(Mathematics) NDA/NA SOLVED PAPER 2023 – II (51 to 100)

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Total Questions: 50

31. What is the equation of directrix of parabola y²= 4bx, where b < 0 and b² + b - 2 = 0?

Correct Answer: (b) x - 2 = 0
Solution:

32. The points (- a, - b) (0, 0), (a, b) and (a², ab) are:

Correct Answer: (d) collinear
Solution:

33. Given that 16p² + 49q² - 4r²- 56pq = 0 which one of the following is a point on a pair of straight lines (px + qy + r)(px + qy - r) = 0?

Correct Answer: (b) (2, -7/2)
Solution:

34. If 3x + y - 5 = 0 is the equation of a chord of the circle x²+ y² - 25 = 0 then what are the coordinates of the mid-point of the chord?

Correct Answer: (b) (3/2 , 1/2)
Solution:(b)

35. Consider the following in respect of the equation

1. The equation represents an ellipse if k = 19
2. The equation represents a hyperbola if k = 12
3. The equation represents a circle if k = 20
How many of the statements given above are correct?

Correct Answer: (c) All three
Solution:

36. Consider the following statements in respect of hyperbola

1. The two foci are independent of 0.
2. The eccentricity is sec θ.
3. The distance between the two foci is 2 units.
How many of the statements given above are correct?

Correct Answer: (c) All three
Solution:

37. Consider the following in respect of the circle

4x² + 4y² - 4ax - 4ay + a² = 0
1. The circle touches both the axes.
2. The diameter of the circle is 2a.
3. The centre of the circle lies on the line x + y = a
How many of the statements given above are correct

Correct Answer: (b) Only two
Solution:

38. For what value of k is the line (k - 3)x - (5 - k²)y + k² - 7k + 6 = 0 parallel to the line x + y = 1?

Correct Answer: (b) -1, 2
Solution:

39. The line x + y = 4 cuts the line joining P(- 1,1) and Q (5, 7) at R. What is PR: RQ equal to ?

Correct Answer: (b) 1 : 2
Solution:

40. What is the sum of the intercepts of the line whose perpendicular distance from origin is 4 units and the angle which the normal makes with positive DIRECTIONS of x-axis is 15°?

Correct Answer: (c) 8√6
Solution: