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?
A
$$\alpha$$ + $$\beta$$ = 2
B
$$\delta$$ $$-$$ $$\gamma$$ = 3
C
$$\delta$$ + $$\beta$$ = 4
D
$$\alpha$$ + $$\beta$$ + $$\gamma$$ = $$\delta$$
2
JEE Advanced 2020 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let a and b be positive real numbers. Suppose $$PQ = a\widehat i + b\widehat j$$ and $$PS = a\widehat i - b\widehat j$$ are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of $$w = \widehat i + \widehat j$$ along PQ and PS, respectively. If |u| + |v| = |w| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?
A
a + b = 4
B
a $$-$$ b = 2
C
The length of the diagonal PR of the parallelogram PQRS is 4
D
w is an angle bisector of the vectors PQ and PS
3
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
4
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
$$\widehat k$$ $$-$$ $${1 \over 2}$$$$\widehat j$$
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