1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t^2}$$. The maximum height reached is

A
100 m
B
300 m
C
200 m
D
125 m
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to this hyperbola at P is

A
$$y = x\sqrt 6 - \sqrt 3 $$
B
$$y = x\sqrt 3 - \sqrt 6 $$
C
$$y = x\sqrt 6 + \sqrt 3 $$
D
$$y = x\sqrt 3 + \sqrt 6 $$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
$$x = {{a + b} \over 2}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le x \le 2a$$, is :

A
$$b\{ 2\sqrt 3 - \ln (2 + \sqrt 3 )\} $$
B
$$b\{ 3\sqrt 2 + \ln (3 + \sqrt 2 )\} $$
C
$$a\{ 2\sqrt 5 - \ln (2 + \sqrt 5 )\} $$
D
$$a\{ 5\sqrt 2 + \ln (5 + \sqrt 2 )\} $$
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