• A. -1
• B. 1
• C. 2
• D. -2

Answer: Option D

Explanation:

• A. 1
• B. -i
• C. -1

Answer: Option B

Explanation:

• A. $\frac{x-y}{x\left(In x-1\right)}$
• B. $\frac{x-y}{x\left(1-In x\right)}$
• C. $\frac{y-x}{x\left(1-In x\right)}$
• D. $\frac{y-x}{x\left(\ln x-1\right)}$

Answer: Option A

Explanation:

• A. $\frac{\ln 5}{xy}$
• B. $-\frac{\ln 5}{xy}$
• C. $-\frac{y}{x}$
• D. $\frac{\ln 5}{x}$

Answer: Option C

Explanation:

• A. $\sqrt{1+x^2}{\tan }^{-1}x$
• B. $\left(1+x^2\right){\tan }^{-1}x$
• C. $\sqrt{1-x^2}{\tan }^{-1}x$

Answer: Option B

Explanation:

• A. $15$
• B. $\frac{2}{9}$
• C. $1$
• D. $25$

Answer: Option C

Explanation:

• B. 1
• C. 2
• D. 3

Answer: Option C

Explanation:

• A. -28
• B. 16
• C. 14
• D. 1/8

Answer: Option A

Explanation:

• A. 15
• B. 25
• C. 30
• D. 35

Answer: Option D

Explanation:

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

Answer: Option C

Explanation:

• A. 2
• B. -2
• C. 1
• D. -1

Answer: Option A

Explanation:

• A. $\frac{\mathrm{\pi }}{4}$
• B. $\frac{\mathrm{\pi }}{6}$
• C. $\frac{\mathrm{\pi }}{12}$
• D. $\frac{\mathrm{\pi }}{24}$

Answer: Option C

Explanation:

• A. 3
• B. 4
• C. 1
• D. 6

Answer: Option A

Explanation:

• A. ${\log }_{e}2$
• B. ${\log }_{e}2-$
• C. $2{\log }_{e}2$
• D. $2{\log }_{e}2,-1$

Answer: Option D

Explanation:

• A. 7/13
• B. 11/14
• C. In2
• D. $9\mathrm{\pi }/4$

Answer: Option D

Explanation: