NDA & NA Exam (II)- 2026 - Mathematics Defence Question Paper

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NDA & NA Exam (II)- 2026 - Mathematics

NDA & NA Exam (II)- 2026 - Mathematics Defence Questions

11.
What is \( 6\sin\left(\frac{\pi}{18}\right) - 8\sin^{3}\left(\frac{\pi}{18}\right) \) equal to?
A.
1/4
B.
1/2
C.
1
D.
2
😑 View Answer Error
ANSWER :
C. 1
12.
How many values of \( \theta \) satisfy the equation \( \tan^{2} \theta + \cot^{2} \theta = 2 \), where \( 0^{\circ} < \theta < 360^{\circ} \)?
A.
1
B.
2
C.
4
D.
8
😑 View Answer Error
ANSWER :
C. 4
13.
What is \( \sin(\tan^{-1} 0.75) \) equal to?
A.
1
B.
4/5
C.
3/5
D.
1/2
😑 View Answer Error
ANSWER :
C. 3/5
14.
What is \( \tan^{2}\left(\frac{1}{2}\cos^{-1}\frac{1}{3}\right) \) equal to?
A.
1/2
B.
1
C.
2
D.
4
😑 View Answer Error
ANSWER :
A. 1/2
15.
What is \( \tan(1125^{\circ})\cot(405^{\circ}) + \tan(765^{\circ})\cot(675^{\circ}) \) equal to?
A.
2
B.
1
C.
0
D.
−2
😑 View Answer Error
ANSWER :
C. 0
16.
If A is a square matrix of order 3 and \( |A| = 2 \), then what is adj(adj A) equal to?
A.
8A
B.
4A
C.
2A
D.
2I, where I is the identity matrix of order 3
😑 View Answer Error
ANSWER :
C. 2A
17.
If A is a square matrix of order 3 such that
A(adj A) = \( \begin{bmatrix} 64 & 0 & 0 \\ 0 & 64 & 0 \\ 0 & 0 & 64 \end{bmatrix} \)
then what is |A| equal to?
A.
4
B.
8
C.
16
D.
64
😑 View Answer Error
ANSWER :
D. 64
18.
Let
\( A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \)
What is the least value of \( \theta \) for which \( A + A' = I \), where I is the identity matrix of order 2?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{6} \)
😑 View Answer Error
ANSWER :
B. \( \frac{\pi}{3} \)
19.
Let A, B and C be the square matrices of order 2 such that AB = AC. Which of the statements given below is/are correct?
I. B and C are not necessarily equal if A is a singular matrix.
II. B and C are equal if A is a non-singular matrix.
Select the answer using the code given below.
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
20.
If A is a square matrix of order 3 and \( |A| = 4 \), then what is |adj A| equal to?
A.
64
B.
16
C.
8
D.
4
😑 View Answer Error
ANSWER :
B. 16
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