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1

IIT-JEE 2003 Screening

Coefficient of $${t^{24}}$$ in $${\left( {1 + {t^2}} \right)^{12}}\left( {1 + {t^{12}}} \right)\left( {1 + {t^{24}}} \right)$$ is
A
$${}^{12}{C_6} + 3$$
B
$${}^{12}{C_6} + 1$$
C
$${}^{12}{C_6}$$
D
$${}^{12}{C_6} + 2$$
2

IIT-JEE 2002 Screening

The sum $$\sum\limits_{i = 0}^m {\left( {\matrix{ {10} \cr i \cr } } \right)\left( {\matrix{ {20} \cr {m - i} \cr } } \right),\,\left( {where\left( {\matrix{ p \cr q \cr } } \right) = 0\,\,if\,\,p < q} \right)}$$ is maximum when $$m$$ is
A
5
B
10
C
15
D
20
3

IIT-JEE 2001 Screening

In the binomial expansion of $${\left( {a - b} \right)^n},\,n \ge 5,$$ the sum of the $${5^{th}}$$ and $${6^{th}}$$ terms is zero. Then $$a/b$$ equals
A
$$\left( {n - 5} \right)/6$$
B
$$\left( {n - 4} \right)/5$$
C
$$5/\left( {n - 4} \right)$$
D
$$6/\left( {n - 5} \right)$$
4

IIT-JEE 2000 Screening

For $$2 \le r \le n,\,\,\,\,\left( {\matrix{ n \cr r \cr } } \right) + 2\left( {\matrix{ n \cr {r - 1} \cr } } \right) + \left( {\matrix{ n \cr {r - 2} \cr } } \right) =$$
A
$$\left( {\matrix{ {n + 1} \cr {r - 1} \cr } } \right)$$
B
$$2\left( {\matrix{ {n + 1} \cr {r + 1} \cr } } \right)$$
C
$$2\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$
D
$$\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$

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