MCQ
The solution of $\frac{{dy}}{{dx}} = x\log x$ is
- A$y = {x^2}\log x - \frac{{{x^2}}}{2} + c$
- B$y = \frac{{{x^2}}}{2}\log x - {x^2} + c$
- C$y = \frac{1}{2}{x^2} + \frac{1}{2}{x^2}\log x + c$
- ✓None of these
==> $\int_{}^{} {dy = } \int_{}^{} {x\log xdx} $ ==>$y = \frac{{x^2}}{{2}} log\ x - \frac{{x^2}}{{4}} + c$.
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$x-2 y=1, x-y+k z=-2, k y+4 z=6, k \in R$
consider the following statements :
$(A)$ The system has unique solution if $k \neq 2$, $k \neq-2$
$(B)$ The system has unique solution if $k =-2$.
$(C)$ The system has unique solution if $k =2$.
$(D)$ The system has no-solution if $k =2$.
$(E)$ The system has infinite number of solutions if $k \neq-2$
Which of the following statements are correct?