1

IIT-JEE 1994

MCQ (Single Correct Answer)
The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$ represents
A
no locus if $$k > 0$$
B
an ellipse if $$k < 0$$
C
a point if $$k = 0$$
D
a hyperbola if $$k > 0$$
2

IIT-JEE 1981

MCQ (Single Correct Answer)
Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have the following property. For any two points $$\left( {{x_1},{y_1}} \right)$$ and $$\left( {{x_2},{y_2}} \right)$$ in the region, the point $$\left( {{{{x_1} + {x_2}} \over 2},{{{y_1} + {y_2}} \over 2}} \right)$$ is also in the region. The inequality defining this region is
A
$${x^2} + 2{y^2} \le 1$$
B
Max $$\left\{ {\left| x \right|,\left| y \right|} \right\} \le 1$$
C
$${x^2} - {y^2} \le 1$$
D
$${y^2} - x \le 0$$
3

IIT-JEE 1981

MCQ (Single Correct Answer)
The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents
A
an ellipse
B
a hyperbola
C
a circle
D
none of these

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