- A$3$
- B$4$
- ✓$5$
- D$7$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$(A)$ determinant of $\left( M ^2+ MN ^2\right)$ is $0$
$(B)$ there is a $3 \times 3$ non-zero matrix $U$ such that $\left( M ^2+ MN ^2\right) U$ is the zero matrix
$(C)$ determinant of $\left( M ^2+ MN ^2\right) \geq 1$
$(D)$ for a $3 \times 3$ matrix $U$, if $\left( M ^2+ MN ^2\right) U$ equals the zero matrix then $U$ is the zero matrix
($A$) $f$ is discontinuous exactly at three points in $\left[-\frac{1}{2}, 2\right]$
($B$) $f$ is discontinuous exactly at four points in $\left[-\frac{1}{2}, 2\right]$
($C$) $g$ is $NOT$ differentiable exactly at four points in $\left(-\frac{1}{2}, 2\right)$
($D$) $g$ is $NOT$ differentiable exactly at five points in $\left(-\frac{1}{2}, 2\right)$
$(S1)$: $f^{\prime}\left(-\frac{3}{2}\right)+f^{\prime}\left(-\frac{1}{2}\right)+f^{\prime}\left(\frac{1}{2}\right)+f^{\prime}\left(\frac{3}{2}\right)=2$
$( S 2): \int_{-2}^{2} f ( x ) dx =12$Then,
$2\left(a_1+a_2+\ldots .+a_n\right)=b_1+b_2+\ldots . .+b_n$
holds for some positive integer $n$, is. . . . . . .