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

Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be two points on the hyperbola $${{{x^2}} \over 4} - {{{y^2}} \over 9} = 1$$. If ($$\alpha,\beta$$) is the point of intersection of normals to the hyperbola at A and B, then $$\beta$$ is equal to

A
$${{12} \over 3}$$
B
$${{13} \over 3}$$
C
$$ - {{12} \over 3}$$
D
$$ - {{13} \over 3}$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor axis is inclined at an angle 60$$^\circ$$, then the eccentricity of the ellipse is

A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over 2}$$
C
$${{\sqrt 7 } \over 3}$$
D
$${1 \over {\sqrt 3 }}$$
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the distance between the plane $$\alpha x - 2y + z = k$$ and the plane containing the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}$$ and $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ is $$\sqrt 6 $$, then $$|k|$$ is

A
36
B
12
C
6
D
$$2\sqrt 3 $$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is

A
$${\cos ^{ - 1}}{2 \over 3}$$
B
$${\cos ^{ - 1}}{1 \over 5}$$
C
$${\cos ^{ - 1}}{3 \over 4}$$
D
$${\cos ^{ - 1}}{1 \over 3}$$
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