3D Geometry · NDA previous year questions

198 questions asked across 18 exam years, newest first

Year-wise papers Topic-wise questions

Practise this topic

2016 11 questions

Q262016 · 18 Sept 2016
Out of 15 points in a plane, n points are in the same straight line. 445 triangles can be formed by joining these points. What is the value of n ?
1. A.3
2. B.4
3. C.5
4. D.6
Show answer
Answer: C
Q602016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : Let Q be the image of the point P(-2, 1, -5) in the plane $3 x - 2 y + 2 z + 1 = 0$ . Consider the following : 1. The coordinates of Q are (4, -3, -1). 2. PQ is of length more than 8 units. 3. The point (1, -1, -3) is the mid-point of the line segment PQ and lies on the given plane. Which of the above statements are correct?
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
Show answer
Answer: D
Q612016 · 18 Sept 2016
Consider the following for the next two (02) items that follow : Let Q be the image of the point P(-2, 1, -5) in the plane $3 x - 2 y + 2 z + 1 = 0$ . Consider the following : 1. The direction ratios of the line segment PQ are $< 3, - 2, 2 >$ . 2. The sum of the squares of direction cosines of the line segment PQ is unity. Which of the above statements is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
Show answer
Answer: C
Q622016 · 18 Sept 2016
A line L passes through the point P(5, -6, 7) and is parallel to the planes $x + y + z = 1$ and $2 x - y - 2 z = 3$ . What are the direction ratios of the line of intersection of the given planes?
1. A. $< 1, 4, 3 >$
2. B. $< - 1, - 4, 3 >$
3. C. $< 1, - 4, 3 >$
4. D. $< 1, - 4, - 3 >$
Show answer
Answer: C
Q632016 · 18 Sept 2016
A line L passes through the point P(5, -6, 7) and is parallel to the planes $x + y + z = 1$ and $2 x - y - 2 z = 3$ . What is the equation of the line L?
1. A. $\frac{x - 5}{- 1} = \frac{y + 6}{4} = \frac{z - 7}{- 3}$
2. B. $\frac{x + 5}{- 1} = \frac{y - 6}{4} = \frac{z + 7}{- 3}$
3. C. $\frac{x - 5}{- 1} = \frac{y + 6}{- 4} = \frac{z - 7}{3}$
4. D. $\frac{x - 5}{- 1} = \frac{y + 6}{- 4} = \frac{z - 7}{- 3}$
Show answer
Answer: A
Q62016 · 17 Apr 2016
Suppose $ω$ is a cube root of unity with $ω \neq = 1$ . Suppose $P$ and $Q$ are the points on the complex plane defined by $ω$ and $ω^{2}$ . If $O$ is the origin, then what is the angle between $O P$ and $O Q$ ?
1. A. $6 0^{\circ}$
2. B. $9 0^{\circ}$
3. C. $12 0^{\circ}$
4. D. $15 0^{\circ}$
Show answer
Answer: C
Q72016 · 17 Apr 2016
Suppose $ω_{1}$ and $ω_{2}$ are two distinct cube roots of unity different from 1. Then what is $(ω_{1} - ω_{2})^{2}$ equal to?
1. A.3
2. B.1
3. C.-1
4. D.-3
Show answer
Answer: D
Q452016 · 17 Apr 2016
For the next three (3) items that follow: A plane $P$ passes through the line of intersection of the planes $2 x - y + 3 z = 2, x + y - z = 1$ and the point $(1, 0, 1)$ . What are the direction ratios of the line of intersection of the given planes?
1. A. $⟨ 2, - 5, - 3 ⟩$
2. B. $⟨ 1, - 5, - 3 ⟩$
3. C. $⟨ 2, 5, 3 ⟩$
4. D. $⟨ 1, 3, 5 ⟩$
Show answer
Answer: A
Q462016 · 17 Apr 2016
For the next three (3) items that follow: A plane $P$ passes through the line of intersection of the planes $2 x - y + 3 z = 2, x + y - z = 1$ and the point $(1, 0, 1)$ . What is the equation of the plane $P$ ?
1. A. $2 x + 5 y - 2 = 0$
2. B. $5 x + 2 y - 5 = 0$
3. C. $x + z - 2 = 0$
4. D. $2 x - y - 2 z = 0$
Show answer
Answer: B
Q472016 · 17 Apr 2016
For the next three (3) items that follow: A plane $P$ passes through the line of intersection of the planes $2 x - y + 3 z = 2, x + y - z = 1$ and the point $(1, 0, 1)$ . If the plane $P$ touches the sphere $x^{2} + y^{2} + z^{2} = r^{2}$ , then what is $r$ equal to?
1. A. $\frac{2}{29}$
2. B. $\frac{4}{29}$
3. C. $\frac{5}{29}$
4. D.1
Show answer
Answer: C
Q482016 · 17 Apr 2016
If $f (x_{1}) - f (x_{2}) = f (\frac{x _{1} - x _{2}}{1 - x _{1} x _{2}})$ for $x_{1}, x_{2} \in (- 1, 1)$ , then what is $f (x)$ equal to?
1. A. $ln (\frac{1 - x}{1 + x})$
2. B. $ln (\frac{2 + x}{1 - x})$
3. C. $tan^{- 1} (\frac{1 - x}{1 + x})$
4. D. $tan^{- 1} (\frac{1 + x}{1 - x})$
Show answer
Answer: A