1
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language
Let the plane $P$ contain the line $2 x+y-z-3=0=5 x-3 y+4 z+9$ and be

parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then the distance of the point

$\mathrm{A}(8,-1,-19)$ from the plane $\mathrm{P}$ measured parallel to the line $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$

is equal to ______________.
Your input ____
2
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language
If the line $x=y=z$ intersects the line

$x \sin A+y \sin B+z \sin C-18=0=x \sin 2 A+y \sin 2 B+z \sin 2 C-9$,

where $A, B, C$ are the angles of a triangle $A B C$, then $80\left(\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}\right)$

is equal to ______________.
Your input ____
3
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Change Language
A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is ___________.
Your input ____
4
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
Change Language
Let an ellipse with centre $(1,0)$ and latus rectum of length $\frac{1}{2}$ have its major axis along $\mathrm{x}$-axis. If its minor axis subtends an angle $60^{\circ}$ at the foci, then the square of the sum of the lengths of its minor and major axes is equal to ____________.
Your input ____
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