Teachoo MCQ Test

10 Question MCQ (including Assertion)

Chapter 11 Class 11 - Intro to Three Dimensional Geometry | 10 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 960
Question 1 of 10
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Question 1 of 10
A room is modeled in the first octant with one corner at the origin \((0,0,0)\). A ceiling fan hangs at the exact center of the ceiling. If room dimensions are length \(= 6\text{ m}\) (\(x\)-axis), width \(= 8\text{ m}\) (\(y\)-axis), and height \(= 4\text{ m}\) (\(z\)-axis), what are the coordinates of the ceiling fan?
Select one option. Answers are shown after the test.
Question 2 of 10
The equation satisfied by all points equidistant from \((1, 2, 3)\) and \((3, 2, -1)\) is:
Select one option. Answers are shown after the test.
Question 3 of 10
Assertion (A): The foot of the perpendicular drawn from \(P(5, -2, 8)\) onto the \(XY\)-plane is \((5, -2, 0)\).
Reason (R): The length of the perpendicular drawn from \(P(5, -2, 8)\) to the \(XY\)-plane is \(8\text{ units}\).
Select one option. Answers are shown after the test.
Question 4 of 10
A point \(P\) lies on the line joining \(O(0,0,0)\) and \(Q(6, 12, 18)\). If the altitude (\(z\)-coordinate) of \(P\) is \(6\), its full coordinates are:
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Question 5 of 10
The triangle formed by vertices \(A(0, 7, 10)\), \(B(-1, 6, 6)\), and \(C(-4, 9, 6)\) is:
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Question 6 of 10
Two opposite main diagonal vertices of a cube are \((0, 0, 0)\) and \((4, 4, 4)\). What is the total surface area of the cube?
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Question 7 of 10
If a point \(P(x, y, z)\) lies in the \(ZX\)-plane, then:
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Question 8 of 10
A spherical signal range centered at origin has radius \(r = 5\). Which point lies strictly inside the signal range?
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Question 9 of 10
If \(A(1, 3, 0)\), \(B(2, 4, k)\), and \(C(3, 5, -2)\) are collinear points in 3D space, then the value of \(k\) is:
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Question 10 of 10
Assertion (A): The plane \(z = 0\) is the \(XY\)-plane.
Reason (R): The distance between the parallel planes \(z = 3\) and \(z = -3\) is \(0\text{ units}\).
Select one option. Answers are shown after the test.