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

21.
Let A and B be symmetric matrices of the same order. Which of the following statements is/are correct?
I. (AB − BA) is also a symmetric matrix.
II. (BA − AB) is a skew-symmetric 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
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ANSWER :
B. II only
22.
If \( A = \begin{bmatrix} -1 & 2 \\ 3 & -4 \end{bmatrix} \), then what is \( |A^{-1}| \) equal to?
A.
−2
B.
−1
C.
−1/2
D.
2
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ANSWER :
C. −1/2
23.
Let S be the set of all real numbers and R be a relation on S defined by xRy if and only if \( |x| \leq y \). Then R is
A.
reflexive only
B.
transitive only
C.
both reflexive and transitive
D.
neither reflexive nor transitive
😑 View Answer Error
ANSWER :
B. transitive only
24.
4-digit numbers are formed with 1, 2, 3 and 4. What is the number of the 4-digit numbers in which at least one digit is repeated?
A.
256
B.
244
C.
232
D.
220
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ANSWER :
C. 232
25.
Given
\( S = \{(x, y, z) \in \mathbb{R}^{3} : xyz = 210, x < y < z\} \),
where x, y, z are positive integers.
What is the total number of elements in S?
A.
10
B.
12
C.
13
D.
More than 13
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ANSWER :
C. 13
26.
If \( x = 4 + i \), where \( i = \sqrt{-1} \), then what is \( x^{3} + 2x^{2} - 63x + 171 \) equal to?
A.
−1
B.
0
C.
1
D.
2
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ANSWER :
C. 1
27.
Let \( \alpha \) and \( \beta \) be the roots of the equation
\( x^{2} - p(x + 1) - q = 0 \)
What is
\( \frac{\alpha^{2} + 2\alpha + 1}{\alpha^{2} + 2\alpha + q} + \frac{\beta^{2} + 2\beta + 1}{\beta^{2} + 2\beta + q} \)
equal to?
A.
−1
B.
0
C.
1
D.
2
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ANSWER :
C. 1
28.
If the sum of the roots of the equation
\( \frac{1}{2x + p} + \frac{1}{2x + q} = \frac{1}{r} \)
is zero, then what is r equal to?
A.
p − q
B.
p + q
C.
(p − q)/2
D.
(p + q)/2
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ANSWER :
D. (p + q)/2
29.
Let \( \alpha \) and \( \beta \) be the roots of the equation \( ax^{2} + bx + c = 0 \) and \( p_{n} = \alpha^{n} + \beta^{n} \), where \( n > 1 \). What is
\( ap_{n+1} + bp_{n} + cp_{n-1} \)
equal to?
A.
0
B.
1
C.
a + b + c
D.
a − b + c
😑 View Answer Error
ANSWER :
A. 0
30.
If p, q and r are in AP, then what is
\( p^{3} + 3pr(p + r) + r^{3} \)
equal to?
A.
\( q^{3} \)
B.
\( 2q^{3} \)
C.
\( 3q^{3} \)
D.
\( 8q^{3} \)
😑 View Answer Error
ANSWER :
D. \( 8q^{3} \)
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