NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

41. What is the length of the line segment PQ?

From the point P(3, - 1, 11) a perpendicular is drawn on the line L given by the equation x/2 = (y - 2)/3 = (z - 3)/4. Let Q be the foot of the perpendicular.

Correct Answer: (c) √53 units
Solution:

42. What are the intercepts made by the plane ABC on the axes?

A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively.

Correct Answer: (a) 3, 6, 9
Solution:

43. What is the equation of plane ABC?

A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively.

Correct Answer: (d) 6x + 3y + 2z = 18
Solution:The plane passes through the point A(3, 0, 0) B(0, 6, 0) and C(0, 0, 9) So, it should satisfy the equation given in option for all the three points.

44. What is the length of one of the diagonals of the cuboid?

A point P (1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.

Correct Answer: (b) √14 units
Solution:

45. What is the equation of the plane passing through P(1, 2, 3) and parallel to xy-plane?

A point P (1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.

Correct Answer: (c) z = 3
Solution:Equation of plane passing through (1, 2, 3) and parallel to xy-plane is z=3. Option (c) is correct.

46. The decimal number (127.25)₁₀, when converted to binary number, takes the form

Correct Answer: (d) (1111111.01)₂
Solution:


47. Consider the following in respect of two non-singular matrices A and B of same order:

1. det (A + B) = det A + det B
2. (A + B)⁻¹ = A⁻¹ + B⁻¹

Which of the above is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:


48. Solve the following equation

Correct Answer: (a)
Solution:


49. Solve the following equation

Correct Answer: (e) a and d
Solution:

50. How many words can be formed using all the letters of the word 'NATION' so that all the three vowels should never come together?

Correct Answer: (c) 288
Solution: