Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Entrances Gallery>Q 39

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IMPORTANT

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$Q, R$ and $S$ are points on the line joining the points $P (a, x)$ and $T (b, y)$ such that $P Q = Q R = R S = S T,$ then $(\frac{5 a + 3 b}{8}, \frac{5 x + 3 y}{8})$ is the mid-point of the line segment

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Important Questions on Cartesian System of Rectangular Coordinates

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 1

If the line segment joining

(2, 3)

and

(- 1, 2)

is divided internally in the ratio

3 : 4

by the line

x + 2 y = k

, then

k

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 2

The polar coordinates of the vertices of a triangle are

(0, 0), (3, \frac{π}{2})

and

(3, \frac{π}{6})

. Then, the triangle is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 3

If the points

(- 2, 0), (- 1, \frac{1}{\sqrt{3}})

and

(\cos θ, \sin θ)

are collinear, then the number of values of

θ \in [0, 2 π]

is

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 4

The incentre of the triangle formed by the axes and the line

\frac{x}{a} + \frac{y}{b} = 1

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 5

The diagonals of a parallelogram

P Q R S

are along the lines

x + 3 y = 4

and

6 x - 2 y = 7

. Then,

P Q R S

must be a

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 6

The coordinates of three consecutive vertices of a parallelogram are

(1, 3), (- 1, 2)

and

(2, 5) .

The coordinates of the fourth vertex are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 7

In a

Δ A B C,

the coordinates of

B

are

(0, 0),

A B = 2, ∠ A B C = \frac{π}{3}

and the middle point of

B C

has the coordinates

(2, 0)

. The centroid of the triangle is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 11 - Cartesian System of Rectangular Coordinates>Work Book Exercise>Q 8

The points

(α, β), (α, δ), (γ, δ)

and

(γ, β)

taken in order, where

α, β, γ, δ

are different real numbers, are