• A. $2$
• B. $1$
• C. $0$
• D. $\sqrt{2}$

Answer: Option D

Explanation:

• A. $a^3$
• B. $a^{\frac{13}{4}}$
• C. $a^{\frac{15}{4}}$
• D. $a^{\frac{11}{4}}$

Answer: Option C

Explanation:

• A. $\frac{2}{7}\hat{i}+\frac{4}{7}\hat{j}+\frac{5}{7}\hat{k}$
• B. $\frac{1}{7}\hat{i}+\frac{2}{7}\hat{j}+\frac{3}{7}\hat{k}$
• C. $\frac{3}{7}\hat{i}+\frac{6}{7}\hat{j}\frac{2}{7}\hat{k}$
• D. $\frac{3}{5}\hat{i}+\frac{6}{5}\hat{j}\frac{2}{5}\hat{k}$

Answer: Option C

Explanation:

• A. 1, 2
• B. -1, 2
• C. 1, -2
• D. -1, -2

Answer: Option C

Explanation:

• A. $\overline{A}.B$
• B. $A\otimes B$
• C. $A+\overline{B}$
• D. $A+B$

Answer: Option B

Explanation:

• A. $\frac{11}{\sqrt{38}}\left(3\hat{i}+5\hat{j}-2\hat{k}\right)$
• B. $\frac{11}{7}\left(3\hat{i}+2\hat{j}-6\hat{k}\right)$
• C. $\frac{31}{7}\left(3\hat{i}+2\hat{j}-6\hat{k}\right)$
• D. $\frac{3}{\sqrt{38}}\left(3\hat{i}+5\hat{j}-2\hat{k}\right)$

Answer: Option A

Explanation:

• A. 180 °
• B. 120°
• C. 90°
• D. 0°

Answer: Option D

Explanation:

• A. $-{\mathrm{xe}}^{-\mathrm{x}}-{\mathrm{e}}^{\mathrm{x}}+\mathrm{k}$
• B. ${\mathrm{xe}}^{\mathrm{x}}+{\mathrm{e}}^{\mathrm{x}}+\mathrm{k}$
• C. ${\mathrm{xe}}^{\mathrm{x}}+\mathrm{k}$
• D. $-{\mathrm{xe}}^{-\mathrm{x}}+{\mathrm{e}}^{-\mathrm{x}}+\mathrm{k}$

Answer: Option A

Explanation:

• A. $\frac{2}{3}{\left(c^x\right)}^{\frac{3}{2}}+C$
• B. $\frac{1}{2}\sqrt{c^x}+C$
• C. $2c^{\frac{x}{2}}+C$
• D. $-c^{\frac{x}{2}}+C$

Answer: Option C

Explanation:

• A. $1 + 2e^{2x}$
• B. $1 + e^{2x}$
• C. $1 +\frac{1}{2} e^{2x}$
• D. $x^2 + e^{2x}$

Answer: Option A

Explanation:

• A. $\sin \left(x{e}^x\right) + C$
• B. $\cos \left(x{e}^x\right) + C$
• C. $\tan \left(x{e}^x\right) + C$
• D. ${\cos }^2 \left(x{e}^x\right) + C$

Answer: Option C

Explanation:

• A. $-2\le x\le 2$
• B. $-2<x<2$
• C. $0\le x\le 2$
• D. $-2\le x\le 0$

Answer: Option B

Explanation:

• A. $\frac{\pi }{3}$
• B. $\frac{3\pi }{4}$
• C. $\frac{2\pi }{3}$
• D. $\frac{\pi }{6}$

Answer: Option C

Explanation:

• A. (-1, 0)
• B. (-c, 0)
• C. (c, -c)
• D. (-c, c)

Answer: Option B

Explanation:

• A. 3
• B. 2
• C. 7
• D. 5

Answer: Option B

Explanation: