3D Geometry · NDA previous year questions

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2024 11 questions

Q652024 · 1 Sept 2024
Direction: Consider the following for the items that follow: Let $2 x^{2} + 2 y^{2} + 2 z^{2} + 3 x + 3 y + 3 z - 6 = 0$ be a sphere. What is the diameter of the sphere?
1. A. $\frac{5 3}{4}$
2. B. $\frac{5 3}{2}$
3. C. $\frac{3 5}{4}$
4. D. $\frac{3 5}{2}$
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Answer: B
Q662024 · 1 Sept 2024
The centre of the sphere lies on the plane
1. A.2x + 2y + 2z - 3 = 0
2. B.4x + 4y + 4z - 3 = 0
3. C.4x + 8y + 8z - 15 = 0
4. D.4x + 8y + 8z + 15 = 0
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Answer: D
Q672024 · 1 Sept 2024
Direction: Consider the following for the items that follow: Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8. Which of the following are the direction ratios of S?
1. A.〈-7, -6, 1〉
2. B.〈-7, 6, 1〉
3. C.〈-6, 5, 1〉
4. D.〈6, 5, 1〉
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Answer: B
Q682024 · 1 Sept 2024
If $⟨ l, m, n ⟩$ are direction cosines of S, then what is the value. of $43 (l^{2} - m^{2} - n^{2})$ ?
1. A.6
2. B.5
3. C.4
4. D.1
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Answer: A
Q692024 · 1 Sept 2024
Direction: Consider the following for the items that follow: Let L : x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P : x + 2y + 3z + 1 = 0 be a plane. What are the direction ratios of the line?
1. A.〈2, 1, -1〉
2. B.〈0, -1, 2〉
3. C.〈0, 1, -1〉
4. D.〈2, 3, -3〉
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Answer: C
Q522024 · 21 Apr 2024
If $(1, - 1, 2)$ and $(2, 1, - 1)$ are the end points of a diameter of a sphere $x^{2} + y^{2} + z^{2} + 2 ux + 2 v y + 2 w z - 1 = 0$ , then what is $u + v + w$ equal to?
1. A.-2
2. B.-1
3. C.1
4. D.2
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Answer: A
Q532024 · 21 Apr 2024
The number of points represented by the equation $x = 5$ on the $x y$ -plane is
1. A.Zero
2. B.One
3. C.Two
4. D.Infinitely many
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Answer: D
Q542024 · 21 Apr 2024
If $⟨ l, m, n ⟩$ are the direction cosines of a normal to the plane $2 x - 3 y + 6 z + 4 = 0$ , then what is the value of $49 (7 l^{2} + m^{2} - n^{2})$ ?
1. A.0
2. B.1
3. C.3
4. D.71
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Answer: B
Q552024 · 21 Apr 2024
A line through $(1, - 1, 2)$ with direction ratios $⟨ 3, 2, 2 ⟩$ meets the plane $x + 2 y + 3 z = 18$ . What is the point of intersection of line and plane?
1. A. $(4, 4, 1)$
2. B. $(2, 4, 1)$
3. C. $(4, 1, 4)$
4. D. $(3, 4, 7)$
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Answer: C
Q562024 · 21 Apr 2024
If $p$ is the perpendicular distance from origin to the plane passing through $(1, 0, 0)$ , $(0, 1, 0)$ and $(0, 0, 1)$ , then what is $3 p^{2}$ equal to?
1. A.4
2. B.3
3. C.2
4. D.1
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Answer: D
Q572024 · 21 Apr 2024
If the direction cosines <l, m, n> of a line are connected by relation $l + 2 m + n = 0, 2 l - 2 m + 3 n = 0$ , then what is the value of $l^{2} + m^{2} - n^{2}$ ?
1. A. $\frac{1}{101}$
2. B. $\frac{29}{101}$
3. C. $\frac{41}{101}$
4. D. $\frac{92}{101}$
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Answer: B