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JEE Advanced

Explore popular questions from Straight Lines for JEE Advanced. This collection covers Straight Lines previous year JEE Advanced questions hand picked by experienced teachers.

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Straight Lines

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Q 1. The straight lines {tex} x + y = 0,3 x + y - 4 = 0 , x + 3 y - 4 = 0 {/tex} form a triangle which is

isosceles

B

equilateral

C

right angled

D

none of these

Explanation

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Q 2. Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line {tex} L {/tex} has intercepts {tex} p {/tex} and {tex} q , {/tex} then

A

{tex} a ^ { 2 } + b ^ { 2 } = p ^ { 2 } + q ^ { 2 } {/tex}

{tex} \frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = \frac { 1 } { p ^ { 2 } } + \frac { 1 } { q ^ { 2 } } {/tex}

C

{tex} a ^ { 2 } + p ^ { 2 } = b ^ { 2 } + q ^ { 2 } {/tex}

D

{tex} \frac { 1 } { a ^ { 2 } } + \frac { 1 } { p ^ { 2 } } = \frac { 1 } { b ^ { 2 } } + \frac { 1 } { q ^ { 2 } } {/tex}

Explanation


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Q 3. The locus of a variable point whose distance from {tex} ( - 2,0 ) {/tex} is {tex} 2 / 3 {/tex} times its distance from the line {tex} x = - \frac { 9 } { 2 } {/tex} is

ellipse

B

parabola

C

hyperbola

D

none of these

Explanation

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Q 4. The incentre of the triangle with vertices {tex} ( 1 , \sqrt { 3 } ) , ( 0,0 ) {/tex} and {tex} ( 2,0 ) {/tex} is

A

{tex} \left( 1 , \frac { \sqrt { 3 } } { 2 } \right) {/tex}

B

{tex} \left( \frac { 2 } { 3 } , \frac { 1 } { \sqrt { 3 } } \right) {/tex}

C

{tex} \left( \frac { 2 } { 3 } , \frac { \sqrt { 3 } } { 2 } \right) {/tex}

{tex} \left( 1 , \frac { 1 } { \sqrt { 3 } } \right) {/tex}

Explanation

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Q 5. The number of integer values of {tex} m , {/tex} for which the {tex} x {/tex} -coordinate of the point of intersection of the lines {tex} 3 x + 4 y = 9 {/tex} and {tex} y = m x + 1 {/tex} is also an integer, is

2

B

0

C

4

D

1

Explanation

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Q 6. Let {tex} 0 < \alpha < \frac { \pi } { 2 } {/tex} be fixed angle. If {tex} P = ( \cos \theta , \sin \theta ) {/tex} and {tex} Q = ( \cos ( \alpha - \theta ) , \sin ( \alpha - \theta ) ) {/tex} then {tex} Q {/tex} is obtained from {tex} P {/tex} by

A

clockwise rotation around origin through an angle {tex} \alpha {/tex}

B

anticlockwise rotation around origin through an angle {tex} \alpha {/tex}

C

reflection in the line through origin with slope tan {tex} \alpha {/tex}

reflection in the line through origin with slope tan {tex} ( \alpha / 2 ) {/tex}

Explanation

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Q 7. Let {tex} P = ( - 1,0 ) , Q = ( 0,0 ) {/tex} and {tex} \mathrm { R } = ( 3,3 \sqrt { 3 } ) {/tex} be three points. Then the equation of the bisector of the angle {tex} P Q R {/tex} is

A

{tex} \frac { \sqrt { 3 } } { 2 } x + y = 0 {/tex}

B

{tex} x + \sqrt { 3 } y = 0 {/tex}

{tex} \sqrt { 3 } x + y = 0 {/tex}

D

{tex} x + \frac { \sqrt { 3 } } { 2 } y = 0 {/tex}

Explanation

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Q 8. Orthocentre of triangle with vertices {tex} ( 0,0 ) , ( 3,4 ) {/tex} and {tex} ( 4,0 ) {/tex} is

A

{tex} \left( 3 , \frac { 5 } { 4 } \right) {/tex}

B

{tex} ( 3,12 ) {/tex}

{tex} \left( 3 , \frac { 3 } { 4 } \right) {/tex}

D

{tex} ( 3,9 ) {/tex}

Explanation

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Q 9. If the bisectors of the lines {tex} x ^ { 2 } - 2 p x y - y ^ { 2 } = 0 {/tex} be {tex} x ^ { 2 } - 2 q x y {/tex} {tex} - y ^ { 2 } = 0 , {/tex} then

{tex} p q + 1 = 0 {/tex}

B

{tex} p q - 1 = 0 {/tex}

C

{tex} p + q = 0 {/tex}

D

{tex} p - q = 0 {/tex}

Explanation


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Q 10. The angle between the pair of straight lines {tex} y ^ { 2 } \sin ^ { 2 } \theta - x y \sin ^ { 2 } \theta {/tex} {tex} + x ^ { 2 } \left( \cos ^ { 2 } \theta - 1 \right) = 1 {/tex} is

A

{tex} \frac { \pi } { 3 } {/tex}

B

{tex} \frac { \pi } { 4 } {/tex}

C

{tex} \frac { 2 \pi } { 3 } {/tex}

None of these

Explanation