Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 25

MEDIUM

NDA & NA EE

IMPORTANT

Earn 100

Consider the following statements

$I .$ The area of equilateral triangle is a rational number.

$I I .$ In a triangle, the centroid divides the joint of circumcentre and orthocentre in the ratio $1 : 2 .$

$I I I .$ Circumcentre is the only point which is equidistant from all the three vertex of a triangle.

Which of the above statement(s) are correct?

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Important Questions on Straight Line

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 26

The real value(s) of

a

for which the value of

m

satisfying the equation

(a^{2} - 1) m^{2} - (2 a - 3) m + a = 0

gives the slope of a line parallel to the

y

-axis is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 27

The equation of the lines on which the perpendiculars from the origin make

30 °

angle with

X -

axis and which form a triangle of area

\frac{50}{\sqrt{3}}

with axes, are

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 28

What is the equation of line passing through

(0, 1)

and making an angle with the

Y

-axis equal to the inclination of the line

x - y = 4

with

X

-axis?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 29

The equation of a straight line which makes an angle

45 °

with the

X

-axis with

y

-intercept

101

units is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 30

What is the value of

λ,

if the straight line

(2 x + 3 y + 4) + λ (6 x - y + 12) = 0

is parallel to

Y

-axis?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 31

What is the equation of a straight line which passes through

(3, 4)

and the sum of whose

x

and

y

-intercepts is

14

?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 32

What is the equation of the straight line passing through

(5, - 2)

and

(- 4, 7)

?

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 10 - Straight Line>Exercise 1>Q 33

The equation of the line, the reciprocals of whose intercepts on the axes are

m

and

n

, is given by