(Mathematics) NDA/NA SOLVED PAPER 2024 – I (51 to 100)

Total Questions: 50

1. If (a, b) is the centre and c is the radius of the circle x² + y² + 2x + 6y + 1 = 0 then what is the value of a²+ b² + c²?

Correct Answer: (a) 19
Solution:

2. If (1, - 1, 2) and (2, 1, -1) are the end points of a diameter of a sphere x² + y²+ z² + 2ux + 2vy + 2wz - 1 = 0 then what is u + v + w equal to?

Correct Answer: (a) -2
Solution:

3. The number of points represented by the equation x = 5 on the xy-plane is

Correct Answer: (d) infinitely many
Solution:

4. If are the directions cosines of a normal to the plane 2x - 3y + 6z + 4 = 0 then what is the value of 49 (7l² + m² - n²)?

Correct Answer: (b) 1
Solution:

5. A line through (1, -1, 2) with directions ratios meets the plane x + 2y + 3z = 18. What is the point of intersection of line and plane?

Correct Answer: (c) (4, 1, 4)
Solution:

6. If p is the perpendicular distance from origin to the plane passing through (1, 0, 0), (0, 1, 0) and (0, 0, 1), then what is 3p² equal to ?

Correct Answer: (d) 1
Solution:

7. If the directions cosines of a line are connected by relation l + 2m + n = 0, 2l - 2m + 3n = 0, then what is the value of l²+ m²- n²?

Correct Answer: (b) 29/101
Solution:

8. If a variable line passes through the point of intersection of the lines x + 2y - 1 = 0 and 2x - y - 1 = 0 and meets the coordinate axes in A and B, then what is the locus of the mid-point of AB?

Correct Answer: (b) x + 3y = 10xy
Solution:(b)

9. 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?

Correct Answer: (b) x sin θ - y cos θ + 1 = 0
Solution:

10. Two points P and Q lie on line y = 2x + 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?

Correct Answer: (a)
Solution: