# JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank

### done Critical Thinking

• A) ${{x}^{2}}+{{y}^{2}}-ax-by=0$

B) ${{x}^{2}}+{{y}^{2}}+ax+by=0$

C) ${{x}^{2}}+{{y}^{2}}-2ax-2by=0$

D) None of these

• A) $(0,0)$

B) $\left( \frac{1}{2},\frac{1}{2} \right)$

C) $\left( \frac{1}{3},\frac{1}{3} \right)$

D) $\left( \frac{1}{4},\frac{1}{4} \right)$

• A) $\frac{ab}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}$

B) $\frac{bc}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}$

C) $\frac{ca}{\sqrt{({{a}^{2}}+{{b}^{2}})+4{{h}^{2}}}}$

D) $\frac{c}{\sqrt{{{(a-b)}^{2}}+4{{h}^{2}}}}$

• A) $x+4y=13$and $y=4x-7$

B) $4x+y=13$and $4y=x-7$

C) $4x+y=13$and $y=4x-7$

D) $y-4x=13$and $y+4x=7$

• A) $\frac{27}{4}sq$. units

B) $27sq.$units

C) $\frac{27}{2}sq.$ units

D) None of these

• A) ${{H}^{2}}$

B) $-{{H}^{2}}$

C) $2{{H}^{2}}$

D) $4{{H}^{2}}$

• A) $\frac{{{n}^{2}}}{2|lm|}$

B) $\frac{{{n}^{2}}}{|lm|}$

C) $\frac{n}{2|lm|}$

D) $\frac{{{n}^{2}}}{4|lm|}$

• A) Straight line

B) Pair of straight lines

C) Circle

D) Ellipse

• A) $\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab-{{h}^{2}}}$

B) $\frac{c(a-b)+{{f}^{2}}+{{g}^{2}}}{\sqrt{ab-{{h}^{2}}}}$

C) $\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab+{{h}^{2}}}$

D) None of these

• A) ${{x}^{2}}+2xy\sec 2\alpha +{{y}^{2}}=0$

B) ${{x}^{2}}+2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0$

C) ${{x}^{2}}-2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0$

D) ${{x}^{2}}-2xy\sec 2\alpha +{{y}^{2}}=0$

• A) $pq+1=0$

B) $pq-1=0$

C) $p+q=0$

D) $p-q=0$

• A) $\frac{\pi }{3}$

B) $\frac{\pi }{4}$

C) $\frac{2\pi }{3}$

D) None of these

• A) Two values of $a$

B) $\forall a$

C) For one value of $a$

D) For no value of $a$

• A) A right angled triangle

B) An isosceles triangle

C) An equilateral triangle

D) None of these

• A) 3

B) 9

C) 10

D) 100

• A) $a+b=2|h|$

B) $a+b=-2h$

C) $a-b=2|h|$

D) ${{(a-b)}^{2}}=4{{h}^{2}}$

• A) ${{a}^{2}}({{m}^{2}}+1)={{c}^{2}}$

B) ${{a}^{2}}({{m}^{2}}-1)={{c}^{2}}$

C) ${{a}^{2}}({{m}^{2}}+1)={{c}^{2}}$

D) ${{a}^{2}}({{m}^{2}}-1)=2{{c}^{2}}$

• A) ${{\tan }^{-1}}\left( \frac{3}{2\sqrt{2}} \right)$

B) ${{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)$

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

D) ${{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)$

• A) $(am+hl)x=(bl+hm)y$

B) $(am-hl)x=(bl-hm)y$

C) $(am-hl)x=(bl+hm)y$

D) None of these

• A) $3{{a}^{2}}+10ab+3{{b}^{2}}=0$

B) $3{{a}^{2}}+2ab+3{{b}^{2}}=0$

C) $3{{a}^{2}}-10ab+3{{b}^{2}}=0$

D) $3{{a}^{2}}-2ab+3{{b}^{2}}=0$

• A) ${{y}^{2}}-4y-21=0$

B) ${{y}^{2}}+4y-21=0$

C) ${{y}^{2}}-4y+21=0$

D) ${{y}^{2}}+4y+21=0$

• A) $(b+d)(ad+be)+{{(e-a)}^{2}}(a+c+e)=0$

B) $(b+d)(ad+be)+{{(e+a)}^{2}}(a+c+e)=0$

C) $(b-d)(ad-be)+{{(e-a)}^{2}}(a+c+e)=0$

D) $(b-d)(ad-be)+{{(e+a)}^{2}}(a+c+e)=0$

• A) ${{f}^{2}}+{{g}^{2}}=c(b-a)$

B) ${{f}^{4}}+{{g}^{4}}=c(b{{f}^{2}}+a{{g}^{2}})$

C) ${{f}^{4}}-{{g}^{4}}=c(b{{f}^{2}}-a{{g}^{2}})$

D) ${{f}^{2}}+{{g}^{2}}=a{{f}^{2}}+b{{g}^{2}}$

• A) (0, 0)

B) (-2, - 2)

C) (-1, -1)

D) (-1, -2)