MCQ
${{{d^{20}}y} \over {d{x^{20}}}}(2\cos x\cos 3x)$=
- A${2^{20}}(\cos 2x - {2^{20}}\cos 4x)$
- ✓${2^{20}}(\cos 2x + {2^{20}}\cos 4x)$
- C${2^{20}}(\sin 2x + {2^{20}}\sin 4x)$
- D${2^{20}}(\sin 2x - {2^{20}}\sin 4x)$
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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?
$x\,\, + \,\,y\,\, = \,\,\frac{{2\pi }}{3},\,{\rm{cos}}\,{\rm{x + }}\,{\rm{ cos}}\,{\rm{y}}\,{\rm{ = }}\,\frac{3}{2},$ where $x$ and $y$ are real in