1

### IIT-JEE 2008

MCQ (More than One Correct Answer)
A straight line through the vertex p of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
A
$${1 \over {PS}} + {1 \over {ST}} < {2 \over {\sqrt {QS \times SR} }}$$
B
$${1 \over {PS}} + {1 \over {ST}} > {2 \over {\sqrt {QS \times SR} }}$$
C
$${1 \over {PS}} + {1 \over {ST}} < {4 \over {QR}}$$
D
$${1 \over {PS}} + {1 \over {ST}} > {4 \over {QR}}$$
2

### IIT-JEE 2008

MCQ (More than One Correct Answer)
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)
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)
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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NEET

Class 12