Day 46: CBSE Class 12 Maths

1. A.
   $\cot(\log x)$
2. B.
   $y$
3. C.
   $-y$
4. D.
   $\tan(\log x)$

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1. A.
   16
2. B.
   64
3. C.
   256
4. D.
   512

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1. A.
   $30$
2. B.
   $120$
3. C.
   $15$
4. D.
   $225$

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1. A.
   $3e^{4y} + 4e^{-3x} + C = 0$
2. B.
   $e^{3x + 4y} + C = 0$
3. C.
   $3e^{-3y} + 4e^{4x} + 12C = 0$
4. D.
   $3e^{-4y} + 4e^{3x} + 12C = 0$

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1. A.
   $\displaystyle\int_{a}^{b} f(x)\, dx = \int_{a}^{b} f(a + b - x)\, dx$
2. B.
   $\displaystyle\int_{-a}^{a} f(x)\, dx = 0$, if f is an even function
3. C.
   $\displaystyle\int_{-a}^{a} f(x)\, dx = 2\int_{0}^{a} f(x)\, dx$, if f is an odd function
4. D.
   $\displaystyle\int_{0}^{2a} f(x)\, dx = \int_{0}^{a} f(x)\, dx - \int_{0}^{a} f(2a + x)\, dx$

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