Coordinate Geometry · NDA previous year questions

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2016 24 questions

Q482016 · 18 Sept 2016
An equilateral triangle has one vertex at $(0, 0)$ and another at $(3, 3)$ . What are the coordinates of the third vertex?
1. A. $(0, 23)$ only
2. B. $(3, - 3)$ only
3. C. $(0, 23)$ or $(3, - 3)$
4. D.Neither $(0, 23)$ nor $(3, - 3)$
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Answer: C
Q492016 · 18 Sept 2016
What is the equation of the right bisector of the line segment joining (1, 1) and (2, 3)?
1. A. $2 x + 4 y - 11 = 0$
2. B. $2 x - 4 y - 5 = 0$
3. C. $2 x - 4 y - 11 = 0$
4. D. $x - y + 1 = 0$
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Answer: A
Q502016 · 18 Sept 2016
If the point (a, a) lies between the lines $∣ x + y ∣ = 2$ , then which one of the following is correct?
1. A. $∣ a ∣ < 2$
2. B. $∣ a ∣ < 2$
3. C. $∣ a ∣ < 1$
4. D. $∣ a ∣ < \frac{1}{2}$
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Answer: C
Q512016 · 18 Sept 2016
What is the equation of the straight line which passes through the point of intersection of the straight lines $x + 2 y = 5$ and $3 x + 7 y = 17$ and is perpendicular to the straight line $3 x + 4 y = 10$ ?
1. A. $4 x + 3 y + 2 = 0$
2. B. $4 x - y + 2 = 0$
3. C. $4 x - 3 y - 2 = 0$
4. D. $4 x - 3 y + 2 = 0$
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Answer: D
Q522016 · 18 Sept 2016
If (a, b) is at unit distance from the line $8 x + 6 y + 1 = 0$ , then which of the following conditions are correct? 1. $3 a - 4 b - 4 = 0$ 2. $8 a + 6 b + 11 = 0$ 3. $8 a + 6 b - 9 = 0$ Select the correct answer using the code given below :
1. A.1 and 2 only
2. B.2 and 3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: B
Q532016 · 18 Sept 2016
A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (-3, 5). What is the foot of the perpendicular drawn from the point (3, 3) on this line?
1. A.(1, 3)
2. B.(2, 0)
3. C.(0, 2)
4. D.(1, 1)
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Answer: D
Q542016 · 18 Sept 2016
What is the radius of the circle passing through the point $(2, 4)$ and having centre at the intersection of the lines $x - y = 4$ and $2 x + 3 y + 7 = 0$ ?
1. A.3 units
2. B.5 units
3. C. $33$ units
4. D. $52$ units
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Answer: D
Q552016 · 18 Sept 2016
What is the equation of the hyperbola having latus rectum and eccentricity 8 and $\frac{3}{5}$ respectively?
1. A. $\frac{x ^{2}}{25} - \frac{y ^{2}}{20} = 1$
2. B. $\frac{x ^{2}}{40} - \frac{y ^{2}}{20} = 1$
3. C. $\frac{x ^{2}}{40} - \frac{y ^{2}}{30} = 1$
4. D. $\frac{x ^{2}}{30} - \frac{y ^{2}}{25} = 1$
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Answer: A
Q562016 · 18 Sept 2016
If the ellipse $9 x^{2} + 16 y^{2} = 144$ intercepts the line $3 x + 4 y = 12$ , then what is the length of the chord so formed?
1. A.5 units
2. B.6 units
3. C.8 units
4. D.10 units
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Answer: A
Q572016 · 18 Sept 2016
What is the eccentricity of rectangular hyperbola?
1. A. $2$
2. B. $3$
3. C. $5$
4. D. $6$
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Answer: A
Q582016 · 18 Sept 2016
Consider the following for the next two (02) items that follow: Consider the parabola $y = x^{2} + 7 x + 2$ and the straight line $y = 3 x - 3$ . What are the coordinates of the point on the parabola which is closest to the straight line?
1. A. $(0, 2)$
2. B. $(- 2, - 8)$
3. C. $(- 7, 2)$
4. D. $(1, 10)$
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Answer: B
Q592016 · 18 Sept 2016
Consider the following for the next two (02) items that follow: Consider the parabola $y = x^{2} + 7 x + 2$ and the straight line $y = 3 x - 3$ . What is the shortest distance from the above point on the parabola to the line?
1. A. $\frac{10}{2}$
2. B. $\frac{10}{5}$
3. C. $\frac{1}{10}$
4. D. $\frac{5}{4}$
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Answer: C
Q872016 · 18 Sept 2016
What is the curve which passes through the point $(1, 1)$ and whose slope is $\frac{2 y}{x}$ ?
