Day 230: MHT-CET Maths

1. A.
   $\frac{x^{2}}{2} - 2x + 3\log(x + 1) + \frac{1}{x + 1} + c$ where c is the constant of integration
2. B.
   $\frac{x^{2}}{2} + 2x - 3\log(x + 1) + \frac{1}{x + 1} + c$ where c is the constant of integration
3. C.
   $\frac{x^{2}}{2} - 2x + 3\log(x + 1) - \frac{1}{x + 1} + c$, where c is the constant of integration
4. D.
   $\frac{x^{2}}{2} - 2x - 3\log(x + 1) - \frac{1}{x + 1} + c$, where c is the constant of integration

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1. A.
   20
2. B.
   40
3. C.
   50
4. D.
   51

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1. A.
   $x(\sin x + \cos x) + (\sin x - \cos x) + c$
2. B.
   $x(\sin x - \cos x) + (\sin x - \cos x) + c$
3. C.
   $x(\sin x + \cos x) + (\sin x + \cos x) + c$
4. D.
   $x(\sin x - \cos x) + (\sin x + \cos x) + c$

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1. A.
   Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \le 30, x_2 \le 4x_1, x_1 \ge 0, x_2 \ge 0$.
2. B.
   Minimize $z = 150x_1 + 90x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.
3. C.
   Minimize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.
4. D.
   Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \le 250, x_1 \ge 30, x_2 \ge 4x_1, x_1 \ge 0, x_2 \ge 0$.

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1. A.
   $5$ or $11$
2. B.
   $7$ or $14$
3. C.
   $8$ or $15$
4. D.
   $6$ or $13$

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