NDA & NA Exam (II)- 2023 - Mathematics Defence Question Paper

NDA Previous Year Question Papers Question Papers
NDA & NA Exam (II)- 2023 - Mathematics

NDA & NA Exam (II)- 2023 - Mathematics Defence Questions

11.
Let \( t_{1}, t_{2}, t_{3}, \ldots \) be in GP. What is \( (t_{1}t_{2} \ldots t_{21})^{\frac{1}{21}} \) equal to?
A.
\( t_{10} \)
B.
\( t_{10}^{2} \)
C.
\( t_{11} \)
D.
\( t_{11}^{2} \)
😑 View Answer Error
ANSWER :
C. \( t_{11} \)
12.
Which one of the following is a square root of \( -\sqrt{-1} \)?
A.
\( 1 + i \)
B.
\( \frac{1 - i}{\sqrt{2}} \)
C.
\( \frac{1 + i}{\sqrt{2}} \)
D.
\( \frac{i}{\sqrt{2}} \)
😑 View Answer Error
ANSWER :
B. \( \frac{1 - i}{\sqrt{2}} \)
13.
What is the maximum number of points of intersection of 10 circles?
A.
45
B.
60
C.
90
D.
120
😑 View Answer Error
ANSWER :
C. 90
14.
A set S contains \( (2n + 1) \) elements. There are 4096 subsets of S which contain at most \( n \) elements. What is \( n \) equal to?
A.
5
B.
6
C.
7
D.
8
😑 View Answer Error
ANSWER :
B. 6
15.
If
\( \begin{vmatrix} x^{2} + 3x & x - 1 & x + 3 \\ x + 1 & -2x & x - 4 \\ x - 3 & x + 4 & 3x \end{vmatrix} = ax^{4} + bx^{3} + cx^{2} + dx + e \)
then what is the value of \( e \)?
A.
−1
B.
0
C.
1
D.
2
😑 View Answer Error
ANSWER :
B. 0
16.
If all elements of a third order determinant are equal to 1 or −1, then the value of the determinant is:
A.
0 only
B.
an even number but not necessarily 0
C.
an odd number
D.
0, 1 or −1
😑 View Answer Error
ANSWER :
B. an even number but not necessarily 0
17.
If
\( A = \begin{bmatrix} 2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1 \end{bmatrix} \)
then what is the value of \( \det[adj(adj A)] \)?
A.
5
B.
25
C.
125
D.
625
😑 View Answer Error
ANSWER :
D. 625
18.
If
\( A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \)
then what is \( 23A^{3} - 19A^{2} - 4A \) equal to?
A.
Null matrix of order 3
B.
Identity matrix of order 3
C.
\( \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix} \)
D.
\( \begin{bmatrix} 7 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 7 \end{bmatrix} \)
😑 View Answer Error
ANSWER :
A. Null matrix of order 3
19.
The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of \( C^{2} \)?
A.
3
B.
9
C.
81
D.
729
😑 View Answer Error
ANSWER :
C. 81
20.
If
\( A_{k} = \begin{bmatrix} k - 1 & k \\ k - 2 & k + 1 \end{bmatrix} \)
then what is \( \det(A_{1}) + \det(A_{2}) + \det(A_{3}) + \ldots + \det(A_{100}) \) equal to?
A.
100
B.
1000
C.
9900
D.
10000
😑 View Answer Error
ANSWER :
D. 10000
Prev Next page