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Coordinates of a point in space, the distance between two points, section formula Mock Test for JEE

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Part of Three Dimensional Geometry in JEE Main Mathematics.

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Q1MathsUnit 11: Three Dimensional Geometry
Statement-1: The point A(3,1,6)\boldsymbol{A}(\mathbf{3}, \mathbf{1}, \boldsymbol{6}) is the mirror image of the point B(1,3,4)B(1,3,4) in the plane x−y+z=5\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} Statement-2: The plane x−y+z=5\boldsymbol{x}-\boldsymbol{y}+\boldsymbol{z}=\mathbf{5} bisects the line segment joining A(3,1,6)\boldsymbol{A}(\boldsymbol{3}, \mathbf{1}, \boldsymbol{6}) and B(1,3,4)\boldsymbol{B}(\mathbf{1}, \boldsymbol{3}, \boldsymbol{4})
Q2MathsUnit 11: Three Dimensional Geometry
How many cubes each of surface area 24cm224 c m^{2} can be made out of a cube of edge measure 1m?1 \mathrm{m} ?
Q3MathsUnit 11: Three Dimensional Geometry
In three dimensions, the coordinate axes of a rectangular cartesian coordinate system are
Q4MathsUnit 11: Three Dimensional Geometry
The ratio of the volume and surface area of a sphere of unit radius:
Q5MathsUnit 11: Three Dimensional Geometry
If z1z_{1} and z2z_{2} are zz co-ordinates of the points of trisection of the segment joining the points A(2,1,4),B(−1,3,6)\boldsymbol{A}(\mathbf{2}, \mathbf{1}, \mathbf{4}), \boldsymbol{B}(-\mathbf{1}, \mathbf{3}, \mathbf{6}) then z1+z2=z_{1}+z_{2}=
Q6MathsUnit 11: Three Dimensional Geometry
If the surface area of a sphere is 9856cm2.9856 c m^{2} . Find its diameter.
Q7MathsUnit 11: Three Dimensional Geometry
Perimeter of triangle whose vertices are (0,4,0),(3,4,0) and (0,4,4),(0,4,4), is
Q8MathsUnit 11: Three Dimensional Geometry
In geometry, we take a point, a line and a plane as undefined terms.
Q9MathsUnit 11: Three Dimensional Geometry
A rectangular solid has a square base, with each side of the base measuring 4 meters. If the volume of the solid is 112 cubic meters, what is the surface area of the solid?
Q10MathsUnit 11: Three Dimensional Geometry
Let⁡A→=i^+2j^+3k^,B→=4i^+2j^,C→=\operatorname{Let} \overrightarrow{\boldsymbol{A}}=\hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}+\boldsymbol{3} \hat{\boldsymbol{k}}, \overrightarrow{\boldsymbol{B}}=\boldsymbol{4} \hat{\boldsymbol{i}}+2 \hat{\boldsymbol{j}}, \overrightarrow{\boldsymbol{C}}= 2i^+2j^+2k^.\mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+\mathbf{2} \hat{k} . Then the ratio in which C\boldsymbol{C} divides ABA B is

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