Mathematics (NDA/NA SOLVED PAPER 2019 (I) (51 to 100)

Total Questions: 50

1. Consider the following statements:

1. For an equation of a line,
x cosθ + y sinθ = p, in normal form, the length of the perpendicular from the point (α ,β)  to the line is |α cosθ + β sinθ + p|.
The length of the perpendicular from the point (α,β)  to the line
Which of the above statements is/are correct?

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

2. A circle is drawn on the chord of a circle x² + y² = a as diameter. The chord lies on the line x + y = a. What is the equation of the circle?

Correct Answer: (b) x² + y² - ax - ay = 0
Solution:

3. The sum of the focal distances of a point on an ellipse is constant and equal to:

Correct Answer: (b) length of major axis
Solution:

4. The equation 2x² - 3y² - 6 = 0 represents:

Correct Answer: (d) a hyperbola
Solution:

5. The two parabolas y² = 4ax and x² = 4 ay intersect:

Correct Answer: (a) at two points on the line y = x
Solution:

6. The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c. What is the value of c?

Correct Answer: (d) −4
Solution:

7. If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then what is the value of b?

Correct Answer: (c) 6
Solution:

8. What is the equation of the straight line which is perpendicular to y = x and passes through (3, 2)?

Correct Answer: (b) x + y = 5
Solution:

9. The straight lines x + y - 4 = 0, 3x + y - 4 = 0 and x + 3y − 4 = 0 form a triangle, which is:

Correct Answer: (a) isosceles
Solution:

10. The circle x² + y² + 4x - 7y + 12 = 0, cuts an intercept on Y - axis equal to?

Correct Answer: (a) 1
Solution: