here,

where n = 1,2,3,....

so, for 6th term n = 6

Mean (*x*) =

= 494/10

= 49.4

The point which divides the line in the ratio m:n externally is given by x =

Substituting the values we get,

x = which is undefined.

It is a false statement other options are open sentences

Since the statement is conditional statement ( if....then).

Since for example n = 4 will give LHS as 16 and RHS as 4! = 1.2.3.4= 24

In the word 'MATHAEMATICS' there are 7 consonants which are M-2 ,,H-1,C-1,S-1, T-2 .Since they have to occur together we treat them as a single unit.

Now this single unit together with the remaining 4 vowels which are A-2,E-1,and I-1 will account for 5 letters.

Now in these 5 letters we have A is repeating twice these can be aarranged in different ways.

Corresponding to each of these arrangements the consonents can be arranged in different ways.

Hence the number of ways it can be arranged is =75600

Applying the completing the square

Comparing the above equation with we get its center as (-1,-3) and radius (r1)=

Comparing the above equation with we get its center as (2,1) and radius (r2)=

So distance(d) between the centers is units

After applying general formula of length of common chord as and putting the values of r1, r2 and d we get length as

.As we know that if a lines makes angles * a *,

** In our case line is X-axis itself which we know makes angle of 0 , 90 , 90 with ** X-axis , Y-axis and Z-axis respectively then direction cosine will be

<cos 0 , cos 90, cos 90>

= < 1 0 0 >