NDA Mathematics 2024 Question Paper

Let $A$ and $B$ be matrices of order $3\times 3$. If $|A|=\frac{1}{2\sqrt{2}}$ and $|B|=\frac{1}{729}$, then what is the value of $|2B(adj(3A))|$?

If $z$ is any complex number and $i{z}^3+z^2-z+i=0$, where $i=\sqrt{-1}$, then what is the value of $(|z|+1{)}^2$?

What is the sum of all four digit numbers formed by using all digits 0, 1, 4, 5 without repetition of digits?

If $x$, $y$ and $z$ are the cube roots of unity, then what is the value of $xy+yz+zx$?

A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relatives and 3 of them are his wife's relatives?

A triangle $PQR$ is such that 3 points lie on the side $PQ$, 4 points on $QR$ and 5 points on $RP$ respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?

If ${\log }_{b}a=p$, ${\log }_{d}c=2p$ and ${\log }_{f}e=3p$, then what is $(ace{)}^{\frac{1}{p}}$ equal to?

If $-\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0+a_{1}x+a_2{x}^2+a_3{x}^3+x^4=0$ where $a_0,a_1,a_2,a_3$ are integers, then which one of the following is correct?

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1+z_2}{z_1-z_2}\right|=1$, then what is $Re\left(\frac{z_1}{z_2}\right)+1$ equal to?

If $26!=n{8}^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?