# JEE Main & Advanced Mathematics Straight Line Question Bank

### done Angle between two straight lines, Bisector of angle between two lines

• A) ${{30}^{o}}$

B) ${{60}^{o}}$

C) ${{45}^{o}}$

D) ${{90}^{o}}$

• A) ${{30}^{o}}$

B) ${{60}^{o}}$

C) ${{45}^{o}}$

D) ${{90}^{o}}$

• A) ${{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{ab}$

B) ${{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2}$

C) ${{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2ab}$

D) None of these

• A) ${{\tan }^{-1}}\left( -\frac{6}{7} \right)$

B) ${{\tan }^{-1}}\left( \frac{6}{7} \right)$

C) ${{\tan }^{-1}}\left( -\frac{7}{6} \right)$

D) ${{\tan }^{-1}}\left( \frac{7}{6} \right)$

• A) $2{{\tan }^{-1}}\frac{b}{a}$

B) ${{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}$

C) ${{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}$

D) None of these

• A) $\frac{1+3\sqrt{2}}{7}$

B) $\frac{1-3\sqrt{2}}{7}$

C) $\frac{1\pm 3\sqrt{2}}{7}$

D) $\frac{1\pm 5\sqrt{2}}{7}$

• A) $({{\alpha }_{1}}+{{\alpha }_{2}})$

B) $({{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}})$

C) $2{{\alpha }_{1}}$

D) $2{{\alpha }_{2}}$

• A) ${{90}^{o}}$

B) ${{30}^{o}}$

C) ${{60}^{o}}$

D) None of these

• A) ${{60}^{o}}$

B) ${{30}^{o}}$

C) ${{90}^{o}}$

D) ${{45}^{o}}$

• A) Parallel

B) Inclined at ${{60}^{o}}$to each other

C) Perpendicular to each other

D) Inclined at ${{30}^{o}}$to each other

• A) Parallel to each other

B) Perpendicular to each other

C) Inclined at ${{45}^{o}}$to each other

D) Coincident pair of straight lines

• A) ${{120}^{o}}$

B) ${{135}^{o}}$

C) ${{150}^{o}}$

D) ${{160}^{o}}$

• A) ${{60}^{o}}$

B) ${{120}^{o}}$

C) ${{150}^{o}}$

D) ${{135}^{o}}$

• A) $\infty$

B) ${{\tan }^{-1}}(3)$

C) ${{\tan }^{-1}}\left( \frac{1}{3} \right)$

D) None of these

• A) 1

B) 2

C) 1

D) 2

• A) $x=0$

B) $y=0$

C) $x+y=0$

D) $x-y=0$

• A) ${{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{2}}+{{a}_{2}}{{b}_{1}}}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}$

B) ${{\cot }^{-1}}\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}$

C) ${{\cot }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}$

D) ${{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}$

• A) $\pi /4$

B) $\pi /6$

C) $\pi /3$

D) $3\pi /4$

• A) ${{90}^{o}}$

B) ${{60}^{o}}$

C) ${{45}^{o}}$

D) ${{30}^{o}}$

• A) ${{90}^{o}}$

B) ${{60}^{o}}$

C) ${{75}^{o}}$

D) ${{30}^{o}}$

• A) ${{90}^{o}}$

B) ${{45}^{o}}$

C) ${{180}^{o}}$

D) ${{60}^{o}}$

• A) ${{45}^{o}}$

B) $60{}^\circ$

C) ${{90}^{o}}$

D) ${{180}^{o}}$

• A) Perpendicular

B) Parallel

C) Makes an angle ${{60}^{o}}$with each other

D) None of these

• A) $\frac{1}{2}$

B) 2

C) $-\frac{1}{2}$

D) None of these

• A) Perpendicular

B) Parallel

C) Angle between them is $\frac{\pi }{4}$

D) None of these

• A) ${{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}}=0$

B) ${{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}=0$

C) $a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0$

D) ${{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}=0$

• A) Parallel

B) Perpendicular

C) Equally inclined to axes

D) Coincident

• A) -1

B) 1

C) 4

D) 4

• A) 4

B) 2

C) 3

D) 1

• A) $21x+77y-101=0$

B) $11x-3y+9=0$

C) $31x+77y+101=0$

D) $11x-3y-9=0$

• A) $(4-\sqrt{5})x-(3-2\sqrt{5})y+(2-4\sqrt{5})=0$

B) $(4+\sqrt{5})x-(3+2\sqrt{5})y+(2+4\sqrt{5})=0$

C) $(4+\sqrt{5})x+(3+2\sqrt{5})y+(2+4\sqrt{5})=0$

D) None of these

• A) $y=\pm x$

B) $y=\pm 2x$

C) $y=\pm \frac{1}{\sqrt{2}}x$

D) $y=\pm 3x$

• A) $3x=19$

B) $3y=7$

C) $3x=19$and $3y=7$

D) None of these

• A) $\frac{3x+4y-7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}$

B) $\frac{3x+4y+7}{\sqrt{25}}=\frac{12x+5y+17}{\sqrt{169}}$

C) $\frac{3x+4y+7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}$

D) None of these

• A) $x+y+3=0$

B) $x-y-3=0$

C) $x-y+3=0$

D) $3x+y-7=0$

• A) $\pi /3$

B) $\pi /2$

C) $3\pi /2$

D) $\pi /4$

• A) $\frac{\sqrt{3}}{2}x+y=0$

B) $x+\sqrt{3}y=0$

C) $\sqrt{3}x+y=0$

D) $x+\frac{\sqrt{3}}{2}y=0$