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

Total Questions: 50

11. If two sides of a square lie on the lines 2x + y - 3 = 0 and 4x + 2y + 5 = 0, then what is the area of the square in square units?

Correct Answer: (a) 6.05
Solution:

= 6.05 square units.

12. 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?

Correct Answer: (b)
Solution:

13. ABC is 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 cot θ equal to?

Correct Answer: (b) 1/2
Solution:(b)

14. In the parabola y² = 8x, the focal distance . of a point P lying on it is 8 units. Which of the following statements is/are correct?

(A) The coordinates of P can be (6, 4√3)
(B) The perpendicular distance of P from the directrix of parabola is 8 units.
Select the correct answer using the code given below:

Correct Answer: (c) Both A and B
Solution:

15. 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°?

Correct Answer: (d) 1/√2
Solution:(d)

16. Find the value?

Correct Answer: (e) None of the above
Solution:

17. Find the value?

Correct Answer: (a) (1, √2, 1)
Solution:(a)

18. Consider the following in respect of moment of a force

(A) The moment of force about a point is independent of point of application of force.
(B) The moment of a force about a line is a vector quantity. Which of the statements given above is/are correct?

Correct Answer: (b) B only
Solution:

19. equal to?

Correct Answer: (a)
Solution:

20. Find the value?

Correct Answer: (b) π/3
Solution:(b)