Mathematics (NDA/NA SOLVED PAPER 2022-II) (51 to 100)

Total Questions: 50

1. What is cos 36° - cos 72° equal to?

Correct Answer: (c) 1/2
Solution:

2. If sec x = 25/24 and x lies in the fourth quadrant, then what is the value of tan x + sin x ?

Correct Answer: (b) - 343/600
Solution:

3. What is the value of tan²165°+ cot²165°?

Correct Answer: (b) 14
Solution:(b)

4. Find the value?

Correct Answer: (a) 1/4
Solution:

5. If 1 + 2(sin x + cos x) (sin x - cos x) = 0 where 0 < x < 360°, then how many values does x take??

Correct Answer: (d) Four values
Solution:

6. Consider the following statements in respect of the line passing through origin and inclining at an angle of 75° with the positive direction of x-axis:

1. The line passes through the point (1, 1/(2 - √3).
2. The line entirely lies in first and third quadrants.
Which of the statements given above is/are correct?

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

7. If P(3,4) is the mid-point of a line segment between the axes, then what is the equation of the line ?

Correct Answer: (b) 4x + 3y - 24 = 0
Solution:(b)

8. The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B lies above the origin. What is the equation of line passing through (8, 0) and parallel to the side AC?

Correct Answer: (a) x - √3y - 8 = 0
Solution:(a)

9. The centre of the circle passing through origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line

Correct Answer: (c) 3x - 4y + 6 = 0
Solution:

10. The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity?

Correct Answer: (a) √3/2
Solution: