1

JEE Advanced 2020 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-2

Let $$\alpha $$

^{2}+ $$\beta $$^{2}+ $$\gamma $$^{2}$$ \ne $$ 0 and $$\alpha $$ + $$\gamma $$ = 1. Suppose the point (3, 2, $$-$$1) is the mirror image of the point (1, 0, $$-$$1) with respect to the plane $$\alpha $$x + $$\beta $$y + $$\gamma $$z = $$\delta $$. Then which of the following statements is/are TRUE?2

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

+4

-2

Let L

$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$ 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 L

_{1}and L_{2}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 L

_{1}and L_{2}and passes through the point of intersection of L_{1}and L_{2}. If the line L bisects the acute angle between the lines L_{1}and L_{2}, then which of the following statements is/are TRUE?3

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 L

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

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

For which point(s) Q on L

_{2}can we find a point P on L_{1}and a point R on L_{3}so that P, Q and R are collinear?4

JEE Advanced 2019 Paper 1 Offline

MCQ (More than One Correct Answer)

+4

-1

Let L

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

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

respectively. If L

_{1}and L_{2}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 L

_{3}is a line which is perpendicular to both L_{1}and L_{2}and cuts both of them, then which of the following options describe(s) L_{3}?Questions Asked from 3D Geometry (MCQ (Multiple Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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