`mn`
`m+n`
`2(m+n)`
`-(m+n)`
`1`
`2`
`3`
`4`
`5`
`7`
`8`
`15`
`2475`
`2530`
`4905`
`5049`
one
two
three
Infinitely many
`270`
`735`
`1409`
`1470`
`(n(n -1))/ sqrt(2)`
`sqrt(2)(n -1)`
`(n(n +1))/ sqrt(2)`
`(n(n -1))/ (2)`
`1//(mn)`
`m//n`
`n//m`
`1`
`-15`
`-3`
`9`
`-4`
`(n(n -1))/ sqrt(2)`
`sqrt(2)(n -1)`
`(n(n +1))/ sqrt(2)`
`(n(n -1))/ (2)`
` - 1/2`
`- 5/6`
`- 3/2`
`1`
`23/20`
`13/22`
`43/20`
`33/20`
AP
GP
HP
None of these
`Rs. 50`
`Rs. 51`
`Rs. 105`
`Rs. 110`
`6729`
`8712`
`8729`
`9276`
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
`2`
`3`
`4`
`5`
`2n - 1`
`2n + 1`
`4n - 3`
None of these
`501`st term
`502`nd term
`508`th term
`509`th term
`3n - n^2`
`2n - 3`
`2n + 3`
`2n - 5`
`n/(n + 1)`
`n^2/(n + 1)`
`(n + 1)/ n`
`(n + 1)/( 2n)`
Only I
Only II
Both I and II
Neither I nor II
`2(c -a)`
`2(d- c)`
`2(f- d)`
`(d -c)`
27th
28th
29th
No such term exists
`p + q`
`pq`
`1`
`0`
`12.2`
`12.8`
`13.2`
`13.8`
`16250`
`11830`
`10360`
`14280`
`n - m + 1: m`
`n - m + 1 : n`
`m : n - m + 1`
`n : n - m + 1`
`17//2`
`33//2`
`11`
`187//2`
`2^n - n - 1`
`1 - 2^(-n)`
`2^(-n) + n - 1`
`2^n - 1`
in AP only
in GP only
in both AP and GP
Neither in AP nor in GP
8
9
10
11
`1`
`3`
`6`
`9`
`AP`
`GP`
`HP`
None of these
`8`
`12`
`14`
`16`
`1//2`
`3//2`
`2`
`2//3`
`- 13.5`
`13.5`
`-27`
`27`
9th
10th
11th
12th
`sqrt3/2 `
`(3 sqrt3)/2`
`(2 sqrt3)/3`
`sqrt 3`
one
two
four
Infinitely many
`G_1G_2`
ln `(G_1G_2)`
`G_1/G_2`
ln `(G_1/G_2)`
in AP only
in GP only
in both AP and GP
Neither in AP nor in GP
The 9th power of the 4th term
The 4th power of the 9th term
The 5th power of the 9th term
The 9th power of the 5th term
`AP`
`GP`
`HP`
None of these
`(10)/9 (10^(100) -1) - 100`
`(10)/9 (10^(99) -1) - 100`
`100 (100^(10) -1)`
` 9/(100) ( 10^(100) - 1)`
`a+ 2r`
`ar^2`
`a(r^5 - 1)// (r- 1) 5`
`a(r^5 - 1) // [5(r- 1)]`
1
3
5
Cannot be determined
`1`
`1.01`
`1.001`
`1.1`
`(89)/(128)`
`(57)/(384)`
`(85)/(128)`
None of these
`- 27//2`
`27//2`
`- 33//2`
`33//2`
`p = q != r`
`p != q != r`
`p != q = r`
`p = q = r`
`3`
`4`
`8`
`10`
`6`
`14`
`27//14`
`56//15`
`(sqrt(13) + 1)/2`
`(sqrt(13) - 1)/2`
`(sqrt(13) + 1)/3`
`sqrt(13)`
`256` sq cm
`512` sq cm
`1024` sq cm
`512//3` sq cm
`1`
`5//2`
`3` or `3//2`
`9` or `3`
`G_1G_2`
ln `(G_1G_2)`
`G_1/G_2`
ln `(G_1/G_2)`
`4`
`root(3)(5)`
`2 root(3)(18)`
None of these
`8`
`10`
`12`
`16`
`10 root(3)(3)`
`20 root(3)(3)`
`40 root(3)(3)`
`70 root(3)(3)`
`2^(n//2)`
`2^((n+ 1)//2)`
`2^(n+ 1) - 1`
`2^(n - 1)`
` ge 2^3`
` ge 2^6`
` le 2^6`
None of these
`6`
`16`
`0`
`32`
`(2pq)/A`
`2Apq`
`2Ap^2q^2`
None of these
`16`
`8`
`0`
`3`
`205`
`225`
`238`
`241`
`1/(2n + 1)`
`(2n)/(2n + 1)`
`n/(2n + 1)`
`(2n)/(n + 1)`
` \frac{121}{10}`
` \frac{441}{100}`
`100`
` 110`
`605`
`615`
`671`
`693`
`180`
`186`
`196`
`206`
AP
GP
HP
None of the above
x, y and z are in geometric progression
x, y and z are in arithmetic progression
x, y and z are in harmonic progression
None of the above
AP
HP
GP
None of these
`5`
`6`
`7`
`8`
`HP`
`AP`
`GP`
None of these
` a = -1/4 , b = 1`
`a = 1/12 , b = 1/9`
Both (a) and (b)
None of these
`2`
`3`
`5`
`6`
`n(a_1 - a_n)`
`(n-1) (a_1 -a_n)`
`na_1a_n`
`(n-1)a_1a_n`
AP
HP
GP
None of these
AP
GP
HP
None of these
AP
GP
HP
None of these
`3925`
`4100`
`4175`
`8200`
`5/4`
`(16)/5`
`9/2`
`9`
`12`
`18`
`24`
`27`
`4`
`9`
`12.5`
`25`
`A_1^(-1)+A_2^(-1)`
`G_1^(-1)+G_2^(-1)`
`(G_1 G_2)/(A_1+A_2)`
`(A_1+A_2)/(G_1 G_2)`
`8`
`10`
`12`
`16`
Harmonic mean
Geometric mean
Median
Mode
`6` and `3`
`9` and `5`
`12 ` and `7`
`3` and `1`
`n^2`
`n^2 - 1`
`n^2 + 1`
` 1/2 n( n + 1)`
Only I
Only I
Both I and II
Neither I nor II
` (n(n+1))/2`
` (n(n+1)^2)/2`
` (n(n+1)^2)/4`
` (n^2(n+1)^2)/4`