• 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. $\frac{\pi }{3}$
• 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. $\frac{5^{7x}}{7\text{in5}}+c$
• B. $\frac{5^{7x}}{\text{in5}}+c$
• C. $5^{7x}\ln 5+c$
• D. $5^{7x}\left(7\ln 5\right)+c$

Answer: Option A

Explanation:

• A. $\frac{1}{3}$
• B. $\frac{1}{6}$
• C. $\frac{1}{2}$
• D. $-\frac{1}{6}$

Answer: Option B

Explanation:

• A. $x{\left(Inx\right)}^2+2x\ln x+2x+c$
• B. $x{\left(Inx\right)}^2-2x\ln x+2x+c$
• C. $x{\left(Inx\right)}^2-2x\ln x-2x+c$
• D. $x{\left(Inx\right)}^2-2x\ln x+2x+c$

Answer: Option D

Explanation:

• A. $e^x \sin x + c$
• B. $e^x \cos x + c$
• C. $e^x \tan x + c$
• D. $e^x secx + c$

Answer: Option A

Explanation:

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

Answer: Option A

Explanation:

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

Answer: Option B

Explanation:

• A. $-\sqrt{x}+C$
• B. $-\sqrt{1-x}+C$
• C. $\sqrt{1-x^2}+C$
• D. $-\sqrt{1-x^2}+C$

Answer: Option D

Explanation:

• A. $\frac{1}{2}{\sin }^{-1}\frac{2x}{5}+k$
• B. $\frac{5}{2}{\sin }^{-1}\frac{2x}{5}+k$
• C. $\frac{5}{2}{\cos }^{-1}\frac{2x}{5}+k$
• D. ${\sin }^{-1}\frac{2x}{5}+k$

Answer: Option A

Explanation: