If α 1 , α 2 , α 3 , β 1 , β 2 , β 3 are the values of n for which ∑ r = 0 n - 1 x 2 r is divisible by ∑ r = 0 n - 1 x r , then the triangle having vertices α 1 , β 1 , α 2 , β 2 and α 3 , β 3 cannot be

a right-angled isosceles triangle

HARD

JEE Main/Advanced

IMPORTANT

Earn 100

A light beam, emanating from the point $(3, 10)$ reflects from the straight line $2 x + y - 6 = 0$ and then passes through the point $B (7, 2)$ . Find the equations of the incident and reflected beams.

Important Questions on The Straight Lines

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>EXERCISE ON LEVEL-II>Q 16

The co-ordinates of the extremities

A

and

B

of a rod are

(1, 2)

and

(3, 4)

respectively.

S (0, 0)

is a point of source of light. The rod

A B

is parallel to the wall and is at equal distance from

S

and the wall. If

y - 10 = 3 (x - 3)

is the shadow of

A B

on the wall.

S, A B

and

C D

are coplanar. Find the co-ordinates of

C

and

D

and the length

C D

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>EXERCISE ON LEVEL-II>Q 17

A man at the crossing of two roads

x - 2 y - 4 = 0

and

2 x - y - 4 = 0,

starts walking along the bisector of the acute angle between the roads and after covering a distance

2 km,

reaches the bank of a straight river at right angle to its path. Find the equation of the bank and the coordinates of the point where his path meets the bank.

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>EXERCISE ON LEVEL-II>Q 18

Q

is any point on the line

x - a = 0

. If

A

is the point

(a, 0)

and

Q R

, the bisector of the angle

O Q A

, meets the

x

-axis in

R

, prove that the locus of foot of the perpendicular from

R

O Q

(x - a) \sqrt{(x^{2} + y^{2})} = a |y|

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>Multiple Choice I>Q 1

If the straight line

y = x - 2

rotates about a point, where it cuts the

x

-axis, and becomes perpendicular to the straight line

a x + b y + c = 0

, then its equation is

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>Multiple Choice I>Q 2

\frac{2}{1! 9!} + \frac{2}{3! 7!} + \frac{1}{5! 5!} = \frac{2^{m}}{n!}

, then the orthocenter of the triangle having sides

x - y + 1 = 0

x + y + 3 = 0

and

2 x + 5 y - 2 = 0

is:

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>Multiple Choice I>Q 3

The area of the triangle having vertices

(- 2, 1), (2, 1)

and

(\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2 m} (n! π x)

; where

x

is rational,

\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2 m} (n! π x)

; where

x

is irrational) is :

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>Multiple Choice I>Q 4

α_{1}, α_{2}, α_{3}, β_{1}, β_{2}, β_{3}

are the values of

n

for which

\sum_{r = 0}^{n - 1} x^{2 r}

is divisible by

\sum_{r = 0}^{n - 1} x^{r},

then the triangle having vertices

(α_{1}, β_{1}), (α_{2}, β_{2})

and

(α_{3}, β_{3})

cannot be

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 2 - The Straight Lines>Multiple Choice I>Q 5

f (x + y) = f (x) f (y), \forall x, y \in R

and

f (1) = 2

, then area enclosed by

3 |x| + 2 |y| \leq 8

A light beam, emanating from the point 3,10 reflects from the straight line 2x+y-6=0 and then passes through the point B7,2. Find the equations of the incident and reflected beams.

Important Questions on The Straight Lines

Learn and Prepare for any exam you want !

A light beam, emanating from the point $(3, 10)$ reflects from the straight line $2 x + y - 6 = 0$ and then passes through the point $B (7, 2)$ . Find the equations of the incident and reflected beams.