1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

In $$\triangle \mathrm{ABC}$$, co-ordinates of $$\mathrm{A}$$ are $$(1,2)$$ and the equation of the medians through $$\mathrm{B}$$ and C are $$x+\mathrm{y}=5$$ and $$x=4$$ respectively. Then the midpoint of $$\mathrm{BC}$$ is

A
$$\left(5, \frac{1}{2}\right)$$
B
$$\left(\frac{11}{2}, 1\right)$$
C
$$\left(11, \frac{1}{2}\right)$$
D
$$\left(\frac{11}{2}, \frac{1}{2}\right)$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A line of fixed length $$\mathrm{a}+\mathrm{b} . \mathrm{a} \neq \mathrm{b}$$ moves so that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of length a and b is

A
a parabola
B
a circle
C
an ellipse
D
a hyperbola
3
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

A
a circle
B
a parabola
C
a straight line
D
a hyperbola
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Chords $$\mathrm{AB}$$ & $$\mathrm{CD}$$ of a circle intersect at right angle at the point $$\mathrm{P}$$. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is

A
4 units
B
$$\frac{\sqrt{65}}{2}$$ units
C
$$\frac{\sqrt{67}}{2}$$ units
D
$$\frac{\sqrt{66}}{2}$$ units
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