$\frac{n +1}{3(n+2)}$

$\frac{n}{3(n+3)}$

$\frac{n}{2(n+3)}$

$\frac{n+2}{3 (n+3)}$

1

5

2

3

$(-\infty ,\frac{1}{2})$

$(1,\infty )$

$(-\infty , \frac{1}{2})\cup (1,\infty )$

$(-\infty ,\frac{1}{2}]\cup [1,\infty )$

$\alpha \beta \theta$

$\alpha \theta$

$\beta \theta$

$\alpha \beta$

8

-8

$\sqrt{8}$

$\pm 8$

720

2880

180

5040

$\frac{8}{21}$

$\frac{3}{7}$

$\frac{10}{21}$

$\frac{11}{21}$

5/3

5/2

5

2

0,0

$-2i,\frac{-\mathrm{\pi }}{2}$

$2i,\frac{\mathrm{\pi }}{2}$

-2,$\mathrm{\pi }$

$\left(\begin{array}{c}-2\\ -2\end{array}\begin{array}{c}2\\ 2\end{array}\right)$

$\left(\begin{array}{c}0\\ 0\end{array}\begin{array}{c}0\\ 0\end{array}\right)$

$\left(\begin{array}{c}0\\ 3\end{array}\begin{array}{c}0\\ 0\end{array}\right)$

$\left(\begin{array}{c}-2\\ 2\end{array}\begin{array}{c}-2\\ 2\end{array}\right)$

5

-5

$\frac{1}{5}$

$-\frac{1}{5}$

$x^2+y^2-2x+6y+4 =0$

$x^2+y^2-2x + 6y +1 =0$

$x^2 + y^2 -4x + 6y + 5 = 0$

$2x^2+ 2y^2 -2x+ 6y + 3 = 0$

(7,4)

(4,7)

(5,8)

(8, 5)

32 Sq. units

16 Sq. units

12 Sq. units

24 Sq. units

$\pm \frac{2}{3}$

$\pm \frac{\sqrt{15}}{6}$

$\pm \frac{7}{6}$

$\pm \frac{\sqrt{23}}{6}$

$\underset{AD}{\to }=\underset{AB}{\to }+\underset{BC}{\to }$

$\underset{DA}{\to }=\underset{DF}{\to } +\underset{DE}{\to }$

$\underset{AD}{\to }=\underset{AB}{\to } +\underset{AC}{\to }$

$\underset{AD}{\to }= \underset{BE}{\to } +\underset{CF}{\to }$

4a -6b=1

4a- 6b = 2

6a - 4b = 1

6a - 4b = 2

$2 \cos 65°$

$\sqrt{2} \cos 20°$

$\sqrt{2} \sin 20°$

$2\sin 20°$

40x + 81 =0

2x + 3 =0

40 y + 81

40 y + 41 =0

$\frac{\mathrm{\pi }}{4}$

$\frac{\mathrm{\pi }}{3}$

$\frac{\mathrm{\pi }}{2}$

$\frac{\mathrm{\pi }}{6}$

${\tan }^{-1} \frac{2}{11}$

${\sin }^{-1} \frac{11}{12}$

${\tan }^{-1} \frac{11}{2}$

${\cos }^{-1} \frac{11}{2}$

$\frac{\mathrm{\pi }}{6}$

$\frac{\mathrm{\pi }}{4}$

$\frac{\mathrm{\pi }}{3}$

$\frac{2\mathrm{\pi }}{3}$

$x<-2,y>\frac{1}{2}$

$-2<x<2,y\ge \frac{1}{2}$

$-2\le x\le 2,y<\frac{1}{2}$

$-x<-2 \& x> , -2<y<2$

y = x

y = x + 1

y =2 y +1

y =2x

$\frac{5}{6}$

$\frac{1}{6}$

$-\frac{1}{6}$

$\frac{1}{3}$

$60°$

$90°$

$120°$

$150°$

$\frac{3}{2}$

$\frac{1}{2}$

1

$\frac{1n5}{xy}$

$\frac{1n5}{-x^2}$

$-\frac{y}{x}$

$\frac{1n5}{ y }$

$\frac{1}{2}(1n2{)}^2$

$\frac{1}{2}1n2$

$\infty$

$x{e}^x+c$

$\tan \left(x{e}^x\right) +c$

$cot\left(X{e}^x\right)+c$

$\cos \left(X{e}^x\right) +c$