Coordinate Geometry · NDA previous year questions

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2010 27 questions

Q412010 · 22 Aug 2010
What is the equation to the straight line joining the origin to the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ ?
1. A. $x + y = 0$
2. B. $x + y + 1 = 0$
3. C. $x - y = 0$
4. D. $x + y + 2 = 0$
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Answer: C
Q422010 · 22 Aug 2010
What is the equation to circle which touches both the axes and has centre on the line $x + y = 4$ ?
1. A. $x^{2} + y^{2} - 4 x + 4 y + 4 = 0$
2. B. $x^{2} + y^{2} - 4 x - 4 y + 4 = 0$
3. C. $x^{2} + y^{2} + 4 x - 4 y - 4 = 0$
4. D. $x^{2} + y^{2} + 4 x + 4 y - 4 = 0$
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Answer: B
Q442010 · 22 Aug 2010
If the straight lines $x - 2 y = 0$ and $k x + y = 1$ intersect at the point $(1, \frac{1}{2})$ , then what is the value of $k$ ?
1. A.1
2. B.2
3. C.1/2
4. D. $- 1/2$
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Answer: C
Q472010 · 22 Aug 2010
A point $P$ moves such that the difference of its distances from two given points $(c, 0)$ and $(- c, 0)$ is constant. What is the locus of the point $P$ ?
1. A.Circle
2. B.Ellipse
3. C.Hyperbola
4. D.Parabola
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Answer: C
Q522010 · 22 Aug 2010
Under which of the following conditions does a general second-degree equation $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ ( $a \neq = 0$ ) represent a circle?
1. A. $h = g, a = b$
2. B. $h = g = f, a = b$
3. C. $h = 0, a = b$
4. D. $h = 0, g^{2} + f^{2} - c = a + b$
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Answer: C
Q532010 · 22 Aug 2010
What is the area of a triangle whose vertices are at $(3, - 1, 2)$ , $(1, - 1, - 3)$ and $(4, - 3, 1)$ ?
1. A. $\frac{165}{2}$
2. B. $\frac{135}{2}$
3. C.4
4. D.2
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Answer: A
Q552010 · 22 Aug 2010
If the latus rectum of an ellipse is equal to half its minor axis, then what is its eccentricity?
1. A. $\frac{1}{2}$
2. B. $3$
3. C. $\frac{3}{2}$
4. D. $\frac{1}{2}$
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Answer: C
Q562010 · 22 Aug 2010
If $A = {2, 3}, B = {4, 5}, C = {5, 6}$ , then what is the number of elements in $A \times (B \cap C)$ ?
1. A.2
2. B.4
3. C.6
4. D.8
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Answer: A
Q572010 · 22 Aug 2010
What is the slope of the line perpendicular to the line $\frac{x}{4} + \frac{y}{3} = 1$ ?
1. A. $\frac{3}{4}$
2. B. $- \frac{3}{4}$
3. C. $- \frac{4}{3}$
4. D. $\frac{4}{3}$
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Answer: D
Q582010 · 22 Aug 2010
$A B C$ is a triangle in which $B C = 10 cm$ , $C A = 6 cm$ and $A B = 8 cm$ . Which one of the following is correct?
1. A. $A B C$ is an acute-angled triangle
2. B. $A B C$ is an obtuse-angled triangle
3. C. $A B C$ is a right-angled triangle
4. D.None of the above
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Answer: C
Q592010 · 22 Aug 2010
If the AM and GM between two numbers are in the ratio $m : n$ , then what is the ratio between the two numbers?
1. A. $\frac{m + m ^{2} - n ^{2}}{m - m ^{2} - n ^{2}}$
2. B. $\frac{m + n}{m - n}$
3. C. $\frac{m ^{2} - n ^{2}}{m ^{2} + n ^{2}}$
4. D. $\frac{m ^{2} + n ^{2} - mn}{m ^{2} + n ^{2} + mn}$
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Answer: A
Q1152010 · 22 Aug 2010
If the area of a triangle with vertices $(- 3, 0)$ , $(3, 0)$ and $(0, k)$ is $9$ square units, then what is the value of $k$ ?
1. A. $3$
2. B. $6$
3. C. $9$
4. D. $12$
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Answer: A
Q122010 · 18 Apr 2010
A circle is drawn with the two foci of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ at the end of the diameter. What is the equation to the circle?
1. A. $x^{2} + y^{2} = a^{2} + b^{2}$
2. B. $x^{2} + y^{2} = a^{2} - b^{2}$
3. C. $x^{2} + y^{2} = 2 (a^{2} + b^{2})$
4. D. $x^{2} + y^{2} = 2 (a^{2} - b^{2})$
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Answer: B
Q132010 · 18 Apr 2010
What is the image of the point $(1, 2)$ on the line $3 x + 4 y - 1 = 0$ ?
1. A. $(- \frac{7}{5}, - \frac{6}{5})$
2. B. $(\frac{7}{8}, \frac{1}{2})$
3. C. $(\frac{7}{8}, - \frac{1}{2})$
4. D. $(- \frac{7}{5}, \frac{1}{2})$
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Answer: A
Q412010 · 18 Apr 2010
If $(4, 0)$ and $(- 4, 0)$ are the foci of an ellipse and the semi-minor axis is 3, then the ellipse passes through which one of the following points?
1. A. $(2, 0)$
2. B. $(0, 5)$
3. C. $(0, 0)$
4. D. $(5, 0)$
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Answer: D
Q542010 · 18 Apr 2010
What are the equations of the directrices of the ellipse $25 x^{2} + 16 y^{2} = 400$ ?
1. A. $3 x \pm 25 = 0$
2. B. $3 y \pm 25 = 0$
3. C. $x \pm 15 = 0$
4. D. $y \pm 25 = 0$
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Answer: B
Q562010 · 18 Apr 2010
Let $E$ be the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ and $C$ be the circle $x^{2} + y^{2} = 9$ . Let $P = (1, 2)$ and $Q = (2, 1)$ . Which one of the following is correct?
1. A. $Q$ lies inside $C$ but outside $E$
2. B. $Q$ lies outside both $C$ and $E$
3. C. $P$ lies inside both $C$ and $E$
4. D. $P$ lies inside $C$ but outside $E$
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Answer: D
Q572010 · 18 Apr 2010
What is the geometric interpretation of the identity $(a - b) \times (a + b) = 2 (a \times b)$ ? 1. If the diagonals of a given parallelogram are used as sides of a second parallelogram, then the area of the second parallelogram is twice that of the given parallelogram. 2. If the semi-diagonals of a given parallelogram are used as sides of a second parallelogram, then the area of the second parallelogram is half that of the given parallelogram. Select the correct answer using the code given below:
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: C
Q582010 · 18 Apr 2010
What is $\int_{0}^{π /2} \frac{s i n ^{3} x}{s i n ^{3} x + c o s ^{3} x} d x$ ?
1. A. $π$
2. B. $\frac{π}{2}$
3. C. $\frac{π}{4}$
4. D.0
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Answer: C
Q702010 · 18 Apr 2010
What is the area of the triangle with vertices (0, 2, 2), (2, 0, -1) and (3, 4, 0)?
1. A.15/2 square units
2. B.15 square units
3. C.7/2 square units
4. D.7 square units
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Answer: A
Q712010 · 18 Apr 2010
If $\frac{1}{2 - - 2}$ is one of the roots of $a x^{2} + b x + c = 0$ where a, b, c are real, then what are the values of a, b, c respectively?
1. A.6, -4, 1
2. B.4, 6, -1
3. C.3, -2, 1
4. D.6, 4, 1
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Answer: A
Q912010 · 18 Apr 2010
Let O (0, 0, 0), P (3, 4, 5), Q (m, n, r) and R (1, 1, 1) be the vertices of a parallelogram taken in order. What is the value of $m + n + r$ ?
1. A.6
2. B.12
3. C.15
4. D.More than 15
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Answer: C
Q932010 · 18 Apr 2010
What is the locus of points, the difference of whose distances from two points being constant?
1. A.Pair of straight lines
2. B.An ellipse
3. C.A hyperbola
4. D.A parabola
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Answer: C
Q1112010 · 18 Apr 2010
Consider the following statements in respect of circles $x^{2} + y^{2} - 2 x - 2 y = 0$ and $x^{2} + y^{2} = 1$ : 1. The radius of the first circle is twice that of the second circle. 2. Both the circles pass through the origin. 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: D
Q1162010 · 18 Apr 2010
Directions: For the next 3 (three) questions to follow: The vertices of a cube are (0, 0, 0), (2, 0, 0), (0, 2, 0), (0, 0, 2), (2, 2, 0), (2, 0, 2), (0, 2, 2), (2, 2, 2) respectively. What is the angle between any two diagonals of the cube?
1. A. $cos^{- 1} (1/2)$
2. B. $cos^{- 1} (1/3)$
3. C. $cos^{- 1} (1/ 3)$
4. D. $cos^{- 1} (2/ 3)$
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Answer: B