1
IIT-JEE 2001 Screening
+2
-0.5
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
$$6/\left( {n - 5} \right)$$
2
IIT-JEE 2000 Screening
+2
-0.5
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
$$\left( {\matrix{ {n + 2} \cr r \cr } } \right)$$
3
IIT-JEE 1999
+2
-0.5
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
4
IIT-JEE 1998
+2
-0.5
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
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