`1/3 [ n - 1/9 (1 - 1/(10)^n ) ]`
`1/3 [ n - 2/9 (1 - 1/(10)^n ) ]`
`1/3 [ n - 1/3 (1 - 1/(10)^n ) ]`
`1/3 [ n - 1/9 (1 + 1/(10)^n ) ]`
`mn`
`m+n`
`2(m+n)`
`-(m+n)`
AP
GP
HP
None of the above
`5`
`7`
`8`
`15`
`2475`
`2530`
`4905`
`5049`
`2^n - n - 1`
`1 - 2^(-n)`
`2^(-n) + n - 1`
`2^n - 1`
one
two
four
Infinitely many
8/5
9/5
2
11/5
-4
-6
-8
-10
in AP only
in GP only
in both AP and GP
Neither in AP nor in GP
in AP only
in GP only
in both AP and GP
Neither in AP nor in GP
one
two
three
Infinitely many
160° only
195° only
Either 160° or 195°
Neither 160° nor 195°
8
9
10
11
`1`
`3`
`6`
`9`
cannot be less than 1
is greater than- 8
is less than- 8
must be greater than 8
`5/9 [ n - 2/9 (1- 1/(10)^n)]`
`1/9 [ 5 - 2/9 (1- 1/(10)^n)]`
`1/9 [ n - 5/9 (1- 1/(10)^n)]`
`5/9 [ n - 1/9 (1- 1/(10)^n)]`
`270`
`735`
`1409`
`1470`
`AP`
`GP`
`HP`
None of these
`(n(n -1))/ sqrt(2)`
`sqrt(2)(n -1)`
`(n(n +1))/ sqrt(2)`
`(n(n -1))/ (2)`
Harmonic mean
Geometric mean
Median
Mode
`G_1G_2`
ln `(G_1G_2)`
`G_1/G_2`
ln `(G_1/G_2)`
` (n(n+1))/2`
` (n(n+1)^2)/2`
` (n(n+1)^2)/4`
` (n^2(n+1)^2)/4`
`5`
`2`
`1`
`0`
`2 : 1`
`3 : 1`
`4 : 1`
`5: 1`
`-1 < x < 1`
`- oo < x < 1`
`1 < x < oo`
None of these
`-1`
`0`
`1`
Cannot be determined due to insufficient data
`AP`
`GP`
`HP`
Arithmetico-geometric progression
in `AP` only
in `GP` only
in both `AP` and `GP`
neither in `AP` nor in `GP`
` (3sqrt(3) (sqrt(3) + 1))/2`
` (3sqrt(3) (sqrt(3) - 1))/2`
`(3(sqrt(3) + 1))/2`
`(3(sqrt(3) - 1))/2`
`HP`
`AP`
`GP`
None of these
`1`
`1.01`
`1.001`
`1.1`
The first terms must be negative
The common difference must be negative
Either the first term or the common difference is negative but not both
Both the first term and the common difference are negative
`1`
`2`
`3`
`4`
`6` and `3`
`9` and `5`
`12 ` and `7`
`3` and `1`
Only I
Only I
Both I and II
Neither I nor II
`(89)/(128)`
`(57)/(384)`
`(85)/(128)`
None of these
`2`
`3`
`4`
`5`
`1`
`1`
`3`
`4`
`2^(n//2)`
`2^((n+ 1)//2)`
`2^(n+ 1) - 1`
`2^(n - 1)`
`17//2`
`33//2`
`11`
`187//2`
`4`
`9`
`12.5`
`25`
`2n - 1`
`2n + 1`
`4n - 3`
None of these
AP
GP
HP
None of these
1
3
5
Cannot be determined
`5`
`6`
`7`
`8`
`p = q != r`
`p != q != r`
`p != q = r`
`p = q = r`
`1//2`
`3//2`
`2`
`2//3`
`3`
`4`
`8`
`10`
`180`
`186`
`196`
`206`