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

11.
If the highest degree coefficient is equal to 1, then what is the total number of quadratic equations which are unchanged on squaring their roots?
A.
6
B.
4
C.
2
D.
None
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ANSWER :
B. 4
12.
Let \( \alpha \) and \( \beta \) be the roots of the quadratic equation \( x^{2} - 2bx + c^{2} = 0 \) where b, c are positive real numbers. Let A be the arithmetic mean of \( \alpha \) and \( \beta \); and G be the geometric mean of \( \alpha \) and \( \beta \). What are the roots of the quadratic equation \( x^{2} - (b + c)x + bc = 0 \)?
A.
A, G
B.
2A, G
C.
A, 2G
D.
2A, 2G
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ANSWER :
A. A, G
13.
If
\( 1 - \log_{10} 2 = \log_{10}(5^{x} + 4^{x} + 3^{x} + 2^{x} + 1) \),
then what is a value of x?
A.
10
B.
5
C.
1
D.
0
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ANSWER :
D. 0
14.
Let
\( f(x) = \begin{vmatrix} x^{3} & \sin x & \cos x \\ 6 & -1 & 0 \\ q & q^{2} & q^{3} \end{vmatrix} \)
where q is any constant, then what is \( \frac{d^{3}}{dx^{3}}(f(x)) \) at \( x = 0 \) equal to?
A.
−1
B.
0
C.
1
D.
q
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ANSWER :
B. 0
15.
If
\( \begin{vmatrix} a - b & p - q & x - y \\ b - c & q - r & y - z \\ c - a & r - p & z - x \end{vmatrix} = k\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix} \)
then what is the value of k?
A.
−1
B.
0
C.
\( \frac{1}{2} \)
D.
1
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ANSWER :
B. 0
16.
If p, q, r are the cube roots of unity, then what is
\( \begin{vmatrix} p^{2} + q^{2} & r^{2} & r^{2} \\ p^{2} & q^{2} + r^{2} & p^{2} \\ q^{2} & q^{2} & r^{2} + p^{2} \end{vmatrix} \)
equal to?
A.
−1
B.
0
C.
1
D.
4
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ANSWER :
D. 4
17.
If A is a square matrix such that \( |A| = -2 \), then \( |AA^{T}| \), where \( A^{T} \) is the transpose of A, is equal to
A.
−4
B.
1
C.
2
D.
4
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ANSWER :
D. 4
18.
Consider the following statements:
I. If \( n \times n \) \( (n > 1) \) matrix is symmetric and non-singular, then its inverse is also a symmetric matrix.
II. If \( n \times n \) \( (n > 1) \) matrix is singular, then its adjoint is also a singular matrix.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
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ANSWER :
C. Both I and II
19.
If \( M = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix} \), then what is the value of |M| |adj M|?
A.
8
B.
64
C.
256
D.
512
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ANSWER :
D. 512
20.
If \( M_{k} = \begin{bmatrix} k & k - 1 \\ k - 1 & k \end{bmatrix} \), where k is a natural number, then what is
\( |M_{1}| + |M_{2}| + |M_{3}| + \ldots + |M_{50}| \)
equal to?
A.
50
B.
1250
C.
2500
D.
5000
😑 View Answer Error
ANSWER :
C. 2500
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