1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1
Out of Syllabus

The foot of the perpendicular from a point on the circle $$x^{2}+y^{2}=1, z=0$$ to the plane $$2 x+3 y+z=6$$ lies on which one of the following curves?

A
$$(6 x+5 y-12)^{2}+4(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
B
$$(5 x+6 y-12)^{2}+4(3 x+5 y-9)^{2}=1, z=6-2 x-3 y$$
C
$$(6 x+5 y-14)^{2}+9(3 x+5 y-7)^{2}=1, z=6-2 x-3 y$$
D
$$(5 x+6 y-14)^{2}+9(3 x+7 y-8)^{2}=1, z=6-2 x-3 y$$
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

If the length of the perpendicular drawn from the point $$P(a, 4,2)$$, a $$>0$$ on the line $$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$$ is $$2 \sqrt{6}$$ units and $$Q\left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)$$ is the image of the point P in this line, then $$\mathrm{a}+\sum\limits_{i=1}^{3} \alpha_{i}$$ is equal to :

A
7
B
8
C
12
D
14
3
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1
Out of Syllabus

If the line of intersection of the planes $$a x+b y=3$$ and $$a x+b y+c z=0$$, a $$>0$$ makes an angle $$30^{\circ}$$ with the plane $$y-z+2=0$$, then the direction cosines of the line are :

A
$$\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$$
B
$$\frac{1}{\sqrt{2}}, \pm \,\frac{1}{\sqrt{2}}, 0$$
C
$$\frac{1}{\sqrt{5}},-\frac{2}{\sqrt{5}}, 0$$
D
$$\frac{1}{2},-\frac{\sqrt{3}}{2}, 0$$
4
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

If the plane $$P$$ passes through the intersection of two mutually perpendicular planes $$2 x+k y-5 z=1$$ and $$3 k x-k y+z=5, k<3$$ and intercepts a unit length on positive $$x$$-axis, then the intercept made by the plane $$P$$ on the $$y$$-axis is :

A
$$\frac{1}{11}$$
B
$$\frac{5}{11}$$
C
6
D
7
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