JEE Main 2019 (Online) 12th April Evening Slot | Straight Lines and Pair of Straight Lines Question 87 | Mathematics

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of 60^o with the line x + y = 0. Then an equation of the line L is :

x + $$\sqrt 3 $$y = 8

$$\sqrt 3 $$x + y = 8

( $$\sqrt 3 $$ + 1)x + ( $$\sqrt 3 $$ – 1)y = 8 $$\sqrt 2 $$

( $$\sqrt 3 $$ - 1)x + ( $$\sqrt 3 $$ + 1)y = 8 $$\sqrt 2 $$

JEE Main 2019 (Online) 10th April Evening Slot

MCQ (Single Correct Answer)

-1

Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance $${3 \over 5}$$ from the origin. Then which one of the following points lies on any of these lines ?

$$\left( {{1 \over 4}, - {1 \over 3}} \right)$$

$$\left( { - {1 \over 4},{2 \over 3}} \right)$$

$$\left( { - {1 \over 4}, - {2 \over 3}} \right)$$

$$\left( {{1 \over 4},{1 \over 3}} \right)$$

JEE Main 2019 (Online) 10th April Morning Slot

MCQ (Single Correct Answer)

-1

The region represented by| x – y | $$ \le $$ 2 and | x + y| $$ \le $$ 2 is bounded by a :

rhombus of area 8$$\sqrt 2 $$ sq. units

square of side length 2$$\sqrt 2 $$ units

square of area 16 sq. units

rhombus of side length 2 units

JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

If the two lines x + (a – 1) y = 1 and 2x + a²y = 1 (a$$ \in $$R – {0, 1}) are perpendicular, then the distance of their point of intersection from the origin is :

$${2 \over \sqrt5}$$

$${\sqrt2 \over 5}$$

$${2 \over 5}$$

$$\sqrt{2 \over 5}$$

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