1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
For the following two (02) items:
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $
What is the value of the determinant of the matrix $A ^ 4$
2
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
For the following two (02) items:
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $
Let
$A=\left[\begin{matrix}\cos \theta &\sin \theta \\ -\sin \theta &\cos \theta \end{matrix}\right] $
What is $[adj A ]^ {-1}$ equal to?
3
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Consider the following statements:
Statement-l: If X is an nn matrix, then det(mX) = $m ^ n$ det(X), where m is a scalar.
Statement-II: If Y is a matrix obtained from X by multiplying any row or column by a scalar m, then det (Y) = m det (X).
Which one of the following is correct in respect of the above statements?
4
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Consider the following statements about
the matrix $M=\left[\begin{matrix}71&23&48\\ 57&28&29\\ 65&17&48\end{matrix}\right]$
Statement-I: The inverse of M does not exist.
Statement-II: M is non-singular.
Which one of the following is correct in respect of the above statements?
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