1
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
2
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1 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
$$\frac{1}{2},-\frac{\sqrt{3}}{2}, 0$$
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1 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
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 The length of the perpendicular from the point $$(1,-2,5)$$ on the line passing through $$(1,2,4)$$ and parallel to the line $$x+y-z=0=x-2 y+3 z-5$$ is :

A
$$\sqrt{\frac{21}{2}}$$
B
$$\sqrt{\frac{9}{2}}$$
C
$$\sqrt{\frac{73}{2}}$$
D
1
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