Question 966363
Q.1, IF A AND B ARE SQUARE AND ARE COMMUTATIVE THEN AB IS EQUAL BA ? TRUE OR
FALSE?
<pre>
If A and B are elements of a set with an operation @ that is commutative 
then an operation is commutative then A@B = B@A.  If no symbol for the
operation is used then AB = BA.
</pre>
Q.2,IN HOW MANY WAYS the LETTERs in the word "LEARN" CAN BE ARRANGED, IF VOWELS
OCCUPY ODD PLACES? 12 OR 18 OR 26 OR NONE OF ABOVE ?
<pre>
"LEARN" has 2 vowels, A and E, and 3 consonants L, R, and N. If V represents a
vowel and C represents a consonant, then there are 3 basic forms in which an
arrangement can have vowels in odd positions, where V represents a vowel and
C represents a consonant: 

VCVCC, VCCCV, and CCVCV

1. We choose the form in 3 ways.
2. We choose the letter for the left-most vowel in either of the 2 ways.
3. We choose the letter for the right-most vowel the only 1 remaining way.
4. We choose the letmost consonant in 3 ways.
5. We choose the second consonant in either of the 2 remaining ways.
6. We choose the letter for the right-most consonant the only 1 remaining way.
  
That's 3*2*1*3*2*1 = 36 ways.
</pre>
Q.3 ,GIVEN A STRAIT LINE Y=3X+2, FIND THE AREA  UNDER THE LINE BETWEEN X=2 TO
X=5?  75 OR 35 OR 75/2 or 35/2 ?
<pre>
We draw the graph:

{{{drawing(1200/7,400,-2,7,-2,19,line(2,0,2,8), line(5,0,5,17), line(2,8,5,17),
green(line(-7,-19,2,8),line(5,17,11,35)),line(2,0,5,0),

graph(1200/7,400,-2,7,-2,19)

  )}}}

The figure is a "trapezoid" in the US, or a "trapezium" in the UK.  
Its area is:

the average of the lengths of the two parallel sides multiplied by the 
perpendicular distance between the two parallel sides.

The average of the two parallel sides is {{{(8+17)/2=25/2}}}
The perpendicular distance between the two parallel sides is 3.
So the area is {{{expr(25/2)*(3) = 75/2}}}.

Edwin</pre>