1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
The value of $$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr } } \right) - \left( {\matrix{ {30} \cr 1 \cr } } \right)\left( {\matrix{ {30} \cr {11} \cr } } \right) + \left( {\matrix{ {30} \cr 2 \cr } } \right)\left( {\matrix{ {30} \cr {12} \cr } } \right)....... + \left( {\matrix{ {30} \cr {20} \cr } } \right)\left( {\matrix{ {30} \cr {30} \cr } } \right)$$\$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
A
$$\left( {\matrix{ {30} \cr {10} \cr } } \right)$$
B
$$\left( {\matrix{ {30} \cr {15} \cr } } \right)$$
C
$$\left( {\matrix{ {60} \cr {30} \cr } } \right)$$
D
$$\left( {\matrix{ {31} \cr {10} \cr } } \right)$$
2
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
$$\left( {\sqrt 3 ,2} \right]$$
3
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
$${}^{12}{C_6} + 2$$
4
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+2
-0.5
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
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