1
IIT-JEE 1999
MCQ (Single Correct Answer)
+2
-0.5
The harmonic mean of the roots of the equation $$\left( {5 + \sqrt 2 } \right){x^2} - \left( {4 + \sqrt 5 } \right)x + 8 + 2\sqrt 5 = 0$$ is
A
2
B
4
C
6
D
8
2
IIT-JEE 1999
Subjective
+10
-0
Let a, b, c, d be real numbers in G.P. If u, v, w, satisfy the system of equations
u + 2v + 3w = 6
4u + 5v + 6w = 12
6u + 9v = 4

then show that the roots of the equation $$\left( {{1 \over u} + {1 \over v} + {1 \over w}} \right){x^2}$$
$$ + [{(b - c)^2} + {(c - a)^2} + {(d - b)^2}]x + u + v + w = 0$$ and $$20{x^2} + 10{(a - d)^2}x - 9 = 0$$ are reciprocals of each other.

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 1999
MCQ (Single Correct Answer)
+2
-0.5
Lt $$PQR$$ be a right angled isosceles triangle, right angled at $$P(2, 1)$$. If the equation of the line $$QR$$ is $$2x + y = 3,$$ then the equation representing the pair of lines $$PQ$$ and $$PR$$ is
A
$$3{x^2} - 3{y^2} + 8xy + 20x + 10y + 25 = 0$$
B
$$3{x^2} - 3{y^2} + 8xy - 20x - 10y + 25 = 0$$
C
$$3{x^2} - 3{y^2} + 8xy + 10x + 15y + 20 = 0$$
D
$$3{x^2} - 3{y^2} - 8xy - 10x - 15y - 20 = 0$$
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