NDA & NA Exam (II)- 2019 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2019 - Mathematics

NDA & NA Exam (II)- 2019 - Mathematics Defence Questions

41.
If \( \csc \theta = \frac{29}{21} \), where \( 0 < \theta < 90^{\circ} \), then what is the value of \( 4 \sec \theta + 4 \tan \theta \)?
A.
5
B.
10
C.
15
D.
20
😑 View Answer Error
ANSWER :
B. 10
42.
Consider the following statements:
1. \( \cos \theta + \sec \theta \) can never be equal to 1.5.
2. \( \tan \theta + \cot \theta \) can never be less than 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
43.
A ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is \( 60^{\circ} \). What is the height of the flagstaff?
A.
9 m
B.
10.5 m
C.
13.5 m
D.
15 m
😑 View Answer Error
ANSWER :
C. 13.5 m
44.
What is the length of the chord of a unit circle which subtends an angle \( \theta \) at the centre?
A.
\( \sin \left(\frac{\theta}{2}\right) \)
B.
\( \cos \left(\frac{\theta}{2}\right) \)
C.
\( 2 \sin \left(\frac{\theta}{2}\right) \)
D.
\( 2 \cos \left(\frac{\theta}{2}\right) \)
😑 View Answer Error
ANSWER :
C. \( 2 \sin \left(\frac{\theta}{2}\right) \)
45.
What is \( \tan \left[2 \tan^{-1} \left(\frac{1}{3}\right)\right] \) equal to?
A.
\( \frac{2}{3} \)
B.
\( \frac{3}{4} \)
C.
\( \frac{3}{8} \)
D.
\( \frac{1}{9} \)
😑 View Answer Error
ANSWER :
B. \( \frac{3}{4} \)
46.
What is the scalar projection of \( \vec{a} = \hat{i} - 2\hat{j} + \hat{k} \) on \( \vec{b} = 4\hat{i} - 4\hat{j} + 7\hat{k} \)?
A.
\( \frac{\sqrt{6}}{19} \)
B.
\( \frac{19}{9} \)
C.
\( \frac{9}{19} \)
D.
\( \frac{19}{\sqrt{6}} \)
😑 View Answer Error
ANSWER :
B. \( \frac{19}{9} \)
47.
If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct?
A.
The vectors are parallel
B.
The vectors are perpendicular
C.
The vectors are anti-parallel
D.
The vectors must be unit vectors
😑 View Answer Error
ANSWER :
B. The vectors are perpendicular
48.
Consider the following equations for two vectors \( \vec{a} \) and \( \vec{b} \):
1. \( (\vec{a} + \vec{b}) \cdot (\vec{a} - \vec{b}) = |\vec{a}|^{2} - |\vec{b}|^{2} \)
2. \( |\vec{a} + \vec{b}| |\vec{a} - \vec{b}| = |\vec{a}|^{2} - |\vec{b}|^{2} \)
3. \( |\vec{a} \cdot \vec{b}|^{2} + |\vec{a} \times \vec{b}|^{2} = |\vec{a}|^{2} |\vec{b}|^{2} \)
Which of the above statements are correct?
A.
1, 2 and 3
B.
1 and 2 only
C.
1 and 3 only
D.
2 and 3 only
😑 View Answer Error
ANSWER :
C. 1 and 3 only
49.
Consider the following statements:
1. The magnitude of \( \vec{a} \times \vec{b} \) is same as the area of a triangle with sides \( \vec{a} \) and \( \vec{b} \).
2. If \( \vec{a} \times \vec{b} = \vec{0} \), where \( \vec{a} \neq \vec{0}, \vec{b} \neq \vec{0} \), then \( \vec{a} = \lambda \vec{b} \).
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 :
B. 2 only
50.
If \( \vec{a} \) and \( \vec{b} \) are unit vectors and \( \theta \) is the angle between them, then what is \( \sin^{2} \left(\frac{\theta}{2}\right) \) equal to?
A.
\( \frac{|\vec{a} + \vec{b}|^{2}}{4} \)
B.
\( \frac{|\vec{a} - \vec{b}|^{2}}{4} \)
C.
\( \frac{|\vec{a} + \vec{b}|^{2}}{2} \)
D.
\( \frac{|\vec{a} - \vec{b}|^{2}}{2} \)
😑 View Answer Error
ANSWER :
B. \( \frac{|\vec{a} - \vec{b}|^{2}}{4} \)
Prev Next page