1
JEE Advanced 2023 Paper 1 Online
MCQ (Single Correct Answer)
+3
-1
Let $\ell_1$ and $\ell_2$ be the lines $\vec{r}_1=\lambda(\hat{i}+\hat{j}+\hat{k})$ and $\vec{r}_2=(\hat{j}-\hat{k})+\mu(\hat{i}+\hat{k})$, respectively. Let $X$ be the set of all the planes $H$ that contain the line $\ell_1$. For a plane $H$, let $d(H)$ denote the smallest possible distance between the points of $\ell_2$ and $H$. Let $H_0$ be a plane in $X$ for which $d\left(H_0\right)$ is the maximum value of $d(H)$ as $H$ varies over all planes in $X$.

Match each entry in List-I to the correct entries in List-II.

List - I List - II
(P) The value of $d\left(H_0\right)$ is (1) $\sqrt{3}$
(Q) The distance of the point $(0,1,2)$ from $H_0$ is (2) $\frac{1}{\sqrt{3}}$
(R) The distance of origin from $H_0$ is (3) 0
(S) The distance of origin from the point of intersection of planes $y=z, x=1$ and $H_0$ is (4) $\sqrt{2}$
(5) $\frac{1}{\sqrt{2}}$

The correct option is:
A
$$(P) \rightarrow(2) \quad(Q) \rightarrow(4) \quad(R) \rightarrow(5) \quad(S) \rightarrow(1)$$
B
$$(P) \rightarrow(5) \quad(Q) \rightarrow(4) \quad(R) \rightarrow(3) \quad(S) \rightarrow(1)$$
C
$$(P) \rightarrow(2) \quad(Q) \rightarrow(1) \quad(R) \rightarrow(3) \quad(S) \rightarrow(2)$$
D
$$(P) \rightarrow(5) \quad(Q) \rightarrow(1) \quad(R) \rightarrow(4) \quad(S) \rightarrow(2)$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $$-$$ 2z = 5 and 3x $$-$$ 6y $$-$$ 2z = 7 is
A
14x + 2y $$-$$ 15z = 1
B
$$-$$14x + 2y + 15z = 3
C
14x $$-$$ 2y + 15z = 27
D
14x + 2y + 15z = 31
3
JEE Advanced 2016 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Let $$P$$ be the image of the point $$(3,1,7)$$ with respect to the plane $$x-y+z=3.$$ Then the equation of the plane passing through $$P$$ and containing the straight line $${x \over 1} = {y \over 2} = {z \over 1}$$ is
A
$$x+y-3z=0$$
B
$$3x+z=0$$
C
$$x-4y+7z=0$$
D
$$2x-y=0$$
4
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Consider the lines

$${L_1}:{{x - 1} \over 2} = {y \over { - 1}} = {{z + 3} \over 1},{L_2} : {{x - 4} \over 1} = {{y + 3} \over 1} = {{z + 3} \over 2}$$

and the planes $${P_1}:7x + y + 2z = 3,{P_2} = 3x + 5y - 6z = 4.$$ Let $$ax+by+cz=d$$ be the equation of the plane passing through the point of intersection of lines $${L_1}$$ and $${L_2},$$ and perpendicular to planes $${P_1}$$ and $${P_2}.$$

Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:
List $$I$$
(P.) $$a=$$
(Q.) $$b=$$
(R.) $$c=$$
(S.) $$d=$$

List $$II$$
(1.) $$13$$
(2.) $$-3$$
(3.) $$1$$
(4.) $$-2$$

A
$$P = 3,Q = 2,R = 4,S = 1$$
B
$$P = 1,Q = 3,R = 4,S = 2$$
C
$$P = 3,Q = 2,R = 1,S = 4$$
D
$$P = 2,Q = 4,R = 1,S = 3$$
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