• A. $5$
• B. $25/2$
• C. $25$
• D. $50$

Answer: Option C

Explanation:

• A. $\frac{1}{2}{\left({\tan }^{-1}x\right)}^2$
• B. $\frac{x^2}{2}$
• C. $\frac{1}{2}{\left({\tan }^{-1}u\right)}^2$
• D. $\frac{1}{2}\left({\tan }^{-1}x\right)$

Answer: Option A

Explanation:

• A. -4
• B. 3
• C. 4
• D. 9

Answer: Option B

Explanation:

• A. $\frac{\mathrm{\pi }}{3}$
• B. $\frac{\mathrm{\pi }}{2}$
• C. $\frac{\mathrm{\pi }}{6}$
• D. $\mathrm{\pi }$

Answer: Option B

Explanation:

• A. $\frac{\mathrm{\pi }}{4}$
• B. $1$
• C. $\frac{\mathrm{\pi }}{2}$
• D. $0$

Answer: Option A

Explanation:

• A. π/ 2
• B. π/ 3
• C. 1/6
• D. 1/9

Answer: Option C

Explanation:

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{3}$

Answer: Option B

Explanation:

• A. $\mathrm{\pi }$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{3}$
• D. $\frac{\pi }{4}$

Answer: Option B

Explanation:

• A. $\frac{\mathrm{\pi }}{32}$
• B. $\frac{3\mathrm{\pi }}{32}$
• C. $\frac{5\mathrm{\pi }}{32}$
• D. $\frac{7\mathrm{\pi }}{32}$

Answer: Option C

Explanation:

• A. 10
• B. 12
• C. 8
• D. 360

Answer: Option C

Explanation:

• A. 6
• B. 7
• C. $5\sqrt{2}$
• D. $5\sqrt{3}$

Answer: Option C

Explanation:

• A. 3 - i
• B. 2 + 2i
• C. 1 + i
• D. 4 - i

Answer: Option D

Explanation:

• A. $3\sqrt{2}$
• B. $4\sqrt{3}$
• C. $3\sqrt{3}$
• D. $2\sqrt{3}$

Answer: Option D

Explanation:

• A. $K\omega =\left[H_3{O}^{+}\right]\times \left[O{H}^{-}\right]$
• B. $K_{\omega }=\frac{\left[H_3{O}^{+}\right]\times \left[O{H}^{-}\right]}{{\left[H_{2}O\right]}^2}$
• C. $K_{\omega }=\frac{{\left[H_{2}O\right]}^2}{\left[H_3{O}^{+}\right]\times \left[O{H}^{-}\right]}$
• D. $K_{\omega }={\left[H_{2}O\right]}^2\times \left[O{H}^{-}\right]$

Answer: Option A

Explanation:

• A. $\frac{3}{5}$
• B. $\frac{11}{15}$
• C. $\frac{1}{2}$
• D. $\frac{2}{1}$

Answer: Option D

Explanation: