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**Hint:**The arrows on the magnetic field lines simply indicate the orientation of the magnetic field, pointing to the South Pole. Right hand thumb rule states that if the pointer finger points in the direction the positive charge is moving, and then the middle finger in the direction of the magnetic field and the thumb points in the direction of the magnetic force pushing on the moving charge.

**Complete answer:**

Magnetic field lines are closed loops that have a definite direction and magnitude at every point along the curve of that loop. These fields always follow the laws of vector addition. This now means that magnetic fields are vector quantities. Since we now have a vector on our hands, we must have some way to represent its strength in a region and also its direction!

For strength, we use the number of lines in an area. The more concentrated the lines are in an area, the stronger the field is said to be in that area.

For direction, if we have a bar magnet marked with a north pole and south pole, then the field flows out from the north and back into the bar from the south. But if no such help is present, then we simply use an arrow mark along the line to show the direction of the field (along the line in the direction of the arrow).

Right hand thumb rule states that if the pointer finger points in the direction the positive charge is moving, and then the middle finger in the direction of the magnetic field and the thumb points in the direction of the magnetic force pushing on the moving charge.

In the given figure, arrow A shows the direction of magnetic force experienced by a current carrying wire in a perpendicular magnetic field and it is given by Fleming's left hand rule.

Arrow B shows the direction of magnetic field lines, from North Pole to South Pole.

Arrow C shows the direction of conventional current from positive terminal to negative terminal of the battery.

Arrow D shows the direction of repulsion force exerted by wire in circuit X to the wire of Y due to the fact that direction of current in both parallel wires is opposite.

Arrows E shows the direction of magnetic field lines due to current carrying wire of circuit X which is given by right hand thumb rule.

Hence, the arrows which give the direction of a magnetic field line are B and E.

**Hence the correct answer is Option E.**

**Note:**

The properties of the magnetic field lines are given below.

-They always form closed loops.

-No two magnetic lines intersect.

-Outside they seem to travel from north to south and inside south to north.

-It is a vector quantity.

-The magnetic field lines are crowded near the pole where the field is strong and far from the magnet where the field is weak.

-In case the field lines are parallel and equidistant, they represent a uniform magnetic field. -The Earth's magnetic field is a uniform limited space.

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