3D Geometry · NDA previous year questions

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2012 20 questions

Q542012 · 19 Aug 2012
If a line OP of length r (where 'O' is the origin) makes an angle $α$ with x-axis and lies in the xz-plane, then what are the coordinates of P?
1. A. $(r cos α, 0, r sin α)$
2. B. $(0, 0, r sin α)$
3. C. $(r cos α, 0, 0)$
4. D. $(0, 0, r cos α)$
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Answer: A
Q552012 · 19 Aug 2012
What is the distance of the point (1, 2, 0) from yz-plane is:
1. A.1 unit
2. B.2 units
3. C.3 units
4. D.4 units
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Answer: A
Q562012 · 19 Aug 2012
What are the direction cosines of a line which is equally inclined to the positive directions of the axes?
1. A. $⟨ \frac{1}{3}, \frac{1}{3}, \frac{1}{3} ⟩$
2. B. $⟨ - \frac{1}{3}, \frac{1}{3}, \frac{1}{3} ⟩$
3. C. $⟨ - \frac{1}{3}, - \frac{1}{3}, \frac{1}{3} ⟩$
4. D. $⟨ \frac{1}{3}, \frac{1}{3}, \frac{1}{3} ⟩$
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Answer: A
Q572012 · 19 Aug 2012
What is the angle between the lines $\frac{x - 2}{1} = \frac{y + 1}{- 2} = \frac{z + 2}{1}$ and $\frac{x - 1}{1} = \frac{2 y + 3}{3} = \frac{z + 5}{2}$ ?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{6}$
4. D.None of the above
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Answer: A
Q582012 · 19 Aug 2012
What is the equation to the plane through $(1, 2, 3)$ parallel to $3 x + 4 y - 5 z = 0$ ?
1. A. $3 x + 4 y + 5 z + 4 = 0$
2. B. $3 x + 4 y - 5 z + 14 = 0$
3. C. $3 x + 4 y - 5 z + 4 = 0$
4. D. $3 x + 4 y - 5 z - 4 = 0$
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Answer: C
Q592012 · 19 Aug 2012
What are the direction ratios of the line of intersection of the planes $x = 3 z + 4$ and $y = 2 z - 3$ ?
1. A. $⟨ 1, 2, 3 ⟩$
2. B. $⟨ 2, 1, 3 ⟩$
3. C. $⟨ 3, 2, 1 ⟩$
4. D. $⟨ 1, 3, 2 ⟩$
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Answer: C
Q602012 · 19 Aug 2012
What is the equation to the straight line passing through (a, b, c) and parallel to z-axis?
1. A. $\frac{x - a}{1} = \frac{y - b}{0} = \frac{z - c}{0}$
2. B. $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$
3. C. $\frac{x - a}{0} = \frac{y - b}{1} = \frac{z - c}{0}$
4. D. $\frac{x - a}{0} = \frac{y - b}{1} = \frac{z - c}{1}$
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Answer: B
Q612012 · 19 Aug 2012
What is $lim_{x \to 0} \frac{1 + x - 1}{x}$ equal to?
1. A.0
2. B.1/2
3. C.1
4. D. $- 1/2$
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Answer: B
Q622012 · 19 Aug 2012
What is $lim_{x \to 0} \frac{2 ( 1 - c o s x )}{x ^{2}}$ equal to?
1. A.0
2. B.1/2
3. C.1/4
4. D.1
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Answer: D
Q632012 · 19 Aug 2012
Consider the following : 1. $lim_{x \to 0} \frac{1}{x}$ exists. 2. $lim_{x \to 0} e^{\frac{1}{x}}$ does not exist. Which of the 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: B
Q642012 · 19 Aug 2012
If $x^{m} + y^{m} = 1$ such that $\frac{d y}{d x} = - \frac{x}{y}$ , then what should be the value of m?
1. A.0
2. B.1
3. C.2
4. D.None of the above
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Answer: C
Q662012 · 15 Apr 2012
What is the cosine of angle between the planes $x + y + z + 1 = 0$ and $2 x - 2 y + 2 z + 1 = 0$ ?
1. A.1/2
2. B.1/3
3. C.2/3
4. D.None of the above
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Answer: B
Q672012 · 15 Apr 2012
If $A = [1121]$ and $B = [01 - 1 2]$ , then what is $B^{- 1} A^{- 1}$ equal to?
1. A. $[1 - 1 - 3 2]$
2. B. $[- 1 1 3 - 2]$
3. C. $[- 1 1 32]$
4. D. $[- 1 1 - 3 2]$
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Answer: B
Q702012 · 15 Apr 2012
What is the sum of the squares of direction cosines of the line joining the points $(1, 2, - 3)$ and $(- 2, 3, 1)$ ?
1. A.0
2. B.1
3. C.3
4. D. $\frac{2}{26}$
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Answer: B
Q712012 · 15 Apr 2012
What is the diameter of the sphere $x^{2} + y^{2} + z^{2} - 4 x + 6 y - 8 z - 7 = 0$ ?
1. A.4 units
2. B.5 units
3. C.6 units
4. D.12 units
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Answer: D
Q1162012 · 15 Apr 2012
What are the direction ratios of normal to the plane $2 x - y + 2 z + 1 = 0$ ?
1. A. $⟨ 2, 1, 2 ⟩$
2. B. $⟨ 1, - \frac{1}{2}, 1 ⟩$
3. C. $⟨ 1, - 2, 1 ⟩$
4. D.None of the above
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Answer: B
Q1172012 · 15 Apr 2012
Passage
For the next Four (04) questions that follow : In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
What is the percentage of persons who read all the three papers?
1. A.20%
2. B.25%
3. C.30%
4. D.40%
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Answer: B
Q1182012 · 15 Apr 2012
Passage
For the next Four (04) questions that follow : In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
What is the percentage of persons who read only two papers?
1. A.19%
2. B.31%
3. C.44%
4. D.None of the above
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Answer: A
Q1192012 · 15 Apr 2012
Passage
For the next Four (04) questions that follow : In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
What is the percentage of persons who read only one paper?
1. A.38%
2. B.48%
3. C.51%
4. D.None of the above
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Answer: B
Q1202012 · 15 Apr 2012
Passage
For the next Four (04) questions that follow : In a city, three daily newspapers A, B, C are published, 42% read A; 51% read B; 68% read C; 30% read A and B; 28% read B and C; 36% read A and C; 8% do not read any of the three newspapers.
What is the percentage of persons who read only A but neither B nor C?
1. A.4%
2. B.3%
3. C.1%
4. D.None of the above
Show answer
Answer: C