ডেইলি এক্সাম ৪.৬

1. .Let $\Delta$ $(x)=$$\begin{vmatrix} x+a & x+b &x+a-c \\ x+b & x+c &x-1 \\ x+c & x+d &x-b+d \end{vmatrix}$ ;and $\displaystyle \int_{0}^{2}\Delta(x) dx =-16$, where $\mathrm{a}$, b,c,d are in A.$\mathrm{P}$. then the common difference of the A.$\mathrm{P}$. is& ;

2. Let $A=\begin{bmatrix}5 & 5\alpha &\alpha \\ 0 & \alpha &5\alpha \\ 0 & 0 &5 \end{bmatrix}$ If $\left | A^{2} \right |=25$, then $\left |\alpha \right |$ equals

3. $\left|\begin{matrix}x&y&z\\x^2&y^2&z^2\\x^3-1&y^3-1&z^3-1\\\end{matrix}\right|=0$ এবং $x\ \neq y\ \neq z$ হলে $xyz=?$

4. $p=\left[\begin{array}{lll}3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 5\end{array}\right]$ হলে $|p|$ এর মান কত ?

5. Adj ;$\left ( Adj\begin{bmatrix} 2 &-3 \\ 4& 6 \end{bmatrix} \right )=$