1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

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?

1
Both Statement-1 and Statement-II are correct and Statement-II explains Statement-I
2
 Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-1
3
Statement-I is correct but Statement-II is not correct
4
 Statement-I is not correct but Statement-II is correct
2
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

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?

1
Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
2
Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
3
Statement-I is correct but Statement-II is not correct
4
 Statement-I is not correct but Statement-II is correct
3
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
What is$\cot ^{-1}9+\>\mathrm{cosec}\>{}^{-1}\left(\frac{\sqrt{41}}{4}\right)$
equal to?
1
$\frac{\pi }{4} $
2
$\frac{\pi }{3} $
3
$​​\frac{\pi }{2} $
4
${\pi } $
4
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
How many values of $\theta $, where$- \pi < \theta < \pi$ satisfy both the equations $\cot \theta =-\sqrt{3}$ and $\csc \theta =-2$ simultaneously?
1
4
2
2
3
1
4
None