Coordinate Geometry · NDA previous year questions

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

What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?

1. A.$x^2+y^2-2x-2y-1=0$
2. B.$x^2+y^2+2x+2y+1=0$
3. C.$x^2+y^2-2x-2y+1=0$
4. D.$x^2+y^2-4x-4y+4=0$

What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0 ?

1. A.$y^2=3x$
2. B.$x^2=12y$
3. C.$y^2=12x$
4. D.$y^2=-12x$

What is the distance between the foci of the ellipse $x^2+2y^2=1$ ?

1. A.1
2. B.$\sqrt{2}$
3. C.2
4. D.$2\sqrt{2}$

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

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

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

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

If $z=x+iy$, where $i=\sqrt{-1}$, then what does the equations $z\bar{z}+|z{|}^2+4(z+\bar{z})-48=0$ represent?

1. A.Straight line
2. B.Parabola
3. C.Circle
4. D.Pair of straight lines

Which one of the following is a square root of $2a+2\sqrt{a^2+b^2}$, where $a,b\in \mathbb{R}$?

1. A.$\sqrt{a+ib}+\sqrt{a-ib}$
2. B.$\sqrt{a+ib}-\sqrt{a-ib}$
3. C.$2a+ib$
4. D.$2a-ib$

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

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

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)

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

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

The difference of coordinates of the third vertex is

1. A.0
2. B.√3
3. C.2√2
4. D.2√3

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

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

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)

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

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.$\frac{160}{49}$

What is the slope of the tangent of $y={\cos }^{-1}(\cos x)$ at $x=-\frac{\pi }{4}$?

1. A.-1
2. B.0
3. C.1
4. D.2

What is the radius of the circle $4x^2+4y^2-20x+12y-15=0$?

1. A.14 units
2. B.10.5 units
3. C.7 units
4. D.3.5 units

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)

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