Coordinate Geometry · NDA previous year questions

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2013 31 questions

Q512013 · 11 Aug 2013
If the three vertices of the parallelogram $A B C D$ are $A (1, a)$ , $B (3, a)$ , $C (2, b)$ , then $D$ is equal to
1. A. $(3, b)$
2. B. $(6, b)$
3. C. $(4, b)$
4. D. $(5, b)$
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Answer: Dropped in the final answer key (full marks to everyone)
Q522013 · 11 Aug 2013
The value of $k$ for which the lines $2 x + 3 y + a = 0$ and $5 x + k y + a = 0$ represent family of parallel lines is
1. A.3
2. B.4.5
3. C.7.5
4. D.15
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Answer: C
Q532013 · 11 Aug 2013
What is the equation of the line which passes through $(4, - 5)$ and is perpendicular to $3 x + 4 y + 5 = 0$ ?
1. A. $4 x - 3 y - 31 = 0$
2. B. $3 x - 4 y - 41 = 0$
3. C. $4 x + 3 y - 1 = 0$
4. D. $3 x + 4 y + 8 = 0$
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Answer: A
Q542013 · 11 Aug 2013
The foci of the hyperbola $4 x^{2} - 9 y^{2} - 1 = 0$ are
1. A. $(\pm 13, 0)$
2. B. $(\pm \frac{13}{6}, 0)$
3. C. $(0, \pm \frac{13}{6})$
4. D.None of the above
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Answer: B
Q552013 · 11 Aug 2013
For what value of $k$ are the two straight lines $3 x + 4 y = 1$ and $4 x + 3 y + 2 k = 0$ equidistant from the point $(1, 1)$ ?
1. A. $\frac{1}{2}$
2. B.2
3. C. $- 2$
4. D. $- \frac{1}{2}$
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Answer: D
Q562013 · 11 Aug 2013
A point $P$ moves such that its distances from $(1, 2)$ and $(- 2, 3)$ are equal. Then the locus of $P$ is
1. A.straight line
2. B.parabola
3. C.ellipse
4. D.hyperbola
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Answer: A
Q572013 · 11 Aug 2013
The equation of the locus of a point which is equidistant from the axes is
1. A. $y = 2 x$
2. B. $x = 2 y$
3. C. $y = \pm x$
4. D. $2 y + x = 0$
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Answer: C
Q582013 · 11 Aug 2013
What angle does the line segment joining $(5, 2)$ and $(6, - 15)$ subtend at $(0, 0)$ ?
1. A. $\frac{π}{6}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{2}$
4. D. $\frac{3 π}{4}$
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Answer: C
Q592013 · 11 Aug 2013
The length of latus rectum of the ellipse $4 x^{2} + 9 y^{2} = 36$ is
1. A. $\frac{4}{3}$
2. B. $\frac{8}{3}$
3. C.6
4. D.12
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Answer: B
Q602013 · 11 Aug 2013
What is the equation to the straight line passing through $(5, - 2)$ and $(- 4, 7)$ ?
1. A. $5 x - 2 y = 4$
2. B. $- 4 x + 7 y = 9$
3. C. $x + y = 3$
4. D. $x - y = - 1$
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Answer: C
Q612013 · 11 Aug 2013
What is the angle between the lines $x + y = 1$ and $x - y = 1$ ?
1. A. $\frac{π}{6}$
2. B. $\frac{π}{4}$
3. C. $\frac{π}{3}$
4. D. $\frac{π}{2}$
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Answer: D
Q622013 · 11 Aug 2013
The axis of the parabola $y^{2} + 2 x = 0$ is
1. A. $x = 0$
2. B. $y = 0$
3. C. $x = 2$
4. D. $y = 2$
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Answer: B
Q632013 · 11 Aug 2013
The radius of the circle $x^{2} + y^{2} + x + c = 0$ passing through the origin is
1. A. $\frac{1}{4}$
2. B. $\frac{1}{2}$
3. C.1
4. D.2
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Answer: B
Q642013 · 11 Aug 2013
The centroid of the triangle with vertices $(2, 3)$ , $(- 2, - 5)$ and $(3, 5)$ is at
1. A. $(1, 1)$
2. B. $(2, - 1)$
3. C. $(1, - 1)$
4. D. $(1, 2)$
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Answer: A
Q652013 · 11 Aug 2013
The equation of the line, the reciprocals of whose intercepts on the axes are $m$ and $n$ , is given by
1. A. $n x + m y = mn$
2. B. $m x + n y = 1$
3. C. $m x + n y = mn$
4. D. $m x - n y = 1$
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Answer: B
Q662013 · 11 Aug 2013
If $θ$ is the acute angle between the diagonals of a cube, then which one of the following is correct?
1. A. $θ = 3 0^{\circ}$
2. B. $θ = 4 5^{\circ}$
3. C. $2 cos θ = 1$
4. D. $3 cos θ = 1$
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Answer: D
Q692013 · 11 Aug 2013
What is the distance of the line $2 x + y + 2 z = 3$ from the origin?
1. A.1 unit
2. B.1.5 units
3. C.2 units
4. D.2.5 units
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Answer: A
Q702013 · 11 Aug 2013
If the projections of a straight line segment on the coordinate axes are 2, 3, 6, then the length of the segment is
1. A.5 units
2. B.7 units
3. C.11 units
4. D.49 units
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Answer: B
Q912013 · 11 Aug 2013
What is the area of the parabola $x^{2} = y$ bounded by the line $y = 1$ ?
1. A. $\frac{1}{3}$ square unit
2. B. $\frac{2}{3}$ square unit
3. C. $\frac{4}{3}$ square units
4. D.2 square units
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Answer: C
Q252013 · 14 Apr 2013
Two straight line paths are represented by the equations $2 x - y = 2$ and $- 4 x + 2 y = 6$ . Then the paths will
1. A.cross each other at one point
2. B.not cross each other
3. C.cross each other at two points
4. D.cross each other at infinitely many points
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Answer: B
Q262013 · 14 Apr 2013
For what value of k, the equations $3 x - y = 8$ and $9 x - k y = 24$ will have infinitely many solutions ?
1. A.6
2. B.5
3. C.3
4. D.1
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Answer: C
Q512013 · 14 Apr 2013
Which one of the following points lies inside a circle of radius 6 and centre at (3, 5)?
1. A. $(- 2, - 1)$
2. B. $(0, 1)$
3. C. $(- 1, - 2)$
4. D. $(2, - 1)$
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Answer: B
Q522013 · 14 Apr 2013
What is the equation of a straight line which passes through (3, 4) and the sum of whose x and y intercepts is 14?
1. A. $4 x + 3 y = 24$
2. B. $x + y = 14$
3. C. $4 x - 3 y = 0$
4. D. $3 x + 4 y = 25$
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Answer: A
Q532013 · 14 Apr 2013
The equation of the ellipse whose vertices are at $(\pm 5, 0)$ and foci at $(\pm 4, 0)$ is
1. A. $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$
2. B. $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$
3. C. $\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1$
4. D. $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$
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Answer: A
Q542013 · 14 Apr 2013
The point whose abscissa is equal to its ordinate and which is equidistant from A(-1, 0) and B(0, 5) is
1. A.(1, 1)
2. B.(2, 2)
3. C.(-2, -2)
4. D.(3, 3)
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Answer: B