Coordinate Geometry · NDA previous year questions

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2015 27 questions

Q62015 · 27 Sept 2015
$z \overset{z}{ˉ} + (3 - i) z + (3 + i) \overset{z}{ˉ} + 1 = 0$ represents a circle with
1. A.centre $(- 3, - 1)$ and radius 3
2. B.centre $(- 3, 1)$ and radius 3
3. C.centre $(- 3, - 1)$ and radius 4
4. D.centre $(- 3, 1)$ and radius 4
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Answer: A
Q72015 · 27 Sept 2015
The value of the infinite product $6^{\frac{1}{2}} \times 6^{\frac{1}{2}} \times 6^{\frac{3}{8}} \times 6^{\frac{1}{4}} \times \dots$ is
1. A.6
2. B.36
3. C.216
4. D. $\infty$
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Answer: B
Q82015 · 27 Sept 2015
The $n$ th term of an A.P. is $\frac{3 + n}{4}$ , then the sum of first 105 terms is
1. A.270
2. B.735
3. C.1409
4. D.1470
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Answer: D
Q472015 · 27 Sept 2015
The line $3 x + 4 y - 24 = 0$ intersects the $x$ -axis at $A$ and $y$ -axis at $B$ . Then the circumcentre of the triangle $O A B$ where $O$ is the origin is
1. A. $(2, 3)$
2. B. $(3, 3)$
3. C. $(4, 3)$
4. D.None of the above
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Answer: C
Q482015 · 27 Sept 2015
The product of the perpendiculars from the two points $(\pm 4, 0)$ to the line $3 x cos ϕ + 5 y sin ϕ = 15$ is
1. A.25
2. B.16
3. C.9
4. D.8
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Answer: C
Q492015 · 27 Sept 2015
Two straight lines passing through the point $A (3, 2)$ cut the line $2 y = x + 3$ and $x$ -axis perpendicularly at $P$ and $Q$ respectively. The equation of the line $P Q$ is
1. A. $7 x + y - 21 = 0$
2. B. $x + 7 y + 21 = 0$
3. C. $2 x + y - 8 = 0$
4. D. $x + 2 y + 8 = 0$
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Answer: A
Q502015 · 27 Sept 2015
A straight line $x = y + 2$ touches the circle $4 (x^{2} + y^{2}) = r^{2}$ . The value of $r$ is
1. A. $2$
2. B. $22$
3. C.2
4. D.1
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Answer: B
Q512015 · 27 Sept 2015
If the centre of the circle passing through the origin is $(3, 4)$ , then the intercepts cut off by the circle on $x$ -axis and $y$ -axis respectively are
1. A.3 unit and 4 unit
2. B.6 unit and 4 unit
3. C.3 unit and 8 unit
4. D.6 unit and 8 unit
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Answer: D
Q522015 · 27 Sept 2015
Consider any point $P$ on the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$ in the first quadrant. Let $r$ and $s$ represent its distances from $(4, 0)$ and $(- 4, 0)$ respectively, then $(r + s)$ is equal to
1. A.10 unit
2. B.9 unit
3. C.8 unit
4. D.6 unit
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Answer: A
Q532015 · 27 Sept 2015
The eccentricity of the hyperbola $16 x^{2} - 9 y^{2} = 1$ is
1. A. $\frac{3}{5}$
2. B. $\frac{5}{3}$
3. C. $\frac{4}{5}$
4. D. $\frac{5}{4}$
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Answer: B
Q542015 · 27 Sept 2015
The lines $2 x = 3 y = - z$ and $6 x = - y = - 4 z$
1. A.are perpendicular
2. B.are parallel
3. C.intersect at an angle $4 5^{\circ}$
4. D.intersect at an angle $6 0^{\circ}$
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Answer: A
Q382015 · 19 Apr 2015
For the next three (3) items that follow: Consider the triangle $A B C$ with vertices $A (- 2, 3), B (2, 1)$ and $C (1, 2)$ . What is the circumcentre of the triangle $A B C$ ?
1. A. $(- 2, - 2)$
2. B. $(2, 2)$
3. C. $(- 2, 2)$
4. D. $(2, - 2)$
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Answer: A
Q392015 · 19 Apr 2015
For the next three (3) items that follow: Consider the triangle $A B C$ with vertices $A (- 2, 3), B (2, 1)$ and $C (1, 2)$ . What is the centroid of the triangle $A B C$ ?
