Coordinate Geometry · NDA previous year questions

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2009 15 questions

Q192009 · 30 Aug 2009
What is the length of arc of a circle of radius $5 cm$ subtending a central angle measuring $1 5^{\circ}$ ?
1. A. $5 π /12 cm$
2. B. $7 π /12 cm$
3. C. $π /12 cm$
4. D. $π /5 cm$
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Answer: A
Q392009 · 30 Aug 2009
What does the equation $x d y = y d x$ represent ?
1. A.A family of circles
2. B.A family of parabolas
3. C.A family of hyperbolas
4. D.A family of straight lines
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Answer: D
Q532009 · 30 Aug 2009
The velocity $v$ of a particle at any instant $t$ moving in a straight line is given by $v = s + 1$ where $s$ meter is the distance travelled in $t$ second. What is the time taken by the particle to cover a distance of 9 meter ?
1. A. $1 s$
2. B. $(ln 10) s$
3. C. $2 (ln 10) s$
4. D. $10 s$
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Answer: B
Q542009 · 30 Aug 2009
The curve $y^{2} = - 4 a x (a > 0)$ lies in :
1. A.First and fourth quadrants
2. B.First and second quadrants
3. C.Second and third quadrants
4. D.Third and fourth quadrants
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Answer: C
Q552009 · 30 Aug 2009
The circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ touches :
1. A.Only the x-axis
2. B.Only the y-axis
3. C.Both the axes
4. D.Neither of the axes
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Answer: C
Q582009 · 30 Aug 2009
The middle point of the segment of the straight line joining the points $(p, q)$ and $(q, - p)$ is $(r /2, s /2)$ . What is the length of the segment ?
1. A. $[(s^{2} + r^{2})^{1/2}] /2$
2. B. $[(s^{2} + r^{2})^{1/2}] /4$
3. C. $(s^{2} + r^{2})^{1/2}$
4. D. $s + r$
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Answer: C
Q622009 · 30 Aug 2009
What is the locus of a point which is equidistant from the point $(m + n, n - m)$ and the point $(m - n, n + m)$ ?
1. A. $m x = n y$
2. B. $n x = - m y$
3. C. $n x = m y$
4. D. $m x = - n y$
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Answer: C
Q652009 · 30 Aug 2009
The ellipse $\frac{x ^{2}}{169} + \frac{y ^{2}}{25} = 1$ has the same eccentricity as the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ . What is the ratio of $a$ to $b$ ?
1. A. $5/13$
2. B. $13/5$
3. C. $7/8$
4. D. $8/7$
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Answer: B
Q842009 · 19 Apr 2009
If $x$ -axis is tangent to the circle $x^{2} + y^{2} + 2 g x + 2 f y + k = 0$ , then which one of the following is correct?
1. A. $g^{2} = k$
2. B. $g^{2} = f$
3. C. $f^{2} = k$
4. D. $f^{2} = g$
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Answer: A
Q852009 · 19 Apr 2009
What is the sum of focal radii of any point on an ellipse equal to?
1. A.Length of latus rectum
2. B.Length of major axis
3. C.Length of minor axis
4. D.Length of semi-latus rectum
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Answer: B
Q862009 · 19 Apr 2009
What does an equation of the first degree containing one arbitrary parameter passing through a fixed point represent?
1. A.Circle
2. B.Straight line
3. C.Parabola
4. D.Ellipse
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Answer: B
Q872009 · 19 Apr 2009
What is the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$ ?
1. A. $(1, 10)$
2. B. $(5, 6)$
3. C. $(6, 5)$
4. D. $(7, 4)$
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Answer: B
Q882009 · 19 Apr 2009
Consider the following statements: 1. The equation to a straight line parallel to the axis of $x$ is $y = d$ , where $d$ is a constant. 2. The equation to the axis of $x$ is $x = 0$ . Which of the statements given 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: A
Q912009 · 19 Apr 2009
The points $(1, 3, 4)$ , $(- 1, 6, 10)$ , $(- 7, 4, 7)$ and $(- 5, 1, 1)$ are the vertices of a
1. A.rhombus
2. B.rectangle
3. C.parallelogram
4. D.square
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Answer: A
Q942009 · 19 Apr 2009
What is the eccentricity of an ellipse if its latus rectum is equal to one-half of its minor axis?
1. A.1/4
2. B.1/2
3. C. $3 /4$
4. D. $3 /2$
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Answer: D