1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Out of Syllabus
A variable plane passes through a fixed point (3,2,1) and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz -plane through A, a second plane is drawn parallel zx-plane through B and a third plane is drawn parallel to xy-plane through C. Then the locus of the point of intersection of these three planes, is :
A
$${x \over 3} + {y \over 2} + {z \over 1} = 1$$
B
x + y + z = 6
C
$${1 \over x} + {1 \over y} + {1 \over z} = {{11} \over 6}$$
D
$${3 \over x} + {2 \over y} + {1 \over z} = 1$$
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Out of Syllabus
An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z $$-$$ 1 = 0 and 5x + 8y + 2z + 14 =0, is :
A
$${\sin ^{ - 1}}\left( {\sqrt {{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {17}}}} } \right)$$
B
$${\cos ^{ - 1}}\left( {\sqrt {{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {17}}}} } \right)$$
C
$${\cos ^{ - 1}}\left( {{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {17}}}} \right)$$
D
$${\sin ^{ - 1}}\left( {{\raise0.5ex\hbox{\scriptstyle 3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle {17}}}} \right)$$
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If x = a, y = b, z = c is a solution of the system of linear equations

x + 8y + 7z = 0

9x + 2y + 3z = 0

x + y + z = 0

such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :
A
$$-$$ 1
B
0
C
1
D
2
4
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of $$\Delta$$ABC is :
A
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 1$$
B
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 3$$
C
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = {1 \over 9}$$
D
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 9$$
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