Mathematics (NDA/NA SOLVED PAPER 2021-I) (51 to 100)

Total Questions: 50

11. Consider the following statements in respect of the points (p, p - 3), (q + 3, q) and (6, 3):

1. The points lie on a straight line.
2. The points always lie in the first quadrant only for any value of p and q.
Which of the above statements is/are correct?

Correct Answer: (a) 1 only
Solution:

12. What is the acute angle between the lines x - 2 = 0 and √3x - y - 2 = 0 ?

Correct Answer: (b) 30°
Solution:

13. The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A {4, 2}.

What is the equation of the diagonal BD?

Correct Answer: (a) 2x + y = 0
Solution:

14. If any point on a hyperbola is (3 tan θ, 2 secθ ), then what is the eccentricity of the hyperbola ?

Correct Answer: (d) √13/2
Solution:

15. Consider the following with regard to eccentricity (e) of a conic section :

1. e = 0 for circle
2. e = 1 for parabola
3. e < 1 for ellipse
Which of the above are correct?

Correct Answer: (d) 1, 2 and 3
Solution:All three statements are correct.

16. What is the angle between the two lines having direction ratios (6, 3, 6) and (3, 3, 0)?

Correct Answer: (b) π/4
Solution:

17. If l, m, n are the direction cosines of the line x - 1 =2 (y+ 3)= 1 - z , then what is l⁴+ m⁴ + n⁴ equal to?

Correct Answer: (b) 11/27
Solution:

18. What is the projection of the line segment joining A (1,7,-5) and B(- 3, 4, - 2) on y-axis?

Correct Answer: (c) 3
Solution:

19. What is the number of possible values of k for which the line joining the points (k, 1, 3) and (1, - 2, k + 1) also passes through the point (15, 2, -4)?

Correct Answer: (c) Two
Solution:On solving, we will get two different values of k.

20. The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is

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