1

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)
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
$$\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$
2

IIT-JEE 1999

MCQ (Single Correct Answer)
If in the expansion of $${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$ the coefficients of $$x$$ and $${x^2}$$ are $$3$$ and $$-6$$ respectively, then $$m$$ is
A
6
B
9
C
12
D
24
3

IIT-JEE 1998

MCQ (Single Correct Answer)
If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}}} } $$ equals
A
$$\left( {n - 1} \right){a_n}$$
B
$$n{a_n}$$
C
$${1 \over 2}n{a_n}$$
D
None of the above
4

IIT-JEE 1992

MCQ (Single Correct Answer)
The expansion $${\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5}$$ is a polynomial of degree
A
5
B
6
C
7
D
8

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