Mathematics (NDA/NA SOLVED PAPER 2023-I) (51 to 100)

Total Questions: 50

11. What is u + v + w equal to?

Let A(1, - 1, 2) and B(2, 1, - 1) be the end points of the diameter of the sphere
x² + y² + z² + 2wx + 2vy + 2wz - 1 = 0.

Correct Answer: (a) -2
Solution:

12. If P(x, y, z) is any point on the sphere, then what is PA² + PB² equal to?

Let A(1, - 1, 2) and B(2, 1, - 1) be the end points of the diameter of the sphere
x² + y² + z² + 2wx + 2vy + 2wz - 1 = 0.

Correct Answer: (b) 14
Solution:

13. What is the value of k?

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5) They are inclined at an angle π/4 .

Correct Answer: (a) 4
Solution:

14. What are the direction ratios of a line which is perpendicular to both the lines?

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5) They are inclined at an angle π/4 .

Correct Answer: (d) (11, 2, -10)
Solution:

15. Equal to?

Correct Answer: (b)
Solution:

16. Find the value?

Correct Answer: (a) π/2
Solution:

17. What is cos α equal to?

Correct Answer: (b) 4/9
Solution:

18. What is cos2β + cos2γ equal to?

Correct Answer: (a) -32/81
Solution:

19. Consider the following points:

1. (-1,-3, 1)
2. (-1, 3, 2)
3. (-2, 5, 3)
Which of the above points lie on the line joining A and B?

Correct Answer: (b) 2 and 3 only
Solution:

20. Find magnitude?

Correct Answer: (c) √6
Solution: