1
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$x+y+a z=b$$

$$2 x+5 y+2 z=6$$

$$x+2 y+3 z=3$$

has infinitely many solutions, then $$2 a+3 b$$ is equal to :

A
28
B
25
C
20
D
23
2
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The straight lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$ pass through the origin and trisect the line segment of the line L : $$9 x+5 y=45$$ between the axes. If $$\mathrm{m}_{1}$$ and $$\mathrm{m}_{2}$$ are the slopes of the lines $$\mathrm{l_{1}}$$ and $$\mathrm{l_{2}}$$, then the point of intersection of the line $$\mathrm{y=\left(m_{1}+m_{2}\right)}x$$ with L lies on :

A
$$6 x-y=15$$
B
$$6 x+y=10$$
C
$$\mathrm{y}-x=5$$
D
$$y-2 x=5$$
3
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the equation of the plane passing through the line of intersection of the planes $$2 x-y+z=3,4 x-3 y+5 z+9=0$$ and parallel to the line $$\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}$$ is $$a x+b y+c z+6=0$$, then $$a+b+c$$ is equal to :

A
13
B
15
C
14
D
12
4
JEE Main 2023 (Online) 6th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

One vertex of a rectangular parallelopiped is at the origin $$\mathrm{O}$$ and the lengths of its edges along $$x, y$$ and $$z$$ axes are $$3,4$$ and $$5$$ units respectively. Let $$\mathrm{P}$$ be the vertex $$(3,4,5)$$. Then the shortest distance between the diagonal OP and an edge parallel to $$\mathrm{z}$$ axis, not passing through $$\mathrm{O}$$ or $$\mathrm{P}$$ is :

A
$$\frac{12}{\sqrt{5}}$$
B
$$12 \sqrt{5}$$
C
$$\frac{12}{5}$$
D
$$\frac{12}{5 \sqrt{5}}$$
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