Coordinate Geometry · NDA previous year questions

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2014 26 questions

Q482014 · 20 Apr 2014
What is the equation of the line midway between the lines $3 x - 4 y + 12 = 0$ and $3 x - 4 y = 6$ ?
1. A. $3 x - 4 y - 9 = 0$
2. B. $3 x - 4 y + 9 = 0$
3. C. $3 x - 4 y - 3 = 0$
4. D. $3 x - 4 y + 3 = 0$
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Answer: D
Q492014 · 20 Apr 2014
What is the sum of the major and minor axes of the ellipse whose eccentricity is 4/5 and length of latus rectum is 14.4 unit?
1. A.32 unit
2. B.48 unit
3. C.64 unit
4. D.None of the above
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Answer: C
Q502014 · 20 Apr 2014
What is the equation of parabola whose vertex is at $(0, 0)$ and focus is at $(0, - 2)$ ?
1. A. $y^{2} + 8 x = 0$
2. B. $y^{2} - 8 x = 0$
3. C. $x^{2} + 8 y = 0$
4. D. $x^{2} - 8 y = 0$
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Answer: C
Q752014 · 20 Apr 2014
For the next two (02) items that follow: Consider an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ . What is the area of the greatest rectangle that can be inscribed in the ellipse?
1. A. $ab$
2. B. $2 ab$
3. C. $ab /2$
4. D. $ab$
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Answer: B
Q762014 · 20 Apr 2014
For the next two (02) items that follow: Consider an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ . What is the area included between the ellipse and the greatest rectangle inscribed in the ellipse?
1. A. $ab (π - 1)$
2. B. $2 ab (π - 1)$
3. C. $ab (π - 2)$
4. D.None of the above
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Answer: C
Q1152014 · 20 Apr 2014
For the next three (03) items that follow: The vertices of a triangle ABC are $A (2, 3, 1)$ , $B (- 2, 2, 0)$ and $C (0, 1, - 1)$ . What is the cosine of angle ABC?
1. A. $\frac{1}{3}$
2. B. $\frac{1}{2}$
3. C. $\frac{2}{6}$
4. D.None of the above
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Answer: A
Q1162014 · 20 Apr 2014
For the next three (03) items that follow: The vertices of a triangle ABC are $A (2, 3, 1)$ , $B (- 2, 2, 0)$ and $C (0, 1, - 1)$ . What is the area of the triangle?
1. A. $62$ square unit
2. B. $32$ square unit
3. C. $103$ square unit
4. D.None of the above
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Answer: B
Q1172014 · 20 Apr 2014
For the next three (03) items that follow: The vertices of a triangle ABC are $A (2, 3, 1)$ , $B (- 2, 2, 0)$ and $C (0, 1, - 1)$ . What is the magnitude of the line joining mid points of the sides AC and BC?
1. A. $\frac{1}{2}$ unit
2. B.1 unit
3. C. $\frac{3}{2}$ unit
4. D.2 unit
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Answer: C

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