1

IIT-JEE 1995 Screening

MCQ (Single Correct Answer)
Consider a circle with its centre lying on the focus of the parabola $${y^2} = 2px$$ such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is
A
$$\left( {{p \over 2},p} \right)$$ or $$\left( {{p \over 2},- p} \right)$$
B
$$\left( { {p \over 2}, {p \over 2}} \right)$$
C
$$\left( -{{p \over 2},p} \right)$$
D
$$\left( { - {p \over 2}, - {p \over 2}} \right)$$
2

IIT-JEE 1994

MCQ (Single Correct Answer)
Let $$E$$ be the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and $$C$$ be the circle $${x^2} + {y^2} = 9$$. Let $$P$$ and $$Q$$ be the points $$(1, 2)$$ and $$(2, 1)$$ respectively. Then
A
$$Q$$ lies inside $$C$$ but outside $$E$$
B
$$Q$$ lies outside both $$C$$ and $$E$$
C
$$P$$ lies inside both $$C$$ and $$E$$
D
$$P$$ lies inside $$C$$ but outside $$E$$
3

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 $$k > 0$$
4

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
$${y^2} - x \le 0$$

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