1
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x+ y2 + z2 - 2x - 3y - 4z = 0.

If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct ?
A
0 < p < 0.5
B
0.5 < p < 1
C
1 < p < 1.5
D
p > 1.5
2
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x+ y2 + z2 - 2x - 3y - 4z = 0.

What is the equation of the line through the origin and the centre of the sphere ?
A
x = y = z
B
2x = 3y = 4z
C
6x = 3y = 4z
D
6x = 4y = 3z
3
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (2) items that follow :

Let the plane $\frac{2x}{k} + \frac{2y}{3} + \frac{z}{3} = 2 $ pass through the point (2, 3, -6).

What are the direction ratios of the normal to the plane ?
A
<3, 2, 1>
B
<2, 3, 6>
C
<6, 3, 2>
D
<1, 2, 3>
4
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (2) items that follow :

Let the plane $\frac{2x}{k} + \frac{2y}{3} + \frac{z}{3} = 2 $ pass through the point (2, 3, -6).

If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to ?
A
10
B
11
C
12
D
13
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