# JEE Main & Advanced Mathematics Straight Line Question Bank

### done Distance between two lines, Perpendicular distance of the line from a point Position of point w.r.t. line

• A) $\left[ \frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]$

B) $\left[ \frac{b}{a}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]$

C) $\left[ \frac{a}{b}(a\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]$

D) None of these

• A) $\left| \frac{{{a}^{2}}-ab+{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|$

B) $\left| \frac{{{b}^{2}}-ab-{{a}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|$

C) $\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|$

D) None of these

• A) 3/2

B) 3/10

C) 6

D) None of these

• A) $\frac{130}{17\sqrt{29}}$

B) $\frac{13}{7\sqrt{29}}$

C) $\frac{130}{17}$

D) None of these

• A) $(3,\,1),(-7,\,11)$

B) $(3,\,1),(7,\,11)$

C) $(-3,\,1),(-7,\,11)$

D) $(1,\,3),(-7,\,11)$

• A) ${{a}^{2}}+{{b}^{2}}={{p}^{2}}$

B) ${{a}^{2}}+{{b}^{2}}=\frac{1}{{{p}^{2}}}$

C) $\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{{{p}^{2}}}$

D) $\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}$

• A) $\frac{x'y''+x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}$

B) $\frac{x'y''-x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}$

C) $\frac{x'x''+y'y''}{\sqrt{{{(x''+x')}^{2}}+{{(y''+y')}^{2}}}}$

D) $\frac{x'x''+y'y''}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}$

• A) k

B) $2k$

C) ${{k}^{2}}$

D) $2{{k}^{2}}$

• A) $\frac{7}{13}$

B) $\frac{12}{13}$

C) $\frac{5}{13}$

D) $\frac{1}{13}$

• A) 6

B) 7

C) 5

D) 8

• A) 4

B) 5

C) 3

D) 1

• A) $\frac{7}{2}$

B) 4

C) $\frac{7}{10}$

D) None of these

• A) $4/\sqrt{15}$

B) $2/\sqrt{15}$

C) $4/3\sqrt{3}$

D) $1/\sqrt{5}$

• A) ${{a}^{2}}$

B) ${{b}^{2}}$

C) ${{a}^{2}}+{{b}^{2}}$

D) ${{a}^{2}}-{{b}^{2}}$

• A) $7:3$

B) 3 : 7

C) $2:3$

D) None of these

• A) A. P.

B) G.P.

C) H. P.

D) None of these

• A) $2\frac{2}{5}$

B) $3\frac{1}{5}$

C) $4\frac{2}{5}$

D) $3\frac{2}{5}$

• A) $\frac{1}{\sqrt{52}}$

B) $\frac{11}{\sqrt{52}}$

C) $\frac{4}{\sqrt{13}}$

D) $\frac{6}{\sqrt{13}}$

• A) (4, 7)

B) (7, 4)

C) (5, 7)

D) (-5, -3)

• A) $5\sqrt{2}$

B) $2\sqrt{5}$

C) $3\sqrt{5}$

D) $5\sqrt{3}$

• A) $\sqrt{2}$

B) $\frac{5}{\sqrt{2}}$

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

D) 6

• A) $\frac{35}{\sqrt{34}}$

B) $\frac{1}{3\sqrt{34}}$

C) $\frac{35}{3\sqrt{34}}$

D) $\frac{35}{2\sqrt{34}}$

• A) $\frac{2}{5}$

B) $\frac{12}{5}$

C) $\frac{5}{12}$

D) $\frac{3}{5}$

• A) Point lies on the same side of the lines

B) Point lies on the different sides of the line

C) Point lies on one of the line

D) None of these

• A) $c\cos \alpha$

B) $c{{\sin }^{2}}\alpha$

C) $c{{\sec }^{2}}\alpha$

D) $c{{\cos }^{2}}\alpha$

• A) $5\sqrt{2}$

B) $2\sqrt{5}$

C) $3\sqrt{5}$

D) $5\sqrt{3}$

• A) $\frac{\sqrt{5}}{2}$

B) $\frac{2}{5}$

C) $\frac{2}{\sqrt{5}}$

D) $\frac{1}{\sqrt{5}}$

• A) 1 : 2

B) 2 : 1

C) 2 : 3

D) 3 : 4

• A) $\frac{7}{13}$

B) $\frac{12}{13}$

C) $\frac{5}{13}$

D) $\frac{1}{13}$

• A) $(1,\,-1)$

B) $(1,\,1)$

C) $(0,0)$

D) $(0,\,1)$

• A) $\sqrt{3/2}$

B) $\sqrt{2}$

C) $\sqrt{2/3}$

D) None of these

• A) $(0,\,\,\pi /2)$

B) $(0,\,\pi )$

C) $(\pi /4,\pi /2)$

D) $(0,\,\,\pi /4)$

• A) (0, -1) and (0, 0)

B) (4, -3) and (0, 1)

C) (-3, -4) and (1, 2)

D) (-1, -1) and (3, 7)

• A) $20\sqrt{2}\beta =11\alpha$

B) $20\sqrt{2}\alpha =11\beta$

C) $11\sqrt{2}\beta =20\alpha$

D) None of these

• A) Below both the lines

B) Above both the lines

C) In between the lines

D) None of these

• A) On the same side of the line

B) On different side of the line

C) One point on the line and the other outside the line

D) Both point on the line