NDA & NA Exam (I)- 2014 - Mathematics Defence Question Paper

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NDA & NA Exam (I)- 2014 - Mathematics

NDA & NA Exam (I)- 2014 - Mathematics Defence Questions

41.
What is the value of \( \cos 36^{\circ} \)?
A.
\( \frac{\sqrt{5}-1}{4} \)
B.
\( \frac{\sqrt{5}+1}{4} \)
C.
\( \frac{\sqrt{10+2\sqrt{5}}}{4} \)
D.
\( \frac{\sqrt{10-2\sqrt{5}}}{4} \)
😑 View Answer Error
ANSWER :
B. \( \frac{\sqrt{5}+1}{4} \)
42.
Consider the following statements:
1. Value of \( \sin\theta \) oscillates between −1 and 1.
2. Value of \( \cos\theta \) oscillates between 0 and 1.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
43.
If x and y are positive and \( xy > 1 \), then what is \( \tan^{-1}x + \tan^{-1}y \) equal to?
A.
\( \tan^{-1}\left(\frac{x+y}{1-xy}\right) \)
B.
\( \pi + \tan^{-1}\left(\frac{x+y}{1-xy}\right) \)
C.
\( \pi - \tan^{-1}\left(\frac{x+y}{1-xy}\right) \)
D.
\( \tan^{-1}\left(\frac{x-y}{1+xy}\right) \)
😑 View Answer Error
ANSWER :
B. \( \pi + \tan^{-1}\left(\frac{x+y}{1-xy}\right) \)
44.
Consider the following statements:
1. \( n\left(\sin^{2} 67\frac{1}{2}^{\circ} - \sin^{2} 22\frac{1}{2}^{\circ}\right) > 1 \) for all positive integers \( n \geq 2 \).
2. If x is any positive real number, then \( nx > 1 \) for all positive integers \( n \geq 2 \).
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
45.
Consider the following statements:
1. If \( 3\theta \) is an acute angle such that \( \sin 3\theta = \cos 2\theta \), then the measurement of \( \theta \) in radian equals to \( \frac{\pi}{10} \).
2. One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
46.
From an aeroplane above a straight road the angles of depression of two positions at a distance 20 m apart on the road are observed to be \( 30^{\circ} \) and \( 45^{\circ} \). The height of the aeroplane above the ground is
A.
\( 10\sqrt{3} \) m
B.
\( 10(\sqrt{3}-1) \) m
C.
\( 10(\sqrt{3}+1) \) m
D.
20 m
😑 View Answer Error
ANSWER :
C. \( 10(\sqrt{3}+1) \) m
47.
Consider the following statements:
1. There exists no triangle ABC for which \( \sin A + \sin B = \sin C \).
2. If the angles of a triangle are in the ratio 1 : 2 : 3, then its sides will be in the ratio \( 1 : \sqrt{3} : 2 \).
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
C. Both 1 and 2
48.
Consider the following statements:
1. \( \sin|x| + \cos|x| \) is always positive.
2. \( \sin(x^{2}) + \cos(x^{2}) \) is always positive.
Which of the above statements is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
D. Neither 1 nor 2
49.
What is \( \frac{1+\sin A}{1-\sin A} - \frac{1-\sin A}{1+\sin A} \) equal to?
A.
\( \sec A - \tan A \)
B.
\( 2\sec A \tan A \)
C.
\( 4\sec A \tan A \)
D.
\( 4 cosec A \cot A \)
😑 View Answer Error
ANSWER :
C. \( 4\sec A \tan A \)
50.
What is \( \frac{\cot 224^{\circ} - \cot 134^{\circ}}{\cot 226^{\circ} + \cot 316^{\circ}} \) equal to?
A.
\( -cosec 88^{\circ} \)
B.
\( -cosec 2^{\circ} \)
C.
\( -cosec 44^{\circ} \)
D.
\( -cosec 46^{\circ} \)
😑 View Answer Error
ANSWER :
B. \( -cosec 2^{\circ} \)
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