JEE Main 2021 (Online) 27th August Evening Shift | Straight Lines and Pair of Straight Lines Question 29 | Mathematics

JEE Main 2021 (Online) 27th August Evening Shift

MCQ (Single Correct Answer)

-1

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $$-$$ n = 0 and mn + nl + lm = 0, is :

$${\pi \over 2}$$

$$\pi - {\cos ^{ - 1}}\left( {{4 \over 9}} \right)$$

$${\cos ^{ - 1}}\left( {{8 \over 9}} \right)$$

$${\pi \over 3}$$

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

3x² $$-$$ 2y $$-$$ 6 = 0

3x² + 2y $$-$$ 6 = 0

2x² + 3y $$-$$ 9 = 0

2x² $$-$$ 3y + 9 = 0

JEE Main 2021 (Online) 26th August Morning Shift

MCQ (Single Correct Answer)

-1

Let ABC be a triangle with A($$-$$3, 1) and $$\angle$$ACB = $$\theta$$, 0 < $$\theta$$ < $${\pi \over 2}$$. If the equation of the median through B is 2x + y $$-$$ 3 = 0 and the equation of angle bisector of C is 7x $$-$$ 4y $$-$$ 1 = 0, then tan$$\theta$$ is equal to :

$${1 \over 2}$$

$${3 \over 4}$$

$${4 \over 3}$$

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

The point P (a, b) undergoes the following three transformations successively :

(a) reflection about the line y = x.

(b) translation through 2 units along the positive direction of x-axis.

(c) rotation through angle $${\pi \over 4}$$ about the origin in the anti-clockwise direction.

If the co-ordinates of the final position of the point P are $$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$$, then the value of 2a + b is equal to :