NDA & NA Exam (II)- 2015 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2015 - Mathematics

NDA & NA Exam (II)- 2015 - Mathematics Defence Questions

41.
What is the sum of n terms of the series \( \sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + \ldots \)?
A.
\( \frac{n(n-1)}{\sqrt{2}} \)
B.
\( \sqrt{2} n(n+1) \)
C.
\( \frac{n(n+1)}{\sqrt{2}} \)
D.
\( \frac{n(n-1)}{2} \)
😑 View Answer Error
ANSWER :
C. \( \frac{n(n+1)}{\sqrt{2}} \)
42.
The coefficient of \( x^{99} \) in the expansion of \( (x-1)(x-2)(x-3)\ldots(x-100) \) is
A.
5050
B.
5000
C.
−5050
D.
−5000
😑 View Answer Error
ANSWER :
C. −5050
43.
\( z\bar{z} + (3 - i)z + (3 + i)\bar{z} + 1 = 0 \) represents a circle with
A.
centre (−3, −1) and radius 3
B.
centre (−3, 1) and radius 3
C.
centre (−3, −1) and radius 4
D.
centre (−3, 1) and radius 4
😑 View Answer Error
ANSWER :
A. centre (−3, −1) and radius 3
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
A.
60
B.
56
C.
52
D.
48
😑 View Answer Error
ANSWER :
C. 52
45.
If \( \log_{8} m + \log_{8} \frac{1}{6} = \frac{2}{3} \), then m is equal to
A.
24
B.
18
C.
12
D.
4
😑 View Answer Error
ANSWER :
A. 24
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
A.
\( \frac{c^{2}}{ab} \)
B.
\( \frac{2c^{2}}{ab} \)
C.
\( \frac{c^{2}}{2ab} \)
D.
\( \frac{c^{2}}{4ab} \)
😑 View Answer Error
ANSWER :
B. \( \frac{2c^{2}}{ab} \)
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
A.
\( x + 5y \pm 5\sqrt{2} = 0 \)
B.
\( x - 5y \pm 5\sqrt{2} = 0 \)
C.
\( 5x + y \pm 5\sqrt{2} = 0 \)
D.
\( 5x - y \pm 5\sqrt{2} = 0 \)
😑 View Answer Error
ANSWER :
A. \( x + 5y \pm 5\sqrt{2} = 0 \)
48.
Consider any point P on the ellipse \( \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 \) in the first quadrant. Let r and s represent its distances from (4, 0) and (−4, 0) respectively, then \( (r + s) \) is equal to
A.
10 unit
B.
9 unit
C.
8 unit
D.
6 unit
😑 View Answer Error
ANSWER :
A. 10 unit
49.
A straight line \( x = y + 2 \) touches the circle \( 4(x^{2} + y^{2}) = r^{2} \). The value of r is
A.
\( \sqrt{2} \)
B.
\( 2\sqrt{2} \)
C.
2
D.
1
😑 View Answer Error
ANSWER :
B. \( 2\sqrt{2} \)
50.
The three lines \( 4x + 4y = 1 \), \( 8x - 3y = 2 \), \( y = 0 \) are
A.
the sides of an isosceles triangle
B.
concurrent
C.
mutually perpendicular
D.
the sides of an equilateral triangle
😑 View Answer Error
ANSWER :
B. concurrent
Prev Next page