Coordinate Geometry · NDA previous year questions

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2022 18 questions

Q122022 · 4 Sept 2022
What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm ?
1. A. $1 + 2$ cm
2. B. $2 + 2$ cm
3. C. $2 + 3$ cm
4. D. $3 + 3$ cm
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Answer: C
Q562022 · 4 Sept 2022
Consider the following statements in respect of the line passing through origin and inclining at an angle of $7 5^{\circ}$ with the positive direction of x-axis : 1. The line passes through the point $(1, \frac{1}{2 - 3})$ . 2. The line entirely lies in first and third quadrants. 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: C
Q572022 · 4 Sept 2022
If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?
1. A.3x + 4y − 25 = 0
2. B.4x + 3y − 24 = 0
3. C.4x − 3y = 0
4. D.3x − 4y + 7 = 0
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Answer: B
Q582022 · 4 Sept 2022
The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid- point of AB is at the origin and B lies above the origin. What is the equation of line passing through (8, 0) and parallel to the side AC ?
1. A. $x - 3 y - 8 = 0$
2. B. $x + 3 y - 8 = 0$
3. C. $3 x + y - 83 = 0$
4. D. $3 x - y - 83 = 0$
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Answer: A
Q592022 · 4 Sept 2022
The centre of the circle passing through the origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line
1. A.2x − y + 1 = 0
2. B.3x − 2y − 1 = 0
3. C.3x − 4y + 6 = 0
4. D.2x + 3y − 26 = 0
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Answer: C
Q602022 · 4 Sept 2022
The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity ?
1. A. $\frac{3}{2}$
2. B. $3$
3. C. $\frac{5}{2}$
4. D. $5$
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Answer: A
Q612022 · 4 Sept 2022
An equilateral triangle is inscribed in a parabola $x^{2} = 3 y$ where one vertex of the triangle is at the vertex of the parabola. If p is the length of side of the triangle and q is the length of the latus rectum, then which one of the following is correct ?
1. A. $p = q$
2. B. $p = 3 q$
3. C. $p = 23 q$
4. D. $23 p = q$
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Answer: C
Q622022 · 4 Sept 2022
Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4), and D(8, 14, 12). Which of the following statements is/are correct? 1. The points are the vertices of a rectangle ABCD. 2. The mid-point of A C is the same as that of BD. 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: B
Q802022 · 10 Apr 2022
What does the equation $x \frac{d y}{d x} - 2 y = 0$ represent ?
1. A.A family of straight lines
2. B.A family of circles
3. C.A family of parabolas
4. D.A family of ellipses
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Answer: C
Q812022 · 10 Apr 2022
If the points with coordinates $(- 5, 0)$ , $(5 p^{2}, 10 p)$ and $(5 q^{2}, 10 q)$ are collinear, then what is the value of pq where $p \neq = q$ ?
1. A.-2
2. B.-1
3. C.1
4. D.2
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Answer: C
Q822022 · 10 Apr 2022
What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes ?
1. A.x + y - 1 = 0
2. B.x - y - 1 = 0
3. C.x + y + 1 = 0
4. D.x - y - 2 = 0
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Answer: C
Q832022 · 10 Apr 2022
What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?
1. A. $x^{2} + y^{2} - 2 x - 2 y - 1 = 0$
2. B. $x^{2} + y^{2} + 2 x + 2 y + 1 = 0$
3. C. $x^{2} + y^{2} - 2 x - 2 y + 1 = 0$
4. D. $x^{2} + y^{2} - 4 x - 4 y + 4 = 0$
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Answer: C
Q842022 · 10 Apr 2022
What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0 ?
1. A. $y^{2} = 3 x$
2. B. $x^{2} = 12 y$
3. C. $y^{2} = 12 x$
4. D. $y^{2} = - 12 x$
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Answer: D
Q852022 · 10 Apr 2022
What is the distance between the foci of the ellipse $x^{2} + 2 y^{2} = 1$ ?
1. A.1
2. B. $2$
3. C.2
4. D. $22$
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Answer: B
Q872022 · 10 Apr 2022
A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What is the sum of the absolute values of the intercepts?
1. A.2
2. B.3
3. C.4
4. D.6
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Answer: A
Q882022 · 10 Apr 2022
Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel (a ≠ 0, b ≠ 0)?
1. A.a - b = 0 only
2. B.a + b = 0 only
3. C. $a^{2} - b^{2} = 0$
4. D.ab + 1 = 0
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Answer: C
Q892022 · 10 Apr 2022
What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p is a real number) by the coordinate axes ?
1. A.x - y = 0
2. B.x + y = 0
3. C.x - y = p
4. D.x + y = p
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Answer: A
Q902022 · 10 Apr 2022
If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a > 0, then which one of the following is correct ?
1. A.2x - 3y = 0
2. B.3x - 2y = 0
3. C.4x - 6y + 5a = 0
4. D.4x - 6y - 5a = 0
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Answer: C