1. A. $(\frac{1}{3}, 1)$
2. B. $(\frac{1}{3}, 2)$
3. C. $(1, \frac{2}{3})$
4. D. $(\frac{1}{2}, 3)$
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Answer: B
Q402015 · 19 Apr 2015
For the next three (3) items that follow: Consider the triangle $A B C$ with vertices $A (- 2, 3), B (2, 1)$ and $C (1, 2)$ . What is the foot of the altitude from the vertex $A$ of the triangle $A B C$ ?
1. A. $(1, 4)$
2. B. $(- 1, 3)$
3. C. $(- 2, 4)$
4. D. $(- 1, 4)$
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Answer: D
Q412015 · 19 Apr 2015
The perpendicular distance between the straight lines $6 x + 8 y + 15 = 0$ and $3 x + 4 y + 9 = 0$ is
1. A.3/2 units
2. B.3/10 unit
3. C.3/4 unit
4. D.2/7 unit
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Answer: B
Q422015 · 19 Apr 2015
The area of a triangle, whose vertices are $(3, 4), (5, 2)$ and the point of intersection of the lines $x = a$ and $y = 5$ , is 3 square units. What is the value of $a$ ?
1. A.2
2. B.3
3. C.4
4. D.5
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Answer: D
Q432015 · 19 Apr 2015
The length of perpendicular from the origin to a line is 5 units and the line makes an angle $12 0^{\circ}$ with the positive direction of $x$ -axis. The equation of the line is
1. A. $x + 3 y = 5$
2. B. $3 x + y = 10$
3. C. $3 x - y = 10$
4. D.None of the above
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Answer: B
Q442015 · 19 Apr 2015
The equation of the line joining the origin to the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ is
1. A. $x - y = 0$
2. B. $x + y = 0$
3. C. $x = 0$
4. D. $y = 0$
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Answer: A
Q452015 · 19 Apr 2015
A line passes through $(2, 2)$ and is perpendicular to the line $3 x + y = 3$ . Its $y$ -intercept is
1. A.3/4
2. B.4/3
3. C.1/3
4. D.3
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Answer: B
Q462015 · 19 Apr 2015
The point on the parabola $y^{2} = 4 a x$ nearest to the focus has its abscissa
1. A. $x = 0$
2. B. $x = a$
3. C. $x = a /2$
4. D. $x = 2 a$
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Answer: A
Q472015 · 19 Apr 2015
The hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ passes through the point $(35, 1)$ and the length of its latus rectum is $\frac{4}{3}$ units. The length of the conjugate axis is
1. A.2 units
2. B.3 units
3. C.4 units
4. D.5 units
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Answer: C
Q482015 · 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 is the length of the line segment?
1. A.19 units
2. B.17 units
3. C.15 units
4. D.13 units
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Answer: D
Q682015 · 19 Apr 2015
For the next three (3) items that follow : Consider the parametric equation $x = \frac{a ( 1 - t ^{2} )}{1 + t ^{2}}$ , $y = \frac{2 a t}{1 + t ^{2}}$ What does the equation represent?
1. A.It represents a circle of diameter $a$
2. B.It represents a circle of radius $a$
3. C.It represents a parabola
4. D.None of the above
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Answer: B
Q692015 · 19 Apr 2015
Consider the parametric equation $x = \frac{a ( 1 - t ^{2} )}{1 + t ^{2}}$ , $y = \frac{2 a t}{1 + t ^{2}}$ What is $\frac{d y}{d x}$ equal to?
1. A. $\frac{y}{x}$
2. B. $- \frac{y}{x}$
3. C. $\frac{x}{y}$
4. D. $- \frac{x}{y}$
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Answer: D
Q702015 · 19 Apr 2015
Consider the parametric equation $x = \frac{a ( 1 - t ^{2} )}{1 + t ^{2}}$ , $y = \frac{2 a t}{1 + t ^{2}}$ What is $\frac{d ^{2} y}{d x ^{2}}$ equal to?
1. A. $\frac{a ^{2}}{y ^{2}}$
2. B. $\frac{a ^{2}}{x ^{2}}$
3. C. $- \frac{a ^{2}}{x ^{2}}$
4. D. $- \frac{a ^{2}}{y ^{3}}$
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Answer: D