Coordinate Geometry · NDA previous year questions

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2021 32 questions

Q142021 · 14 Nov 2021
If $z = x + i y$ , where $i = - 1$ , then what does the equations $z \overset{z}{ˉ} + ∣ z ∣^{2} + 4 (z + \overset{z}{ˉ}) - 48 = 0$ represent?
1. A.Straight line
2. B.Parabola
3. C.Circle
4. D.Pair of straight lines
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Answer: C
Q152021 · 14 Nov 2021
Which one of the following is a square root of $2 a + 2 a^{2} + b^{2}$ , where $a, b \in R$ ?
1. A. $a + ib + a - ib$
2. B. $a + ib - a - ib$
3. C. $2 a + ib$
4. D. $2 a - ib$
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Answer: A
Q252021 · 14 Nov 2021
Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?
1. A.25
2. B.50
3. C.75
4. D.100
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Answer: B
Q342021 · 14 Nov 2021
Consider the following statements in respect of the roots of the equation $x^{3} - 8 = 0$ : 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. 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
Q512021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. A circle is passing through the points (5, -8), (-2, 9) and (2, 1).
What are the coordinates of the center of the circle?
1. A.(-2, -50)
2. B.(-50, -20)
3. C.(-24, -58)
4. D.(-58, -24)
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Answer: D
Q522021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. A circle is passing through the points (5, -8), (-2, 9) and (2, 1).
If r is the radius of the circle, then which one of the following is correct?
1. A.r < 10
2. B.10 < r < 30
3. C.30 < r < 60
4. D.r > 60
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Answer: D
Q532021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The two vertices of and equilateral triangle are (0, 0) and (2, 2). Consider the following statements: 1. The third vertex has at least one irrational coordinate. 2. The area is irrational.
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: C
Q542021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The two vertices of and equilateral triangle are (0, 0) and (2, 2). Consider the following statements: 1. The third vertex has at least one irrational coordinate. 2. The area is irrational.
The difference of coordinates of the third vertex is
1. A.0
2. B.√3
3. C.2√2
4. D.2√3
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Answer: D
Q552021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5).
The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5). What is the equation of the diagonal BD?
1. A.2x - 3y + 2 = 0
2. B.3x - 2y + 5 = 0
3. C.2x - 3y + 8 = 0
4. D.3x - 2y - 5 = 0
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Answer: C
Q562021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The coordinates of three consecutive vertices of a parallelogram ABCD are A(1, 3), B(-1, 2) and C(3, 5).
What is the area of the parallelogram?
1. A.1 square unit
2. B. $\frac{3}{2}$ square units
3. C.2 square units
4. D. $\frac{5}{2}$ square units
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Answer: C
Q582021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The equations of the sides AB, BC and CA of a triangle ABC are x - 2 = 0, y + 1 = 0 and x + 2y - 4 = 0 respectively.
What are the coordinates of circumcentre of the triangle?
1. A.(4, 0)
2. B.(2, 1)
3. C.(0, 4)
4. D.(2, -1)
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Answer: A
Q602021 · 14 Nov 2021
Directions
Direction: Consider the following for the next two (02) items that follow. The two ends of the latus rectum of a parabola are (-2, 4) and (-2, -4).
Consider the following statements in respect of such parabolas: 1. One of the parabolas passes through the origin (0, 0). 2. The focus of one of the parabolas lies at (-2, 0). 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: C
Q652021 · 14 Nov 2021
ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β?
1. A. $\frac{40}{49}$
2. B. $\frac{64}{49}$
3. C. $\frac{120}{49}$
4. D. $\frac{160}{49}$
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Answer: B
Q802021 · 14 Nov 2021
What is the slope of the tangent of $y = cos^{- 1} (cos x)$ at $x = - \frac{π}{4}$ ?
1. A.-1
2. B.0
3. C.1
4. D.2
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Answer: A
Q112021 · 18 Apr 2021
What is the radius of the circle $4 x^{2} + 4 y^{2} - 20 x + 12 y - 15 = 0$ ?
1. A.14 units
2. B.10.5 units
3. C.7 units
4. D.3.5 units
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Answer: D
Q122021 · 18 Apr 2021
A parallelogram has three consecutive vertices (-3, 4), (0, -4) and (5, 2). The fourth vertex is
1. A.(2, 10)
2. B.(2, 9)
3. C.(3, 9)
4. D.(4, 10)
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Answer: A
Q132021 · 18 Apr 2021
If the lines y + px = 1 and y - qx = 2 are perpendicular, then which one of the following is correct?
1. A.pq + 1 = 0
2. B.p + q + 1 = 0
3. C.pq - 1 = 0
4. D.p - q + 1 = 0
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Answer: C
Q142021 · 18 Apr 2021
If A, B and C are in AP, then the straight line Ax + 2By + C = 0 will always pass through a fixed point. The fixed point is
1. A.(0, 0)
2. B.(-1, 1)
3. C.(1, -2)
4. D.(1, -1)
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Answer: D
Q152021 · 18 Apr 2021
If the image of the point (-4, 2) by a line mirror is (4, -2), then what is the equation of the line mirror?
1. A.y = x
2. B.y = 2x
3. C.4y = x
4. D.y = 4x
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Answer: B
Q162021 · 18 Apr 2021
$tan^{- 1} x + cot^{- 1} x = \frac{π}{2}$ holds, when
1. A. $x \in R$
2. B. $x \in R - (- 1, 1)$ only
3. C. $x \in R - {0}$ only
4. D. $x \in R - [- 1, 1]$ only
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Answer: A
Q382021 · 18 Apr 2021
A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord?
1. A.√2 - 1 units
2. B.√3 - 1 units
3. C.√2 units
4. D.√3 units
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Answer: D
Q922021 · 18 Apr 2021
A particle starts from origin with a velocity (in m/s) given by the equation $\frac{d x}{d t} = x + 1$ . The time (in seconds) taken by the particle to traverse a distance of $24 m$ is:
1. A. $ln 24$
2. B. $ln 5$
3. C. $2 ln 5$
4. D. $2 ln 4$
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Answer: C
Q932021 · 18 Apr 2021
What is $\int_{0}^{a} \frac{f ( a - x )}{f ( x ) + f ( a - x )} d x$ equal to?
1. A. $a$
2. B. $2 a$
3. C.0
4. D. $\frac{a}{2}$
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Answer: D
Q942021 · 18 Apr 2021
What is $lim_{x \to 2} \frac{x ^{3} + x ^{2}}{x ^{2} + 3 x + 2}$ equal to?
1. A.0
2. B.1
3. C.2
4. D.3
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Answer: B
Q952021 · 18 Apr 2021
If $\int_{0}^{a} [f (x) + f (- x)] d x = \int_{- a}^{a} g (x) d x$ , then what is $g (x)$ equal to?
1. A. $f (x)$
2. B. $f (- x) + f (x)$
3. C. $- f (x)$
4. D.None of the above.
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Answer: A