1
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Let $$S$$ be the reflection of a point $$Q$$ with respect to the plane given by

$$\vec{r}=-(t+p) \hat{\imath}+t \hat{\jmath}+(1+p) \hat{k}$$

where $$t, p$$ are real parameters and $$\hat{\imath}, \hat{\jmath}, \hat{k}$$ are the unit vectors along the three positive coordinate axes. If the position vectors of $$Q$$ and $$S$$ are $$10 \hat{\imath}+15 \hat{\jmath}+20 \hat{k}$$ and $$\alpha \hat{\imath}+\beta \hat{\jmath}+\gamma \hat{k}$$ respectively, then which of the following is/are TRUE ?
A
$$3(\alpha+\beta)=-101$$
B
$$3(\beta+\gamma)=-71$$
C
$$3(\gamma+\alpha)=-86$$
D
$$3(\alpha+\beta+\gamma)=-121$$
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Let O be the origin and $$\overrightarrow {OA} = 2\widehat i + 2\widehat j + \widehat k$$ and $$\overrightarrow {OB} = \widehat i - 2\widehat j + 2\widehat k$$ and $$\overrightarrow {OC} = {1 \over 2}\left( {\overrightarrow {OB} - \lambda \overrightarrow {OA} } \right)$$ for some $$\lambda$$ > 0. If $$\left| {\overrightarrow {OB} \times \overrightarrow {OC} } \right| = {9 \over 2}$$, then which of the following statements is (are) TRUE?
A
Projection of $$\overrightarrow {OC}$$ on $$\overrightarrow {OA}$$ is $$- {3 \over 2}$$
B
Area of the triangle OAB is $${9 \over 2}$$
C
Area of the triangle ABC is $${9 \over 2}$$
D
The acute angle between the diagonals of the parallelogram with adjacent sides $${\overrightarrow {OA} }$$ and $${\overrightarrow {OC} }$$ is $${\pi \over 3}$$
3
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
$$\alpha$$ + $$\beta$$ + $$\gamma$$ = $$\delta$$
4
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
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