1

JEE Advanced 2024 Paper 1 Online

MCQ (More than One Correct Answer)

+4

-2

Let $\mathbb{R}^3$ denote the three-dimensional space. Take two points $P=(1,2,3)$ and $Q=(4,2,7)$. Let $\operatorname{dist}(X, Y)$ denote the distance between two points $X$ and $Y$ in $\mathbb{R}^3$. Let

$$ \begin{gathered} S=\left\{X \in \mathbb{R}^3:(\operatorname{dist}(X, P))^2-(\operatorname{dist}(X, Q))^2=50\right\} \text { and } \\ T=\left\{Y \in \mathbb{R}^3:(\operatorname{dist}(Y, Q))^2-(\operatorname{dist}(Y, P))^2=50\right\} . \end{gathered} $$

Then which of the following statements is (are) TRUE?

2

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 $$P_{2}$$ ?

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

Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on $$P_{1}$$ and $$P_{2}$$ ?

3

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 ?

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

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 ?

4

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?Questions Asked from 3D Geometry (MCQ (Multiple Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2024 Paper 2 Online (1)
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JEE Advanced 2020 Paper 2 Offline (1)
JEE Advanced 2020 Paper 1 Offline (1)
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JEE Advanced 2015 Paper 1 Offline (2)
JEE Advanced 2014 Paper 1 Offline (1)
JEE Advanced 2013 Paper 2 Offline (1)
JEE Advanced 2013 Paper 1 Offline (1)
IIT-JEE 2012 Paper 2 Offline (1)
IIT-JEE 2006 (1)

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