Mathematics NDA/NA SOLVED PAPER 2018 (II) (51 to 100)

Total Questions: 50

1. The equation of a circle whose end points of a diameter are (x₁, y₁ ) and (x₂, y₂) is?

Correct Answer: (d) (x − x₁) (x − x₂) + (y − y₁) (y − y₂) = 0
Solution:

2. The second degree equation x² + 4y² - 2x - 4y + 2 = 0 represents?

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

3. The angle between the two lines lx + my + n = 0 and l' x + m' y + n' is given by tan⁻¹θ. What is θ equal to?

Correct Answer: (c)
Solution:

4. Consider the following statements:

Correct Answer: (b) 2 and 3
Solution:

5. What is the equation of straight line passing through the point of intersection of the lines x/2 + y/3 = 1 and x/3 + y/2 = 1 and parallel to the line 4x + 5y - 6 = 0?

Correct Answer: (a) 20x + 25y - 54 = 0
Solution:

6. What is the distance of the point (2, 3, 4) from the plane 3x - 6y + 2z + 11 = 0?

Correct Answer: (a) 1 unit
Solution:

7. Coordinates of the points O, P, Q and R respectively: (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 4, 6) L, M, N and KOR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2?

Correct Answer: (c) 3, 1
Solution:

LMNK is a parallelogram we know that, if we join mid- point of any quadrilateral we get a parallelogram

8. Simplify the question?

Correct Answer: (d) 3x + 2y - 3z = -2, 3x - 6y + 3z = 0
Solution:

9. Consider the following statements:

1. The angle between the planes 2x - y + z = 1 and x + y + 2z = 3 is π/3
2. The distance between the planes  6x - 3y + 6z + 2 = 0 and 2x - y + 2z + 4 = 0 is 10/9
Which of the above statement is/are correct?

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

10. Consider the following statements :

Correct Answer: (d) Statement I is false, but Statement II is true
Solution: