1
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Let $$P_{1}$$ and $$P_{2}$$ be two planes given by

\begin{aligned} &P_{1}: 10 x+15 y+12 z-60=0 \\\\ &P_{2}:-2 x+5 y+4 z-20=0 \end{aligned}

Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $$P_{1}$$ and $$P_{2}$$ ?
A
$$\frac{x-1}{0}=\frac{y-1}{0}=\frac{z-1}{5}$$
B
$$\frac{x-6}{-5}=\frac{y}{2}=\frac{z}{3}$$
C
$$\frac{x}{-2}=\frac{y-4}{5}=\frac{z}{4}$$
D
$$\frac{x}{1}=\frac{y-4}{-2}=\frac{z}{3}$$
2
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
$$3(\alpha+\beta+\gamma)=-121$$
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 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
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