1
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
In obtaining the solution of the system of equations x + y + z = 7 x + 2y + 3z = 16 and x + 3y + 4z = 22 by Cramer's rule, the value of y is obtained by dividing D by $D_{2}$ where 
$D=\left|\begin{matrix}1&1&1\\ 1&2&3\\ 1&3&4\end{matrix}\right|$ What is the value of the determinant $D_{2}$ ?
1
-13
2
 -3
3
3
4
13
2
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
The value of the determinant $\left|\begin{matrix}a&b&c\\ l&m&n\\ p&q&r\end{matrix}\right|$ is equal to
1
$ \left|\begin{matrix}a&b&c\\ p&q&r\\ l&m&n\end{matrix}\right|$
2
$\left|\begin{matrix}l&m&n\\ a&b&c\\ p&q&r\end{matrix}\right| $
3
$\left|\begin{matrix}p&q&r\\ a&b&c\\ l&m&n\end{matrix}\right|$
4
$\left|\begin{matrix}a&p&l\\ b&q&m\\ c&r&n\end{matrix}\right|$
3
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
If a, b, c are the sides of a triangle ABC and p is the perimeter of the triangle, then what is equal to? det $\left|\begin{matrix}p+c&a&b\\ c&p+a&b\\ c&a&p+b\end{matrix}\right|$
1
$p ^ 3$
2
$ 2p ^ 3$
3
$3p ^ 3$
4
$ 4p ^ 3$
4
NDA Mathematics 14th September 2025
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language
For the following two (02) items:
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 $A ^ 4$
1
0
2
1
3
$cos 4\theta - sin 4\theta$
4
$cos^2 4 \theta - sin^2 4 \theta$