3D Geometry · NDA previous year questions

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2017 11 questions

Q502017 · 10 Sept 2017
The length of the normal from origin to the plane $x + 2 y - 2 z = 9$ is equal to
1. A.2 units
2. B.3 units
3. C.4 units
4. D.5 units
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Answer: B
Q522017 · 10 Sept 2017
The point of intersection of the line joining the points $(- 3, 4, - 8)$ and $(5, - 6, 4)$ with the $X Y$ -plane is
1. A. $(\frac{7}{3}, - \frac{8}{3}, 0)$
2. B. $(- \frac{7}{3}, - \frac{8}{3}, 0)$
3. C. $(- \frac{7}{3}, \frac{8}{3}, 0)$
4. D. $(\frac{7}{3}, \frac{8}{3}, 0)$
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Answer: A
Q532017 · 10 Sept 2017
If the angle between the lines whose direction ratios are $⟨ 2, - 1, 2 ⟩$ and $⟨ x, 3, 5 ⟩$ is $\frac{π}{4}$ , then the smaller value of $x$ is
1. A.52
2. B.4
3. C.2
4. D.1
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Answer: B
Q542017 · 10 Sept 2017
A variable plane passes through a fixed point $(a, b, c)$ and cuts the axes in $A, B$ and $C$ respectively. The locus of the centre of the sphere $O A B C$ , $O$ being the origin, is
1. A. $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$
2. B. $\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 1$
3. C. $\frac{a}{x} + \frac{b}{y} + \frac{c}{z} = 2$
4. D. $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 2$
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Answer: C
Q552017 · 10 Sept 2017
The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ , $2 x + 3 y + 4 z = 7$ , and perpendicular to the plane $x - 5 y + 3 z = 5$ is given by
1. A. $x + 2 y + 3 z - 6 = 0$
2. B. $x + 2 y + 3 z + 6 = 0$
3. C. $3 x + 4 y + 5 z - 8 = 0$
4. D. $3 x + 4 y + 5 z + 8 = 0$
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Answer: A
Q602017 · 23 Apr 2017
A straight line with direction cosines $⟨ 0, 1, 0 ⟩$ is
1. A.parallel to $x$ -axis
2. B.parallel to $y$ -axis
3. C.parallel to $z$ -axis
4. D.equally inclined to all the axes
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Answer: B
Q632017 · 23 Apr 2017
The line passing through the points $(1, 2, - 1)$ and $(3, - 1, 2)$ meets the $y z$ -plane at which one of the following points?
1. A. $(0, - \frac{7}{2}, \frac{5}{2})$
2. B. $(0, \frac{7}{2}, \frac{1}{2})$
3. C. $(0, - \frac{7}{2}, - \frac{5}{2})$
4. D. $(0, \frac{7}{2}, - \frac{5}{2})$
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Answer: D
Q642017 · 23 Apr 2017
Under which one of the following conditions are the lines $x = a y + b$ ; $z = cy + d$ and $x = ey + f$ ; $z = g y + h$ perpendicular?
1. A. $a e + c g - 1 = 0$
2. B. $a e + b f - 1 = 0$
3. C. $a e + c g + 1 = 0$
4. D. $a g + ce + 1 = 0$
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Answer: C
Q652017 · 23 Apr 2017
If $f (x) = \frac{x}{x - 1}$ , then what is $\frac{f ( a )}{f ( a + 1 )}$ equal to?
1. A. $f (- \frac{a}{a + 1})$
2. B. $f (a^{2})$
3. C. $f (\frac{1}{a})$
4. D. $f (- a)$
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Answer: B
Q662017 · 23 Apr 2017
Let $f : [- 6, 6] \to R$ be defined by $f (x) = x^{2} - 3$ . Consider the following: 1. $(f \circ f \circ f) (- 1) = (f \circ f \circ f) (1)$ 2. $(f \circ f \circ f) (- 1) - 4 (f \circ f \circ f) (1) = (f \circ f) (0)$ 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: C
Q672017 · 23 Apr 2017
Let $f (x) = p x + q$ and $g (x) = m x + n$ . Then $f (g (x)) = g (f (x))$ is equivalent to
1. A. $f (p) = g (m)$
2. B. $f (q) = g (n)$
3. C. $f (n) = g (q)$
4. D. $f (m) = g (p)$
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Answer: C