Mathematics (NDA SOLVED PAPER 2020 – II) (51 to 100)

Total Questions: 50

1. The centre of the circle (x - 2a) (x - 2b) + (y - 2c) (y - 2d) = 0 is

Correct Answer: (c) (a + b, c + d)
Solution:

2. The point (1, -1) is one of the vertices of a square. If 3x + 2y = 5 is the equation of one diagonal of the square, then what is the equation of the other diagonal?

Correct Answer: (c) 2x - 3y = 5
Solution:

3. Let P (x y) be any point on the ellipse 25x² + 16y² = 400. If Q (0,3) and R (0,-3) are two points, then what is (PQ + PR) equal to?

Correct Answer: (b) 10
Solution:

4. If the circumcentre of the triangle formed by the lines x + 2 = 0, y + 2 = 0 and kx + y + 2 = 0 is (-1 , -1), then what is the value of k?

Correct Answer: (c) 1
Solution:

5. In the parabola, y² = x, what is the length of the chord passing through the vertex and inclined to the X -axis at an angle θ?

Correct Answer: (b) cosθ . cosec²θ
Solution:

6. Under which condition, are the points(a,b), (c, d) and (a, - c, b - d) collinear?

Correct Answer: (c) ad = bc
Solution:

7. Let ABC be a triangle. If D (2,5) and E (5,9) are the mid-points of the sides AB and AC respectively, then what is the length of the side BC?

Correct Answer: (b) 10
Solution:

8. If the foot of the perpendicular drawn from the point (0, k) to the line 3x - 4y - 5 = 0 is (3,1), then what is the value of k?

Correct Answer: (c) 5
Solution:

9. What is the obtuse angle between the lines whose slopes are 2 - √3 and 2 + √3?

Correct Answer: (b) 120°
Solution:

10. If 3x - 4y - 5 = 0 and 3x - 4y + 15 = 0 are the equations of a pair of opposite sides of a square, then what is the area of the square?

Correct Answer: (c) 16 sq units
Solution: