3D Geometry · NDA previous year questions

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2022 10 questions

Q632022 · 4 Sept 2022
Consider the equation of a sphere $x^{2} + y^{2} + z^{2} - 4 x - 6 y - 8 z - 16 = 0$ . Which of the following statements is/are correct ? 1. z-axis is tangent to the sphere. 2. The centre of the sphere lies on the plane $x + y + z - 9 = 0$ . Select the correct answer using the code given below :
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: B
Q642022 · 4 Sept 2022
A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?
1. A. $⟨ 2/3, 2/3, 1/3 ⟩$
2. B. $⟨ 1/3, 2/3, 2/3 ⟩$
3. C. $⟨ \frac{1}{6}, \frac{1}{6}, \frac{2}{6} ⟩$
4. D. $⟨ \frac{2}{6}, \frac{1}{6}, \frac{1}{6} ⟩$
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Answer: C
Q652022 · 4 Sept 2022
Consider the following statements : 1. The direction ratios of y-axis can be <0, 4, 0> 2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0> Which of the statements given above is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q662022 · 4 Sept 2022
PQRS is a parallelogram. If $PR = a$ and $QS = b$ , then what is $PQ$ equal to ?
1. A. $a + b$
2. B. $a - b$
3. C. $\frac{a + b}{2}$
4. D. $\frac{a - b}{2}$
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Answer: D
Q342022 · 10 Apr 2022
A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane the angles of elevation of the bottom and top of the flagstaff are θ and 2θ respectively. What is the height of the tower ?
1. A.h cos θ
2. B.h sin θ
3. C.h cos 2θ
4. D.h sin 2θ
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Answer: C
Q912022 · 10 Apr 2022
Consider the following for the next three (03) items that follow The Plane $6 x + k y + 3 z - 12 = 0$ where $k \neq = 0$ meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is $x^{2} + y^{2} + z^{2} - 2 x - 3 y - 4 z = 0$ . What is the value of k?
1. A.3
2. B.4
3. C.6
4. D.12
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Answer: B
Q922022 · 10 Apr 2022
Consider the following for the next three (03) items that follow The Plane $6 x + k y + 3 z - 12 = 0$ where $k \neq = 0$ meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is $x^{2} + y^{2} + z^{2} - 2 x - 3 y - 4 z = 0$ . If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct ?
1. A. $0 < p < 0.5$
2. B. $0.5 < p < 1$
3. C. $1 < p < 1.5$
4. D. $p > 1.5$
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Answer: B
Q932022 · 10 Apr 2022
Consider the following for the next three (03) items that follow The Plane $6 x + k y + 3 z - 12 = 0$ where $k \neq = 0$ meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is $x^{2} + y^{2} + z^{2} - 2 x - 3 y - 4 z = 0$ . What is the equation of the line through the origin and the centre of the sphere ?
1. A. $x = y = z$
2. B. $2 x = 3 y = 4 z$
3. C. $6 x = 3 y = 4 z$
4. D. $6 x = 4 y = 3 z$
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Answer: D
Q942022 · 10 Apr 2022
Consider the following for the next two (2) items that follow : Let the plane $\frac{2 x}{k} + \frac{2 y}{3} + \frac{z}{3} = 2$ pass through the point (2, 3, -6). What are the direction ratios of the normal to the plane ?
1. A.<3, 2, 1>
2. B.<2, 3, 6>
3. C.<6, 3, 2>
4. D.<1, 2, 3>
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Answer: A
Q952022 · 10 Apr 2022
Consider the following for the next two (2) items that follow : Let the plane $\frac{2 x}{k} + \frac{2 y}{3} + \frac{z}{3} = 2$ 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 ?
1. A.10
2. B.11
3. C.12
4. D.13
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Answer: B