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

Total Questions: 50

1. What is the distance between the points which divide the line segment joining (4, 3) and (5, 7) internally and externally in the ratio 2 : 3?

Correct Answer: (a)
Solution:

2. What is the angle between the straight lines (m²−mn)y = (mn + n²) x + n³ and (mn+m²)y = (mn−n²)x + m³, where m > n?

Correct Answer: (c)
Solution:

3. What is the equation of the straight line cutting-off an intercept 2 from the negative direction of Y - axis and inclined at 30° with the positive direction of X -axis ?

Correct Answer: (d) x - √3y − 2√3 = 0
Solution:

4. What is the equation of the line passing through the point of intersection of the lines x + 2y - 3 = 0 and 2x - y + 5 = 0 and parrallel to the line y - x + 10 = 0?

Correct Answer: (c) 5x - 5y + 18 = 0
Solution:

5. Consider the following statements:

Correct Answer: (c) I and II
Solution:

6. What is the equation of the ellipse whose vertices are ( ± 5 , 0 ) and foci are at ( ± 4 , 0)?

Correct Answer: (a)
Solution:

7. What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive Y - axis equal to twice its intercept on the positive X -axis?

Correct Answer: (b) 2x + y = 7
Solution:

8. Let the coordinates of the points A B C be (1, 8, 4), (0, -11, 4) and (2, -3, 1) respectively. What are the coordinates of the point D which is the foot of the perpendicular from A on BC?

Correct Answer: (c) (4, 5, -2)
Solution:

9. What is the equation of the plane passing through the points (-2, 6, -6), (-3, 10, -9) and (-5, 0, -6)?

Correct Answer: (a) 2x - y - 2z = 2
Solution:

10. A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the ∆ ABC?

Correct Answer: (c) 9(x² + y² + z²) = 4r²
Solution: