Mathematics (NDA SOLVED PAPER 2020 – II) (51 to 100)Total Questions: 501. The centre of the circle (x - 2a) (x - 2b) + (y - 2c) (y - 2d) = 0 is(a) (2a, 2c)(b) (2b, 2d)(c) (a + b, c + d)(d) (a - b, c - d)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?(a) 3x - 2y = 5(b) 2x - 3y = 1(c) 2x - 3y = 5(d) 2x + 3y = -1Correct Answer: (c) 2x - 3y = 5Solution: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?(a) 12(b) 10(c) 8(d) 6Correct Answer: (b) 10Solution: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?(a) − 1(b) − 2(c) 1(d) 2Correct Answer: (c) 1Solution: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?(a) sinθ . sec²θ(b) cosθ . cosec²θ(c) cot θ . sec²θ(d) 2 tanθ . cosec²θCorrect Answer: (b) cosθ . cosec²θSolution:6. Under which condition, are the points(a,b), (c, d) and (a, - c, b - d) collinear?(a) ab = cd(b) ac = bd(c) ad = bc(d) abc = dCorrect Answer: (c) ad = bcSolution: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?(a) 8(b) 10(c) 12(d) 14Correct Answer: (b) 10Solution: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?(a) 3(b) 4(c) 5(d) 6Correct Answer: (c) 5Solution:9. What is the obtuse angle between the lines whose slopes are 2 - √3 and 2 + √3?(a) 105°(b) 120°(c) 135°(d) 150°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?(a) 4 sq units(b) 9 sq units(c) 16 sq units(d) 25 sq unitsCorrect Answer: (c) 16 sq unitsSolution:Submit Quiz12345Next »