1
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
For $$r = 0,\,1,....,$$ let $${A_r},\,{B_r}$$ and $${C_r}$$ denote, respectively, the coefficient of $${X^r}$$ in the expansions of $${\left( {1 + x} \right)^{10}},$$ $${\left( {1 + x} \right)^{20}}$$ and $${\left( {1 + x} \right)^{30}}.$$
Then $$\sum\limits_{r = 1}^{10} {{A_r}\left( {{B_{10}}{B_r} - {C_{10}}{A_r}} \right)} $$ is equal to
Then $$\sum\limits_{r = 1}^{10} {{A_r}\left( {{B_{10}}{B_r} - {C_{10}}{A_r}} \right)} $$ is equal to
2
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 $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
is where $$\left( {\matrix{ n \cr r \cr } } \right) = {}^n{C_r}$$
3
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 $$k \in $$
4
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
Questions Asked from Mathematical Induction and Binomial Theorem (MCQ (Single Correct Answer))
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced 2014 Paper 2 Offline (1)
IIT-JEE 2010 Paper 2 Offline (1)
IIT-JEE 2005 Screening (1)
IIT-JEE 2004 Screening (1)
IIT-JEE 2003 Screening (1)
IIT-JEE 2002 Screening (1)
IIT-JEE 2001 Screening (1)
IIT-JEE 2000 Screening (1)
IIT-JEE 1999 (1)
IIT-JEE 1998 (1)
IIT-JEE 1992 (1)
IIT-JEE 1986 (1)
IIT-JEE 1983 (2)
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