NDA Mathematics 2020 Question Paper

If matrix $A=\left[\begin{array}{cc}1-i& i\\ -i& 1-i\end{array}\right]$ where $i=\sqrt{-1}$, then which one of the following is correct?

The term independent of $x$ in the binomial expansion of ${\left(\frac{2}{x^2}-\sqrt{x}\right)}^{10}$ is equal to

If $(1+2x-x^2{)}^6=a_0+a_{1}x+a_2{x}^2+\cdots +a_{12}{x}^{12}$, then what is $a_0-a_1+a_2-a_3+\cdots +a_{12}$ equal to?

If $C(20,n+2)=C(20,n-2)$, then what is $n$ equal to?

For how many values of $k$, is the matrix $\left[\begin{array}{ccc}0& k& 4\\ -k& 0& -5\\ -k& k& -1\end{array}\right]$ singular?

The number $(1101101+1011011{)}_2$ can be written in decimal system as

What is the value of $\frac{1}{10}{\log }_{5}1024-{\log }_{5}10+\frac{1}{5}{\log }_{5}3125$?

If $x={\log }_c(ab)$, $y={\log }_a(bc)$, $z={\log }_b(ca)$, then which of the following is correct?

Let $A=\left[\begin{array}{cc}x+y& y\\ 2x& x-y\end{array}\right]$, $B=\left[\begin{array}{c}2\\ -1\end{array}\right]$ and $C=\left[\begin{array}{c}3\\ 2\end{array}\right]$. If $AB=C$, then what is the value of the determinant of the matrix $A$?

If $1.5\le x\le 4.5$, then which one of the following is correct?