3D Geometry · NDA previous year questions

198 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2015 14 questions

Q552015 · 27 Sept 2015
The radius of the sphere $3 x^{2} + 3 y^{2} + 3 z^{2} - 8 x + 4 y + 8 z - 15 = 0$ is
1. A.2
2. B.3
3. C.4
4. D.5
Show answer
Answer: B
Q562015 · 27 Sept 2015
The direction ratios of the line perpendicular to the lines with direction ratios $⟨ 1, - 2, - 2 ⟩$ and $⟨ 0, 2, 1 ⟩$ are
1. A. $⟨ 2, - 1, 2 ⟩$
2. B. $⟨ - 2, 1, 2 ⟩$
3. C. $⟨ 2, 1, - 2 ⟩$
4. D. $⟨ - 2, - 1, - 2 ⟩$
Show answer
Answer: A
Q572015 · 27 Sept 2015
What are the co-ordinates of the foot of the perpendicular drawn from the point $(3, 5, 4)$ on the plane $z = 0$ ?
1. A. $(0, 5, 4)$
2. B. $(3, 5, 0)$
3. C. $(3, 0, 4)$
4. D. $(0, 0, 4)$
Show answer
Answer: B
Q582015 · 27 Sept 2015
The lengths of the intercepts on the co-ordinate axes made by the plane $5 x + 2 y + z - 13 = 0$ are
1. A.5, 2, 1 unit
2. B. $\frac{13}{5}, \frac{13}{2}, 13 unit$
3. C. $\frac{5}{13}, \frac{2}{13}, \frac{1}{13} unit$
4. D.1, 2, 5 unit
Show answer
Answer: B
Q592015 · 27 Sept 2015
If $g (x) = \frac{1}{f ( x )}$ and $f (x) = x, x \neq = 0$ , then which one of the following is correct?
1. A. $f (f (f (g (g (f (x))))))) = g (g (f (g (f (x)))))$
2. B. $f (f (g (g (g (f (x))))))) = g (g (f (g (f (x)))))$
3. C. $f (g (f (g (g (f (g (x)))))))) = g (g (f (g (f (x)))))$
4. D. $f (f (f (g (g (f (x))))))) = f (f (f (g (f (x)))))$
Show answer
Answer: B
Q362015 · 19 Apr 2015
The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances $49 m$ and $36 m$ are $4 3^{\circ}$ and $4 7^{\circ}$ respectively. What is the height of the tower?
1. A. $40 m$
2. B. $42 m$
3. C. $45 m$
4. D. $47 m$
Show answer
Answer: B
Q372015 · 19 Apr 2015
In a triangle $A B C$ , $a = (1 + 3) cm$ , $b = 2 cm$ and angle $C = 6 0^{\circ}$ . Then the other two angles are
1. A. $4 5^{\circ} and 7 5^{\circ}$
2. B. $3 0^{\circ} and 9 0^{\circ}$
3. C. $10 5^{\circ} and 1 5^{\circ}$
4. D. $10 0^{\circ} and 2 0^{\circ}$
Show answer
Answer: A
Q492015 · 19 Apr 2015
For the next two (2) items that follow: The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What are the direction cosines of the line segment?
1. A. $⟨ 12/13, 4/13, 3/13 ⟩$
2. B. $⟨ 12/13, - 4/13, 3/13 ⟩$
3. C. $⟨ 12/13, - 4/13, - 3/13 ⟩$
4. D. $⟨ - 12/13, - 4/13, 3/13 ⟩$
Show answer
Answer: A
Q502015 · 19 Apr 2015
For the next two (2) items that follow: From the point $P (3, - 1, 11)$ , a perpendicular is drawn on the line $L$ given by the equation $\frac{x}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ . Let $Q$ be the foot of the perpendicular. What are the direction ratios of the line segment $P Q$ ?
1. A. $⟨ 1, 6, 4 ⟩$
2. B. $⟨ - 1, 6, - 4 ⟩$
3. C. $⟨ - 1, - 6, 4 ⟩$
4. D. $⟨ 2, - 6, 4 ⟩$
Show answer
Answer: B
Q512015 · 19 Apr 2015
For the next two (2) items that follow: From the point $P (3, - 1, 11)$ , a perpendicular is drawn on the line $L$ given by the equation $\frac{x}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ . Let $Q$ be the foot of the perpendicular. What is the length of the line segment $P Q$ ?
1. A. $47$ units
2. B.7 units
3. C. $53$ units
4. D.8 units
Show answer
Answer: C
Q522015 · 19 Apr 2015
For the next two (2) items that follow: A triangular plane $A B C$ with centroid $(1, 2, 3)$ cuts the coordinate axes at $A, B, C$ respectively. What are the intercepts made by the plane $A B C$ on the axes?
1. A. $3, 6, 9$
2. B. $1, 2, 3$
3. C. $1, 4, 9$
4. D. $2, 4, 6$
Show answer
Answer: A
Q532015 · 19 Apr 2015
A triangular plane $A B C$ with centroid $(1, 2, 3)$ cuts the coordinate axes at $A, B, C$ respectively. What is the equation of the plane $A B C$ ?
1. A. $x + 2 y + 3 z = 1$
2. B. $3 x + 2 y + z = 3$
3. C. $2 x + 3 y + 6 z = 18$
4. D. $6 x + 3 y + 2 z = 18$
Show answer
Answer: D
Q542015 · 19 Apr 2015
For the next two (2) items that follow: A point $P (1, 2, 3)$ is one vertex of a cuboid formed by the coordinate planes and the planes passing through $P$ and parallel to the coordinate planes. What is the length of one of the diagonals of the cuboid?
1. A. $10$ units
2. B. $14$ units
3. C. $4$ units
4. D. $5$ units
Show answer
Answer: B
Q552015 · 19 Apr 2015
A point $P (1, 2, 3)$ is one vertex of a cuboid formed by the coordinate planes and the planes passing through $P$ and parallel to the coordinate planes. What is the equation of the plane passing through $P (1, 2, 3)$ and parallel to $x y$ -plane?
1. A. $x + y = 3$
2. B. $x - y = - 1$
3. C. $z = 3$
4. D. $x + 2 y + 3 z = 14$
Show answer
Answer: C