Three Dimensional Geometry Test

Result

Three Dimensional Geometry Test - 25

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

A

B

C

D
Question 2
4 / -1

The plane 2x - 2y + z + 5 = 0 is a tangent to the sphere (x - 2)² + (y - 2)² + (z - 1)² = r², if r equals

A
1

B
2

C
4

D
None of these
Question 3
4 / -1

The centre and radius of the sphere x² + y² + z² + 3x - 4z + 1 = 0 are

A

B

C

D
Question 4
4 / -1

The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x² + y² + z² + 4x - 2y - 6z = 155 is

A
26

B

C
13

D
39
Question 5
4 / -1

The radius of the sphere x² + y² + z² = x + 2y + 3z is

A
√14/2

B
√7

C
7/2

D
√7/2
Question 6
4 / -1

If (2, 3, 5) is one end of a diameter of the sphere x² + y² + z² - 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are

A
(4, 9, -3)

B
(4, -3, 3)

C
(4, 3, 5)

D
(4, 3, -3)
Question 7
4 / -1

A plane x + y + z = -a√3 touches the sphere 2x² + 2y² + 2z² - 2x + 4y - 4z + 3 = 0, then the value of a is

A
1/√3

B
1/2√3

C
1 - (1/√3)

D
1 + (1/√3)
Question 8
4 / -1

The plane x + 2y - z = 4 cuts the sphere x² + y² + z² - x + z - 2 = 0 in a circle of radius

A
√2

B
2

C
1

D
3

Solution
Question 9
4 / -1

A

B
(-1, -1, 0)

C
(1, 1, 1)

D
Question 10
4 / -1

A

B

C

D