Coordinate Geometry · NDA previous year questions

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2014 26 questions

Q422014 · 28 Sept 2014
$A (3, 4)$ and $B (5, - 2)$ are two points and P is a point such that PA = PB. If the area of triangle PAB is 10 square unit, what are the coordinates of P?
1. A. $(1, 0)$ only
2. B. $(7, 2)$ only
3. C. $(1, 0)$ or $(7, 2)$
4. D.Neither $(1, 0)$ nor $(7, 2)$
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Answer: C
Q432014 · 28 Sept 2014
What is the product of the perpendiculars drawn from the points $(\pm a^{2} - b^{2}, 0)$ upon the line $b x cos α + a y sin α = ab$ ?
1. A. $a^{2}$
2. B. $b^{2}$
3. C. $a^{2} + b^{2}$
4. D. $a + b$
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Answer: B
Q442014 · 28 Sept 2014
Which one of the following is correct in respect of the equations $\frac{x - 1}{2} = \frac{y - 2}{3}$ and $2 x + 3 y = 5$ ?
1. A.They represent two lines which are parallel.
2. B.They represent two lines which are perpendicular.
3. C.They represent two lines which are neither parallel nor perpendicular.
4. D.The first equation does not represent a line.
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Answer: B
Q452014 · 28 Sept 2014
For the next two (02) items that follow : Consider the circles $x^{2} + y^{2} + 2 a x + c = 0$ and $x^{2} + y^{2} + 2 b y + c = 0$ . What is the distance between the centres of the two circles?
1. A. $a^{2} + b^{2}$
2. B. $a^{2} + b^{2}$
3. C. $a + b$
4. D. $2 (a + b)$
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Answer: A
Q462014 · 28 Sept 2014
For the next two (02) items that follow : Consider the circles $x^{2} + y^{2} + 2 a x + c = 0$ and $x^{2} + y^{2} + 2 b y + c = 0$ . The two circles touch each other if
1. A. $c = a^{2} + b^{2}$
2. B. $\frac{1}{c} = \frac{1}{a ^{2}} + \frac{1}{b ^{2}}$
3. C. $c = \frac{1}{a ^{2}} + \frac{1}{b ^{2}}$
4. D. $c = \frac{1}{a ^{2} + b ^{2}}$
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Answer: B
Q472014 · 28 Sept 2014
For the next three (03) items that follow : The line $2 y = 3 x + 12$ cuts the parabola $4 y = 3 x^{2}$ . Where does the line cut the parabola?
1. A.At $(- 2, 3)$ only
2. B.At $(4, 12)$ only
3. C.At both $(- 2, 3)$ and $(4, 12)$
4. D.Neither at $(- 2, 3)$ nor at $(4, 12)$
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Answer: C
Q482014 · 28 Sept 2014
What is the length of the latus rectum of the ellipse $25 x^{2} + 16 y^{2} = 400$ ?
1. A.25/2
2. B.25/4
3. C.16/5
4. D.32/5
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Answer: D
Q492014 · 28 Sept 2014
If $f (x) = a x + b$ and $g (x) = c x + d$ such that $f (g (x)) = g (f (x))$ , then which one of the following is correct ?
1. A. $f (c) = g (a)$
2. B. $f (a) = g (c)$
3. C. $f (c) = g (d)$
4. D. $f (d) = g (b)$
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Answer: D
Q842014 · 28 Sept 2014
What is the area of the parabola $y^{2} = 4 b x$ bounded by its latus rectum?
1. A. $2 b^{2} /3 square unit$
2. B. $4 b^{2} /3 square unit$
3. C. $b^{2} square unit$
4. D. $8 b^{2} /3 square unit$
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Answer: D
Q902014 · 28 Sept 2014
What is the area of the triangle OAB where O is the origin, $O A = 3 \hat{i} - \hat{j} + \hat{k}$ and $O B = 2 \hat{i} + \hat{j} - 3 \hat{k}$ ?
1. A. $56 square unit$
2. B. $\frac{5 6}{2} square unit$
3. C. $6 square unit$
4. D. $30 square unit$
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Answer: B
Q82014 · 20 Apr 2014
Let $z = x + i y$ where $x, y$ are real variables and $i = - 1$ . If $∣2 z - 1∣ = ∣ z - 2∣$ , then the point $z$ describes:
1. A.A circle
2. B.An ellipse
3. C.A hyperbola
4. D.A parabola
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Answer: A
Q92014 · 20 Apr 2014
If $∣ z + \overset{z}{ˉ} ∣ = ∣ z - \overset{z}{ˉ} ∣$ , then the locus of $z$ is:
1. A.A pair of straight lines
2. B.A line
3. C.A set of four straight lines
4. D.A circle
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Answer: A
Q392014 · 20 Apr 2014
Consider the following statements: 1. If $3 θ$ is an acute angle such that $sin 3 θ = cos 2 θ$ , then the measurement of $θ$ in radian equals to $\frac{π}{10}$ . 2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle. Which of the above statements 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
Q402014 · 20 Apr 2014
Consider the following statements: 1. $tan^{- 1} 1 + tan^{- 1} (0.5) = π /2$ 2. $sin^{- 1} (1/3) + cos^{- 1} (1/3) = π /2$ Which of the above statements 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: B
Q412014 · 20 Apr 2014
What is $sin^{- 1} sin \frac{3 π}{5}$ equal to?
1. A. $\frac{3 π}{5}$
2. B. $\frac{2 π}{5}$
3. C. $\frac{π}{5}$
4. D.None of the above
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Answer: B
Q422014 · 20 Apr 2014
If $x$ and $y$ are positive and $x y > 1$ , then what is $tan^{- 1} x + tan^{- 1} y$ equal to?
1. A. $tan^{- 1} (\frac{x + y}{1 - x y})$
2. B. $π + tan^{- 1} (\frac{x + y}{1 - x y})$
3. C. $π - tan^{- 1} (\frac{x + y}{1 - x y})$
4. D. $tan^{- 1} (\frac{x - y}{1 + x y})$
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Answer: B
Q462014 · 20 Apr 2014
What is the equation of the line through $(1, 2)$ so that the segment of the line intercepted between the axes is bisected at this point?
1. A. $2 x - y = 4$
2. B. $2 x - y + 4 = 0$
3. C. $2 x + y = 4$
4. D. $2 x + y + 4 = 0$
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Answer: C
Q472014 · 20 Apr 2014
What is the equation of straight line passing through the point $(4, 3)$ and making equal intercepts on the coordinate axes?
1. A. $x + y = 7$
2. B. $3 x + 4 y = 7$
3. C. $x - y = 1$
4. D.None of the above
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Answer: A
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