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

31.
If \( \frac{1}{b - a} + \frac{1}{b - c} = \frac{1}{a} + \frac{1}{c} \), then a, b and c are in
A.
AP
B.
GP
C.
HP
D.
Neither in AP nor in GP nor in HP
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ANSWER :
C. HP
32.
Let P, Q, R and S be the sum of n terms, 2n terms, 3n terms and 4n terms respectively of an AP such that Q = 3P. Which one of the following is correct?
A.
5R = 3S
B.
6R = 5S
C.
8R = 7S
D.
9R = 8S
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ANSWER :
A. 5R = 3S
33.
In a GP, the 3rd, 5th and 7th terms are \( x \), \( x^{2} + 2 \) and \( x^{3} + 10 \) respectively, where \( x > 1 \). What is the 8th term?
A.
18
B.
\( 18\sqrt{3} \)
C.
54
D.
\( 54\sqrt{3} \)
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ANSWER :
B. \( 18\sqrt{3} \)
34.
If \( (1 + i)^{n} - 16 = 0 \), where \( i = \sqrt{-1} \) and n is a positive integer, then what is the least value of n?
A.
2
B.
4
C.
8
D.
16
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ANSWER :
C. 8
35.
What is \( i \times i^{4} \times i^{9} \times i^{16} \times \ldots \times i^{576} \), where \( i = \sqrt{-1} \), equal to?
A.
\( -i \)
B.
−1
C.
1
D.
\( i \)
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ANSWER :
C. 1
36.
If \( z = x + iy \) be such that \( \left|\frac{z + \lambda i}{z - \lambda i}\right| = 1 \), where \( i = \sqrt{-1} \) and \( \lambda \) is a positive real number, then which of the following statements is/are correct?
I. z lies on the line \( y = x \).
II. The amplitude of z is \( \frac{\pi}{4} \).
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 :
D. Neither I nor II
37.
What is
\( \begin{vmatrix} \frac{1}{a} & bc & a^{2} \\ \frac{1}{a} + \frac{1}{b} & c(a + b) & a^{2} + b^{2} \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & ab + bc + ca & a^{2} + b^{2} + c^{2} \end{vmatrix} \)
equal to?
A.
0
B.
3
C.
\( (a + b + c)(ab + bc + ca) \)
D.
\( a^{3} + b^{3} + c^{3} - 3abc \)
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ANSWER :
A. 0
38.
If
\( ae + bg = cf + dh = p, af + bh = ce + dg = q \)
then what is
\( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \times \begin{vmatrix} e & f \\ g & h \end{vmatrix} \)
equal to?
A.
\( p^{2}q^{2} \)
B.
\( pq \)
C.
\( p^{2} + q^{2} \)
D.
\( p^{2} - q^{2} \)
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ANSWER :
D. \( p^{2} - q^{2} \)
39.
If
\( x + ay + a^{2}z = 1, x + by + b^{2}z = 1, x + cy + c^{2}z = 1 \)
where \( a \neq b \neq c \), then what is \( x + y + z \) equal to?
A.
0
B.
1
C.
3
D.
a + b + c
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ANSWER :
B. 1
40.
Let
\( A = \begin{bmatrix} 1 & -\tan \theta \\ \tan \theta & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & \tan \theta \\ -\tan \theta & 1 \end{bmatrix} \)
If \( C = AB^{-1} \), then what is det(C) equal to?
A.
\( \sec^{2} \theta \)
B.
\( \sec^{4} \theta \)
C.
\( \cos^{2} \theta \)
D.
1
😑 View Answer Error
ANSWER :
D. 1
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