Q.1, IF A AND B ARE SQUARE AND ARE COMMUTATIVE THEN AB IS EQUAL BA ? TRUE OR
FALSE?
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.
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 ?
"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.
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 ?
We draw the graph:
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 
The perpendicular distance between the two parallel sides is 3.
So the area is 
.
Edwin
