1
JEE Advanced 2013 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $${S_n} = {\sum\limits_{k = 1}^{4n} {\left( { - 1} \right)} ^{{{k\left( {k + 1} \right)} \over 2}}}{k^2}.$$ Then $${S_n}$$can take value(s)
A
1056
B
1088
C
1120
D
1332
2
IIT-JEE 2008 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $${S_n} = \sum\limits_{k = 1}^n {{n \over {{n^2} + kn + {k^2}}}} $$ and $${T_n} = \sum\limits_{k = 0}^{n - 1} {{n \over {{n^2} + kn + {k^2}}}} $$ for $$n$$ $$=1, 2, 3, ............$$ Then,
A
$${S_n} < {\pi \over {3\sqrt 3 }}$$
B
$${S_n} > {\pi \over {3\sqrt 3 }}$$
C
$${T_n} < {\pi \over {3\sqrt 3 }}$$
D
$${T_n} > {\pi \over {3\sqrt 3 }}$$
3
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
For a positive integer $$n$$, let
$$a\left( n \right) = 1 + {1 \over 2} + {1 \over 3} + {1 \over 4} + .....\,{1 \over {\left( {{2^n}} \right) - 1}}$$. Then
A
$$a\left( {100} \right) \le 100$$
B
$$a\left( {100} \right) > 100$$
C
$$a\left( {200} \right) \le 100$$
D
$$a\left( {200} \right) > 100$$
4
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
For $$0 < \phi < \pi /2,$$ if
$$x = $$$$\sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\phi ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi ,\,\,\,\,z = \sum\limits_{n = 0}^{} {{{\cos }^{2n}}\phi {{\sin }^{2n}}\phi } } } \infty $$ then
A
$$xyz = xz + y$$
B
$$xyz = xy + z$$
C
$$xyz = x + y + z$$
D
$$xyz = yz + x$$
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