1. A.Circle
2. B.Parabola
3. C.Ellipse
4. D.Hyperbola
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Answer: B
Q882016 · 18 Sept 2016
If $x d y = y d x + y^{2} d y$ , $y > 0$ and $y (1) = 1$ , then what is $y (- 3)$ equal to?
1. A.3 only
2. B. $- 1$ only
3. C.Both $- 1$ and 3
4. D.Neither $- 1$ nor 3
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Answer: A
Q332016 · 17 Apr 2016
For the next three (3) items that follow : Consider a parallelogram whose vertices are $A (1, 2), B (4, y), C (x, 6)$ and $D (3, 5)$ taken in order. What is the value of $A C^{2} - B D^{2}$ ?
1. A.25
2. B.30
3. C.36
4. D.40
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Answer: C
Q342016 · 17 Apr 2016
For the next three (3) items that follow : Consider a parallelogram whose vertices are $A (1, 2), B (4, y), C (x, 6)$ and $D (3, 5)$ taken in order. What is the point of intersection of the diagonals?
1. A. $(\frac{7}{2}, 4)$
2. B. $(3, 4)$
3. C. $(\frac{7}{2}, 5)$
4. D. $(3, 5)$
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Answer: A
Q352016 · 17 Apr 2016
For the next three (3) items that follow : Consider a parallelogram whose vertices are $A (1, 2), B (4, y), C (x, 6)$ and $D (3, 5)$ taken in order. What is the area of the parallelogram?
1. A. $\frac{7}{2}$ square units
2. B. $4$ square units
3. C. $\frac{11}{2}$ square units
4. D. $7$ square units
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Answer: D
Q362016 · 17 Apr 2016
A straight line intersects $x$ and $y$ axes at $P$ and $Q$ respectively. If $(3, 5)$ is the middle point of $P Q$ , then what is the area of the triangle $O P Q$ ?
1. A.12 square units
2. B.15 square units
3. C.20 square units
4. D.30 square units
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Answer: D
Q412016 · 17 Apr 2016
For the next two (2) items that follow : Consider the two circles $(x - 1)^{2} + (y - 3)^{2} = r^{2}$ and $x^{2} + y^{2} - 8 x + 2 y + 8 = 0$ What is the distance between the centres of the two circles?
1. A.5 units
2. B.6 units
3. C.8 units
4. D.10 units
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Answer: A
Q422016 · 17 Apr 2016
For the next two (2) items that follow : Consider the two circles $(x - 1)^{2} + (y - 3)^{2} = r^{2}$ and $x^{2} + y^{2} - 8 x + 2 y + 8 = 0$ If the circles intersect at two distinct points, then which one of the following is correct?
1. A. $r = 1$
2. B. $1 < r < 2$
3. C. $r = 2$
4. D. $2 < r < 8$
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Answer: D
Q432016 · 17 Apr 2016
For the next two (2) items that follow: Consider a circle passing through the origin and the points $(a, b)$ and $(- b, - a)$ . On which line does the centre of the circle lie?
1. A. $x + y = 0$
2. B. $x - y = 0$
3. C. $x + y = a + b$
4. D. $x - y = a^{2} - b^{2}$
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Answer: A
Q442016 · 17 Apr 2016
For the next two (2) items that follow: Consider a circle passing through the origin and the points $(a, b)$ and $(- b, - a)$ . What is the sum of the squares of the intercepts cut off by the circle on the axes?
1. A. $(\frac{a ^{2} + b ^{2}}{a ^{2} - b ^{2}})^{2}$
2. B. $2 (\frac{a ^{2} + b ^{2}}{a - b})^{2}$
3. C. $4 (\frac{a ^{2} + b ^{2}}{a - b})^{2}$
4. D.None of the above
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Answer: B
Q1032016 · 17 Apr 2016
If a circle of radius $b$ units with centre at $(0, b)$ touches the line $y = x - 2$ , then what is the value of $b$ ?
1. A. $2 + 2$
2. B. $2 - 2$
3. C. $22$
4. D. $2$
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Answer: A
Q1042016 · 17 Apr 2016
For the next two (2) items that follow : Consider the curves $f (x) = x ∣ x ∣ - 1$ and $g (x) = {\frac{3 x}{2}, 2 x, x > 0 x \leq 0$ Where do the curves intersect?
1. A.At $(2, 3)$ only
2. B.At $(- 1, - 2)$ only
3. C.At $(2, 3)$ and $(- 1, - 2)$
4. D.Neither at $(2, 3)$ nor at $(- 1, - 2)$
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Answer: C