1

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
If $${}^{n - 1}{C_r} = \left( {{k^2} - 3} \right)\,{}^n{C_{r + 1,}}$$ then $$k \in $$
A
$$\left( { - \infty , - 2} \right)$$
B
$$\left[ {2,\infty } \right)$$
C
$$\left[ { - \sqrt 3 ,\sqrt 3 } \right]$$
D
$$\left( {\sqrt 3 ,2} \right]$$
2

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)
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
$${}^{12}{C_6} + 2$$
3

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
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
4

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
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
$$6/\left( {n - 5} \right)$$

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