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

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NDA & NA Exam (I)- 2026 - Mathematics

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

21.
If M' is the transpose of a \( 2 \times 2 \) matrix M, then which of the following is/are correct?
I. \( |M + M'| = |M| + |M'| \) if M is symmetric.
II. \( |M + M'| = 0 \) if M is anti-symmetric.
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 :
B. II only
22.
If M is a square matrix such that \( M^{2} = M \), then how many values of |M| are possible?
A.
One
B.
Two
C.
Three
D.
Four
😑 View Answer Error
ANSWER :
B. Two
23.
Let \( p = (x + y + z) \) and \( q = xyz \). If \( \begin{vmatrix} x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix} \) is positive, then which one of the following is correct?
A.
\( q > p \)
B.
\( q + 1 > p \)
C.
\( q + 2 > p \)
D.
\( q + 2 < p \)
😑 View Answer Error
ANSWER :
C. \( q + 2 > p \)
24.
What is
\( (((A \cap B) \cup (A - B)) - ((A \cap B) \cup (B - A))) \cup A \)
equal to?
A.
\( \phi \)
B.
A
C.
B
D.
\( A \cup B \)
😑 View Answer Error
ANSWER :
B. A
25.
Let A and B be two sets. For some set C, both \( A \cap C \) and \( B \cap C \) are empty sets and \( A \cup C = B \cup C \). Which of the following is/are true?
I. \( C = \phi \)
II. \( A = B \)
III. \( A \cup B = C \)
Select the answer using the code given below:
A.
I only
B.
II only
C.
I and II only
D.
I, II and III
😑 View Answer Error
ANSWER :
B. II only
26.
If \( 2\sec 4\beta = \tan 2\alpha + \cot 2\alpha \), then which one of the following is a possible value of \( (\alpha + \beta) \)?
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{4} \)
C.
\( \frac{\pi}{6} \)
D.
\( \frac{\pi}{8} \)
😑 View Answer Error
ANSWER :
D. \( \frac{\pi}{8} \)
27.
If \( \alpha \) and \( \beta \) are complementary angles such that \( \alpha - \beta = \frac{\pi}{6} \) and \( m \tan \beta = n \tan \alpha \), then what is \( \left(\frac{m + n}{m - n}\right) \) equal to?
A.
2
B.
\( \frac{2}{\sqrt{3}} \)
C.
1
D.
\( \frac{1}{\sqrt{3}} \)
😑 View Answer Error
ANSWER :
A. 2
28.
If \( x = \sec \theta - \tan \theta \) and \( y = \mathrm{cosec} \theta + \cot \theta \), then which one of the following is correct?
A.
\( x + y - xy - 1 = 0 \)
B.
\( x - y + xy + 1 = 0 \)
C.
\( x + y + xy - 1 = 0 \)
D.
\( x - y + xy - 1 = 0 \)
😑 View Answer Error
ANSWER :
B. \( x - y + xy + 1 = 0 \)
29.
If \( \cos \theta = \frac{1}{3} \), then what is the value of \( \sin\left(\frac{\theta}{2}\right) \sin\left(\frac{3\theta}{2}\right) \)?
A.
\( \frac{5}{9} \)
B.
\( \frac{7}{9} \)
C.
\( \frac{10}{9} \)
D.
\( \frac{11}{9} \)
😑 View Answer Error
ANSWER :
A. \( \frac{5}{9} \)
30.
\( \cos x + \sqrt{3} \sin x \) is maximum when x is equal to
A.
\( \frac{\pi}{2} \)
B.
\( \frac{\pi}{3} \)
C.
\( \frac{\pi}{4} \)
D.
\( \frac{\pi}{6} \)
😑 View Answer Error
ANSWER :
B. \( \frac{\pi}{3} \)
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