NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

41. What is the sum of n terms of the series √2 + √8 + √18 + √32 +.... ?

Correct Answer: (c)
Solution:

42. The coefficient of x⁹⁹ in the expansion of (x - 1) (x - 2) (x - 3) ..... (x - 100) is

Correct Answer: (c) -5050
Solution:

43. Solve the following equation

Correct Answer: (a)
Solution:

44. The number of 3-digit even numbers that can be formed from the digits 0, 1, 2, 3, 4 and 5, repetition of digits being not allowed, is

Correct Answer: (c) 52
Solution:No. of digits to be filled at one's place = 3
No. of digits to be filled at 10's place = 5
No. of digits to be filled at 100 "splace=4
∴ Total no. of digits formed = 3 × 5 × 4 = 60
If zero is at 100's place;
Then; no. of digits to be filled at one's place = 2
& no. of digits to be filled at 10's place = 4
∴ No. of digits formed with zero at 100's place = 1 × 2 × 4 = 8
∴ Required no. of digits formed = 60 - 8 = 52.

45. Solve the following equation

Correct Answer: (a) 24
Solution:

46. The area of the figure formed by the lines ax + by + c = 0 , ax - by + c = 0 ax + by- c = 0 and ax-by - c = 0 is

Correct Answer: (b)
Solution:


47. If a line is perpendicular to the line 5x - y = 0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is

Correct Answer: (a) x + 5y ± 5 √2 = 0
Solution:


48. Consider any point P on the ellipse (x²/25) + (y²/9) = 1 in the first quadrant. Let r and s represent its distances from (4, 0) and (-4, 0) respectively, then (r + s) is equal to

Correct Answer: (a) 10 unit
Solution:


49. A straight line x = y + 2 touches the circle 4(x² + y²) = r² The value of r is

Correct Answer: (b) 2√2
Solution:

50. The three lines 4x + 4y = 1 8x - 3y = 2 y = 0 are

Correct Answer: (b) concurrent
Solution: