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

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

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

41.
What is \( x - y \) equal to?
A.
\( \tan^{-1}\left(\frac{828}{845}\right) \)
B.
\( \tan^{-1}\left(\frac{8287}{8450}\right) \)
C.
\( \tan^{-1}\left(\frac{8281}{8450}\right) \)
D.
\( \tan^{-1}\left(\frac{8287}{8471}\right) \)
😑 View Answer Error
ANSWER :
C. \( \tan^{-1}\left(\frac{8281}{8450}\right) \)
42.
What is \( x - y + z \) equal to?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{6} \)
D.
\( \frac{\pi}{4} \)
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ANSWER :
D. \( \frac{\pi}{4} \)
43.
For the next three (3) items that follow:
Consider the triangle ABC with vertices A(−2, 3), B(2, 1) and C(1, 2).

What is the circumcentre of the triangle ABC?
A.
(−2, −2)
B.
(2, 2)
C.
(−2, 2)
D.
(2, −2)
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ANSWER :
A. (−2, −2)
44.
What is the centroid of the triangle ABC?
A.
\( \left(\frac{1}{3}, 1\right) \)
B.
\( \left(\frac{1}{3}, 2\right) \)
C.
\( \left(1, \frac{2}{3}\right) \)
D.
\( \left(\frac{1}{2}, 3\right) \)
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ANSWER :
B. \( \left(\frac{1}{3}, 2\right) \)
45.
What is the foot of the altitude from the vertex A of the triangle ABC?
A.
(1, 4)
B.
(−1, 3)
C.
(−2, 4)
D.
(−1, 4)
😑 View Answer Error
ANSWER :
D. (−1, 4)
46.
The point on the parabola \( y^{2} = 4ax \) nearest to the focus has its abscissa
A.
\( x = 0 \)
B.
\( x = a \)
C.
\( x = \frac{a}{2} \)
D.
\( x = 2a \)
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ANSWER :
A. \( x = 0 \)
47.
A line passes through (2, 2) and is perpendicular to the line \( 3x + y = 3 \). Its y-intercept is
A.
\( \frac{3}{4} \)
B.
\( \frac{4}{3} \)
C.
\( \frac{1}{3} \)
D.
3
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ANSWER :
B. \( \frac{4}{3} \)
48.
The hyperbola \( \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 \) passes through the point \( (3\sqrt{5}, 1) \) and the length of its latus rectum is \( \frac{4}{3} \) units. The length of the conjugate axis is
A.
2 units
B.
3 units
C.
4 units
D.
5 units
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ANSWER :
C. 4 units
49.
The perpendicular distance between the straight lines \( 6x + 8y + 15 = 0 \) and \( 3x + 4y + 9 = 0 \) is
A.
\( \frac{3}{2} \) units
B.
\( \frac{3}{10} \) unit
C.
\( \frac{3}{4} \) unit
D.
\( \frac{2}{7} \) unit
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ANSWER :
B. \( \frac{3}{10} \) unit
50.
The area of a triangle, whose vertices are (3, 4), (5, 2) and the point of intersection of the lines \( x = a \) and \( y = 5 \), is 3 square units. What is the value of a?
A.
2
B.
3
C.
4
D.
5
😑 View Answer Error
ANSWER :
D. 5
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