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

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 2023
MCQ (Single Correct Answer)
+1
-0.25

A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangular axis. If the angle $$\angle$$APB is maximum, then

A
$${x^2} = ab$$
B
$${x^2} = a + b$$
C
$$x = {1 \over {ab}}$$
D
$$x = {{a + b} \over 2}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25

The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents

A
a parabola
B
a hyperbola
C
a circle
D
a pair of straight lines
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25

If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

A
$$(2,3)$$ or $$( - 2, - 3)$$
B
$$( - 2,3)$$ or $$(2,3)$$
C
$$(3,2)$$ or $$( - 3,2)$$
D
$$( - 3,2)$$ or $$(2,3)$$
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