Day 112: MHT-CET Maths

1. A.
   $9x + 20y + 105 = 0$
2. B.
   $9x - 20y - 105 = 0$
3. C.
   $9x - 20y + 105 = 0$
4. D.
   $9x + 20y - 105 = 0$

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1. A.
   $\theta = 2n\pi - \dfrac{\pi}{2}$ or $\theta = 2n\pi, n \in Z$
2. B.
   $\theta = n\pi - \dfrac{\pi}{2}$ or $\theta = n\pi, n \in Z$
3. C.
   $\theta = n\dfrac{\pi}{2} - \pi$ or $\theta = n\dfrac{\pi}{2}, n \in Z$
4. D.
   $\theta = 2n\pi + \dfrac{\pi}{2}$ or $\theta = n\pi, n \in Z$

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1. A.
   $(-2, -1)$
2. B.
   $(8, -2)$
3. C.
   $(2, -3)$
4. D.
   $(4, -4)$

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1. A.
   $\dfrac{162}{7} + \sqrt{3}\dfrac{\pi}{4}$
2. B.
   $\dfrac{162\sqrt{3}}{7} + \sqrt{3}\dfrac{\pi}{2}$
3. C.
   $\dfrac{162\sqrt{3}}{7} + \dfrac{\pi}{2}$
4. D.
   $\dfrac{162\sqrt{3}}{7} - \dfrac{\pi}{2}$

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1. A.
   $c(x^2 + y^2)^{\frac{1}{2}} + e^{\tan^{-1}\left(\frac{y^2}{x}\right)} = 0$, where c is an arbitrary constant
2. B.
   $c(x^2 + y^2)^{\frac{1}{2}} = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant
3. C.
   $c(x^2 - y^2) = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant
4. D.
   $c(x^2 + y^2) = e^{\tan^{-1}\left(\frac{y}{x}\right)}$, where c is an arbitrary constant

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