1
IIT-JEE 1986
+2
-0.5
If $${C_r}$$ stands for $${}^n{C_r},$$ then the sum of the series $${{2\left( {{n \over 2}} \right){\mkern 1mu} !{\mkern 1mu} \left( {{n \over 2}} \right){\mkern 1mu} !} \over {n!}}\left[ {C_0^2 - 2C_1^2 + 3C_2^2 - } \right......... + {\left( { - 1} \right)^n}\left( {n + 1} \right)C_n^2\mathop ]\limits^ \sim \,,$$
where $$n$$ is an even positive integer, is equal to
A
0
B
$${\left( { - 1} \right)^{n/2}}\left( {n + 1} \right)$$
C
$${\left( { - 1} \right)^{n/2}}\left( {n + 2} \right)$$
D
$${\left( { - 1} \right)^n}n$$
2
IIT-JEE 1983
+1
-0.25
Given positive integers $$r > 1,\,n > 2$$ and that the coefficient of $$\left( {3r} \right)$$th and $$\left( {r + 2} \right)$$th terms in the binomial expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal. Then
A
$$n = 2r$$
B
$$n = 2r + 1$$
C
$$n = 3r$$
D
none of these
3
IIT-JEE 1983
+1
-0.25
The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}$$ is
A
$${{{405} \over {256}}}$$
B
$${{{504} \over {259}}}$$
C
$${{{450} \over {263}}}$$
D
none of these
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