1
WB JEE 2024
+1
-0.25

The plane $$2 x-y+3 z+5=0$$ is rotated through $$90^{\circ}$$ about its line of intersection with the plane $$x+y+z=1$$. The equation of the plane in new position is

A
$$3 x+9 y+z+17=0$$
B
$$3 x+9 y+z=17$$
C
$$3 x-9 y-z=17$$
D
$$3 x+9 y-z=17$$
2
WB JEE 2024
+1
-0.25

If the relation between the direction ratios of two lines in $$\mathbb{R}^3$$ are given by

$$l+\mathrm{m}+\mathrm{n}=0,2 l \mathrm{~m}+2 \mathrm{mn}-l \mathrm{n}=0$$

then the angle between the lines is ($$l, \mathrm{~m}, \mathrm{n}$$ have their usual meaning)

A
$$\frac{\pi}{6}$$
B
$$\frac{2 \pi}{3}$$
C
$$\frac{\pi}{2}$$
D
$$\frac{\pi}{4}$$
3
WB JEE 2024
+2
-0.5

Angle between two diagonals of a cube will be

A
$$\cos ^{-1}\left(\frac{1}{3}\right)$$
B
$$\sin ^{-1}\left(\frac{1}{3}\right)$$
C
$$\frac{\pi}{2}-\cos ^{-1}\left(\frac{1}{3}\right)$$
D
$$\frac{\pi}{2}-\sin ^{-1}\left(\frac{1}{3}\right)$$
4
WB JEE 2023
+1
-0.25

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
$$2\sqrt 3$$
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