https://competishun.com/let-f-r-rightarrow-r-be-a-function-such-that-fxx3x2-fprime1x-fprime-prime2fprime-prime-prime3-x-in-r-then-f2-equals/

has infinitely many solutions, then $\beta-\alpha$ equals

$$ \text { If } A=\left[\begin{array}{cc} \cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta \end{array}\right],\left(\theta=\frac{\pi}{24}\right) \text { and } A^5=\left[\begin{array}{ll}...

Contrapositive of the statement “If two numbers are not equal, then their squares are not equal.” is :

Which of the following statements is a tautology?

Let $A$ and $B$ be two invertible matrices of order $3 \times 3$. If $\operatorname{det}\left(A B A^{\top}\right)=8$ and $\operatorname{det}\left(A B^{-1}\right)=8$, then $\operatorname{det}\left(B A^{-1} B^{\top}\right)$ is...

The logical statement (MF ST-1) $[\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)$ is equivalent to

If the system of linear equations $$ \begin{gathered} x-4 y+7 z=g \\ 3 y-5 z=h \\ -2 x+5 y-9 z=k \end{gathered} $$ is consistent, then

If $\mathrm{A}=\left(\begin{array}{ll}2 & 2 \\ 9 & 4\end{array}\right)$ and $\mathrm{I}=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$, then $10 \mathrm{~A}^{-1}$ is equal to

The number of elements in the set $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ and $\left.(I-A)^3=I-A^3\right\}$ where $I$ is $...