A) \[ac\ne 0\]
B) \[p(x).Q(x)=0\]
C) \[{{x}^{\log x{{(1-x)}^{2}}=9}}\]
D) none of these
Correct Answer: A
Solution :
\[\because \]\[^{n}{{C}_{r}}{{=}^{n}}{{C}_{n-r}}\]and\[^{n}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}\]we have, \[\sum\limits_{r=0}^{m}{^{n+r}{{C}_{n}}}=\sum\limits_{r=0}^{m}{^{n+r}{{C}_{r}}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r}}\] \[{{+}^{n+2}}{{C}_{2}}+......{{+}^{n+m}}{{C}_{m}}\] \[=[1+(n+1)]{{+}^{n+2}}{{C}_{2}}{{+}^{n+3}}{{C}_{3}}+....{{+}^{n+m}}{{C}_{m}}\] \[{{=}^{n+m+1}}{{C}_{n+1}}\] \[[{{\because }^{n}}{{C}_{r}}{{=}^{n}}{{C}_{n-r}}]\]
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