3D Geometry · NDA previous year questions

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2011 12 questions

Q122011 · 21 Aug 2011
What is the locus of points of intersection of a sphere and a plane?
1. A.Circle
2. B.Ellipse
3. C.Parabola
4. D.Hyperbola
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Answer: A
Q402011 · 21 Aug 2011
What is the angle between two planes $2 x - y + z = 4$ and $x + y + 2 z = 6$ ?
1. A. $\frac{π}{2}$
2. B. $\frac{π}{3}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{6}$
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Answer: B
Q542011 · 21 Aug 2011
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point P on the plane, the angle of elevation of the bottom of the flag staff is $β$ and that of the top is $α$ . What is the height of the tower ?
1. A. $\frac{h t a n β}{t a n α - t a n β}$
2. B. $\frac{h t a n β}{t a n α + t a n β}$
3. C. $\frac{h c o s β}{c o s α - c o s β}$
4. D. $\frac{h}{c o s ( α - β )}$
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Answer: A
Q552011 · 21 Aug 2011
1. A.p is one of the cube roots of unity
2. B.q is one of the cube roots of unity
3. C. $\frac{p}{q}$ is one of the cube roots of unity
4. D.None of the above
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Answer: C
Q652011 · 21 Aug 2011
An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of two planes from the same point on the ground are $6 0^{\circ}$ and $4 5^{\circ}$ respectively. What is the height of the lower plane from the ground ?
1. A.50 m
2. B. $\frac{100}{3}$ m
3. C. $1003$ m
4. D. $150 (3 + 1)$ m
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Answer: C
Q802011 · 21 Aug 2011
What is the equation of the plane passing through the point $(1, - 1, - 1)$ and perpendicular to each of the planes $x - 2 y - 8 z = 0$ and $2 x + 5 y - z = 0$ ?
1. A. $7 x - 3 y + 2 z = 14$
2. B. $2 x + 5 y - 3 z = 12$
3. C. $x - 7 y + 3 z = 4$
4. D. $14 x - 5 y + 3 z = 16$
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Answer: D
Q812011 · 21 Aug 2011
What is the value of $tan 1 5^{\circ} \cdot tan 19 5^{\circ}$ ?
1. A. $7 - 43$
2. B. $7 + 43$
3. C. $7 + 23$
4. D. $7 + 63$
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Answer: A
Q972011 · 21 Aug 2011
The equation to sphere passing through origin and the points $(- 1, 0, 0)$ , $(0, - 2, 0)$ and $(0, 0, - 3)$ is $x^{2} + y^{2} + z^{2} + f (x, y, z) = 0$ . What is $f (x, y, z)$ equal to?
1. A. $- x - 2 y - 3 z$
2. B. $x + 2 y + 3 z$
3. C. $x + 2 y + 3 z - 1$
4. D. $x + 2 y + 3 z + 1$
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Answer: B
Q662011 · 17 Apr 2011
What is the angle between the lines whose direction cosines are proportional to $⟨ 2, 3, 4 ⟩$ and $⟨ 1, - 2, 1 ⟩$ respectively?
1. A. $9 0^{\circ}$
2. B. $6 0^{\circ}$
3. C. $4 5^{\circ}$
4. D. $3 0^{\circ}$
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Answer: A
Q952011 · 17 Apr 2011
What is the radius of the sphere $x^{2} + y^{2} + z^{2} - x - y - z = 0$ ?
1. A. $\frac{3}{4}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D. $\frac{1}{3}$
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Answer: A
Q1052011 · 17 Apr 2011
Which one of the following points lies on the plane $2 x + 3 y - 6 z = 21$ ?
1. A.(3, 2, 2)
2. B.(3, 7, 1)
3. C.(1, 2, 3)
4. D.(2, 1, -1)
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Answer: B
Q1062011 · 17 Apr 2011
What is the acute angle between the planes $x + y + 2 z = 3$ and $- 2 x + y - z = 11$ ?
1. A. $π /5$
2. B. $π /4$
3. C. $π /6$
4. D. $π /3$
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Answer: D