Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
We need to find the expressions whose simplified form is a rational number.
Rational number: If a number is defined in the form of p/q where p and q are integers and q≠0, then it is called a rational number.
For example: 0,2, 4.3 etc.
Irrational number: If a number can not defined in the form of p/q, where p and q are integers and q≠0, then it is called an irrational number.
First expression is

12 is a rational number.
Second expression is

is an irrational number.
Third expression is

21 is a rational number.
Fourth expression is

5 is a rational number.
Therefore, the correct options are 1, 3 and 4.
No
If two planes intersect each other, the intersection will always be a line. where r 0 r_0 r0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.
Option c: x=6 is a true solution and x=-6 is an extraneous solution.
Explanation:
The equation is 
Dividing both sides of the equation by 2, we get,

Simplifying,

Since, we know by the logarithmic definition, if
, then 
Using this definition, we have,

Hence, 
Now, let us verify if
is the solution.
Substitute
in the equation
to see whether both sides of the equation are true.
We have,

Using the log rule, 
We have,

Hence, both sides of the equation are equal.
Thus,
is the true solution.