MCQ (Single Correct Answer)

1

The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is

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2

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

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3

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)

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4

Angle between two diagonals of a cube will be

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5

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

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6

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

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7

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y $$-$$ z + 4 = 0 and parallel to the x-axis is

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8

The line $$x - 2y + 4z + 4 = 0$$, $$x + y + z - 8 = 0$$ intersect the plane $$x - y + 2z + 1 = 0$$ at the point

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9
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is
WB JEE 2021
10
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.
WB JEE 2021
11
The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The equation changes to
WB JEE 2021
12
The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines

$${{x - 1} \over 2} = {{y + 2} \over 3} = {z \over { - 4}}$$ and $${x \over 2} = {{y - 1} \over { - 3}} = {{z - 2} \over 2}$$ is
WB JEE 2020
13
The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the plane $$2x - 2y + z = 5$$ is
WB JEE 2020
14
The direction ratios of the normal to the plane passing through the points (1, 2, $$-$$3), ($$-$$1, $$-$$2, 1) and parallel to $${{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}$$ is
WB JEE 2019
15
The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is
WB JEE 2019
16
A point P lies on a line through Q(1, $$-$$2, 3) and is parallel to the line $${x \over 1} = {y \over 4} = {z \over 5}$$. If P lies on the plane 2x + 3y $$-$$ 4z + 22 = 0, then segment PQ equals
WB JEE 2018
17
The foot of the perpendicular drawn from the point (1, 8, 4) on the line joining the point (0, $$-$$11, 4) and (2, $$-$$3, 1) is
WB JEE 2018
18
The equation of the plane through (1, 2, $$-$$3) and (2, $$-$$2, 1) and parallel to X-axis is
WB JEE 2017
19
Three lines are drawn from the origin O with direction cosines proportional to (1, $$-$$1, 1), (2, $$-$$3, 0) and (1, 0, 3). The three lines are
WB JEE 2017
20
The cosine of the angle between any two diagonals of a cube is
WB JEE 2016

MCQ (More than One Correct Answer)

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