mathrm{P}=\{-2,-1,0,1\}, \mathrm{S}=\{-4,-3,-2,-1\}, h(x)=x-2, x \in \mathrm{P}$
$(4)$ $k: \mathrm{A} \rightarrow \mathrm{Z}, \mathrm{A}=\left\{-\frac{1}{2}, 0, \frac{1}{2}\right\}, k(\mathrm{x})=4 x^{2}+3, x \in \mathrm{A}$
→$(1)$ $f: \mathrm{A} \rightarrow \mathrm{B}, \mathrm{A}=\{-1,0,1\}, \mathrm{B}=\{1,2,3,4,5,6,7\}, f(x)=2 x+5, x \in \mathrm{A}$
$(2)$ $g: \mathrm{A} \rightarrow \mathrm{N}, \mathrm{A}=\{-1,2,3,4\}, g(x)=3 x+5, x \in \mathrm{A}$
$(3)$ $h: \mathrm{P} \rightarrow \mathrm{S}, \mathrm{P}=\{-2,-1,0,1\}, \mathrm{S}=\{-4,-3,-2,-1\}, h(x)=x-2, x \in \mathrm{P}$
$(4)$ $k: \mathrm{A} \rightarrow \mathrm{Z}, \mathrm{A}=\left\{-\frac{1}{2}, 0, \frac{1}{2}\right\}, k(\mathrm{x})=4 x^{2}+3, x \in \mathrm{A}$
Find the values of the following :
$(1)$ ${ }^{8} \mathrm{C}_{3}$
$(2)$ ${ }^{20} \mathrm{C}_{3}$
$(3)$ ${ }^{5} \mathrm{C}_{4}$
$(4)$ ${ }^{6} \mathrm{C}_{6}$
→$(1)$ ${ }^{8} \mathrm{C}_{3}$
$(2)$ ${ }^{20} \mathrm{C}_{3}$
$(3)$ ${ }^{5} \mathrm{C}_{4}$
$(4)$ ${ }^{6} \mathrm{C}_{6}$
