MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (51 to 100)

Total Questions: 50

41. What is the value of k?

The plane 6x + ky + 3z - 12 = 0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x -3y - 4z = 0.

Correct Answer: (b) 4
Solution:

42. If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct?

The plane 6x + ky + 3z - 12 = 0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x -3y - 4z = 0.

Correct Answer: (b) 0.5 < p < 1
Solution:

43. What is the equation of the line through the origin and the centre of the sphere?

The plane 6x + ky + 3z - 12 = 0 where meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x -3y - 4z = 0.

Correct Answer: (d) 6x = 4y = 3z
Solution:

44. What are the direction ratios of a normal to the plane?

Correct Answer: (a)
Solution:Direction ratios of a normal are <3, 2, 1>

45. If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to?

Correct Answer: (b) 11
Solution:

46. Find the value?

Correct Answer: (c) 8/3, 2/3
Solution:

47. If are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the triangle, then what is equal to?

Correct Answer: (c)
Solution:

48. Consider the following statements:

1. Dot product over vector addition is distributive
2. Cross product over vector addition is distributive
3. Cross product of vectors is associative
Which of the above statements is/are correct?

Correct Answer: (c) 1 and 2 only
Solution:

49. Find the value?

Correct Answer: (b) 2 only
Solution:

50. Find the value?

Correct Answer: (d) -1 < sinθ < 1
Solution: