Coordinate Geometry · NDA previous year questions

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2024 23 questions

Q572024 · 1 Sept 2024
The foci of the ellipse $4 x^{2} + 9 y^{2} = 1$ are at Q and R. If P(x, y) is any point on the ellipse, then what is PQ + PR equal to?
1. A.2
2. B.1
3. C.2/3
4. D.1/3
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Answer: B
Q582024 · 1 Sept 2024
If P(2, 4), Q(8, 12), R(10, 14) and S(x, y) are vertices of a parallelogram, then what is (x + y) equal to?
1. A.8
2. B.10
3. C.12
4. D.14
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Answer: B
Q592024 · 1 Sept 2024
The equation of a circle is $(x^{2} - 4 x + 3) + (y^{2} - 6 y + 8) = 0$ Which of the following statements are correct? I. The end points of a diameter of the circle are at (1, 2) and (3, 4). II. The end points of a diameter of the circle are at (1, 4) and (3, 2). III. The end points of a diameter of the circle are at (2, 4) and (4, 2). Select the answer using the code given below.
1. A.I and II only
2. B.II and III only
3. C.I and III only
4. D.I, II and III
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Answer: A
Q602024 · 1 Sept 2024
Consider the points P(4k, 4k) and Q(4k, -4k) lying on the parabola $y^{2} = 4 k x$ . If the vertex is A, then what is $∠ PAQ$ equal to?
1. A. $6 0^{\circ}$
2. B. $9 0^{\circ}$
3. C. $12 0^{\circ}$
4. D. $13 5^{\circ}$
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Answer: B
Q612024 · 1 Sept 2024
Direction: Consider the following for the items that follow: A triangle ABC is inscribed in the circle $x^{2} + y^{2} = 100$ . B and C have coordinates (6, 8) and (-8, 6) respectively. What is BAC equal to?
1. A. $π /2$
2. B. $π /3$ or $2 π /3$
3. C. $π /4$ or $3 π /4$
4. D. $π /6$ or $5 π /6$
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Answer: C
Q632024 · 1 Sept 2024
Direction: Consider the following for the items that follow: ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2, 3), B(4, 3), C(5, 1) be the vertices. What are the coordinates of vertex D?
1. A.(2, 1)
2. B.(1, 2)
3. C.(1, 1)
4. D.(3, 1)
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Answer: C
Q882024 · 1 Sept 2024
What is the area of the parabola bounded by the latus rectum?
1. A.1/6 square unit
2. B.2/3 square unit
3. C.1 square unit
4. D.4/3 square units
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Answer: A
Q62024 · 21 Apr 2024
A triangle $P QR$ is such that 3 points lie on the side $P Q$ , 4 points on $QR$ and 5 points on $R P$ respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?
1. A.205
2. B.206
3. C.215
4. D.220
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Answer: A
Q72024 · 21 Apr 2024
If $lo g_{b} a = p$ , $lo g_{d} c = 2 p$ and $lo g_{f} e = 3 p$ , then what is $(a ce)^{\frac{1}{p}}$ equal to ?
1. A. $b d^{2} f^{3}$
2. B. $b df$
3. C. $b^{3} d^{2} f$
4. D. $b^{2} d^{2} f^{2}$
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Answer: A
Q512024 · 21 Apr 2024
If (a, b) is the centre and c is the radius of the circle $x^{2} + y^{2} + 2 x + 6 y + 1 = 0$ , then what is the value of $a^{2} + b^{2} + c^{2}$ ?
1. A.19
2. B.18
3. C.17
4. D.11
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Answer: A
Q582024 · 21 Apr 2024
If a variable line passes through the point of intersection of the lines $x + 2 y - 1 = 0$ and $2 x - y - 1 = 0$ and meets the coordinate axes in $A$ and $B$ , then what is the locus of the mid-point of $A B$ ?
1. A. $3 x + y = 10 x y$
2. B. $x + 3 y = 10 x y$
3. C. $3 x + y = 10$
4. D. $x + 3 y = 10$
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Answer: B
Q592024 · 21 Apr 2024
What is the equation to the straight line passing through the point $(- sin θ, cos θ)$ and perpendicular to the line $x cos θ + y sin θ = 9$ ?
1. A. $x sin θ - y cos θ - 1 = 0$
2. B. $x sin θ - y cos θ + 1 = 0$
3. C. $x sin θ - y cos θ = 0$
4. D. $x cos θ - y sin θ + 1 = 0$
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Answer: B
Q602024 · 21 Apr 2024
Two points $P$ and $Q$ lie on line $y = 2 x + 3$ . These two points $P$ and $Q$ are at a distance 2 units from another point $R (1, 5)$ . What are the coordinates of the points $P$ and $Q$ ?
1. A. $(1 + \frac{2}{5}, 5 + \frac{4}{5}), (1 - \frac{2}{5}, 5 - \frac{4}{5})$
2. B. $(3 + \frac{2}{5}, 5 + \frac{4}{5}), (- 1 - \frac{2}{5}, 5 - \frac{4}{5})$
3. C. $(1 - \frac{2}{5}, 5 + \frac{4}{5}), (1 + \frac{2}{5}, 5 - \frac{4}{5})$
4. D. $(3 - \frac{2}{5}, 5 + \frac{4}{5}), (- 1 + \frac{2}{5}, 5 - \frac{4}{5})$
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Answer: A
Q612024 · 21 Apr 2024
If two sides of a square lie on the lines $2 x + y - 3 = 0$ and $4 x + 2 y + 5 = 0$ , then what is the area of the square in square units?
1. A.6.05
2. B.6.15
3. C.6.25
4. D.6.35
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Answer: A
Q622024 · 21 Apr 2024
ABC is a triangle with A(3, 5). The mid-points of sides AB, AC are at (-1, 2), (6, 4) respectively. What are the coordinates of centroid of the triangle ABC?
1. A. $(\frac{8}{3}, \frac{11}{3})$
2. B. $(\frac{7}{3}, \frac{7}{3})$
3. C. $(2, \frac{8}{3})$
4. D. $(\frac{8}{3}, 2)$
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Answer: B
Q632024 · 21 Apr 2024
ABC is an acute angled isosceles triangle. Two equal sides AB and AC lie on the lines 7x - y - 3 = 0 and x + y - 5 = 0. If θ is one of the equal angles, then what is cotθ equal to?
1. A. $\frac{1}{3}$
2. B. $\frac{1}{2}$
3. C. $\frac{2}{3}$
4. D.2
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Answer: B
Q642024 · 21 Apr 2024
In the parabola $y^{2} = 8 x$ , the focal distance of a point P lying on it is 8 units. Which of the following statements is/are correct? 1. The coordinates of $P$ can be $(6, 43)$ . 2. The perpendicular distance of $P$ from the directrix of parabola is 8 units. 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
Q652024 · 21 Apr 2024
What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is 90°?
1. A. $\frac{1}{3}$
2. B. $\frac{1}{2}$
3. C. $\frac{1}{3}$
4. D. $\frac{1}{2}$
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Answer: D
Q662024 · 21 Apr 2024
Let $a = \hat{i} - \hat{j} + \hat{k}$ and $b = \hat{i} + 2 \hat{j} - \hat{k}$ . If $a \times (b \times a) = α \hat{i} - β \hat{j} + γ \hat{k}$ , then what is the value of $α + β + γ$ ?
1. A.8
2. B.7
3. C.6
4. D.1
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Answer: Dropped in the final answer key (full marks to everyone)
Q972024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: The circle $x^{2} + y^{2} - 2 x = 0$ is partitioned by line $y = x$ in two segments. Let $A_{1}, A_{2}$ be the areas of major and minor segments respectively. What is the value of $A_{1}$ ?
1. A. $\frac{π - 2}{4}$
2. B. $\frac{π + 2}{4}$
3. C. $\frac{3 π - 2}{4}$
4. D. $\frac{3 π + 2}{4}$
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Answer: D
Q982024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: The circle $x^{2} + y^{2} - 2 x = 0$ is partitioned by line $y = x$ in two segments. Let $A_{1}, A_{2}$ be the areas of major and minor segments respectively. What is the value of $\frac{2 ( A _{1} + A _{2} )}{A _{1} - 3 A _{2}}$ ?
1. A. $π$
2. B.1
3. C. $- 1$
4. D. $- π$
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Answer: A
Q992024 · 21 Apr 2024
Consider the following for the next two (02) items that follow : Let $3 f (x) + f (\frac{1}{x}) = \frac{1}{x} + 1$ What is $f (x)$ equal to?
1. A. $\frac{1}{8 x} - \frac{x}{8} + \frac{1}{4}$
2. B. $\frac{3}{8 x} - \frac{x}{8} + \frac{3}{4}$
3. C. $\frac{3}{8 x} + \frac{x}{8} + \frac{1}{4}$
4. D. $\frac{3}{8 x} - \frac{x}{8} + \frac{1}{4}$
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Answer: D
Q1002024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Let $3 f (x) + f (\frac{1}{x}) = \frac{1}{x} + 1$ What is $8 \int_{1}^{2} f (x) d x$ equal to?
1. A. $ln (8 e)$
2. B. $ln (4 e)$
3. C. $ln 2$
4. D. $ln 2 - 1$
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Answer: A