1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2 Let L1 and L2 be the following straight lines.

$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$ and $${L_2}:{{x - 1} \over { - 3}} = {y \over { - 1}} = {{z - 1} \over 1}$$.

Suppose the straight line

$$L:{{x - \alpha } \over l} = {{y - 1} \over m} = {{z - \gamma } \over { - 2}}$$

lies in the plane containing L1 and L2 and passes through the point of intersection of L1 and L2. If the line L bisects the acute angle between the lines L1 and L2, then which of the following statements is/are TRUE?
A
$$\alpha$$ $$-$$ $$\gamma$$ = 3
B
l + m = 2
C
$$\alpha$$ $$-$$ $$\gamma$$ = 1
D
l + m = 0
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1 Three lines $${L_1}:r = \lambda \widehat i$$, $$\lambda$$ $$\in$$ R,

$${L_2}:r = \widehat k + \mu \widehat j$$, $$\mu$$ $$\in$$ R and

$${L_3}:r = \widehat i + \widehat j + v\widehat k$$, v $$\in$$ R are given.

For which point(s) Q on L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are collinear?
A
$$\widehat k$$
B
$$\widehat k$$ + $$\widehat j$$
C
$$\widehat k$$ + $${1 \over 2}$$$$\widehat j$$
D
$$\widehat k$$ $$-$$ $${1 \over 2}$$$$\widehat j$$
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1 Let L1 and L2 denote the lines

$$r = \widehat i + \lambda ( - \widehat i + 2\widehat j + 2\widehat k)$$, $$\lambda$$$$\in$$ R

and $$r = \mu (2\widehat i - \widehat j + 2\widehat k),\,\mu \in R$$

respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of the following options describe(s) L3?
A
$$r = {2 \over 9}(2\widehat i - \widehat j + 2\widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
B
$$r = {1 \over 3}(2\widehat i + k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
C
$$r = {2 \over 9}(4\widehat i - \widehat j + \widehat k) + t(2\widehat i + 2\widehat j - \widehat k),\,t \in R$$
D
r = $$t(2\widehat i + 2\widehat j - \widehat k)$$, $$t \in R$$
4
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1 Let P1 : 2x + y $$-$$ z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?
A
The line of intersection of P1 and P2 has direction ratios 1, 2, $$-$$1
B
The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P1 and P2
C
The acute angle between P1 and P2 is 60$$^\circ$$
D
If P3 is the plane passing through the point (4, 2, $$-$$2) and perpendicular to the line of intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P3 is $${2 \over {\sqrt 3 }}$$
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination