Question
_ n _ r=3 ^ r^3-8 r^3+8 equals to
BITSAT
Mathematics
Definite Integration
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 2 7
- B. 3 7
- C. 4 7
- D. 6 7
Answer
A. 2 7
Step-by-step solution
aligned & _ n _ r=3 ^ r^3-8 r^3+8 = ( 3^3-8 3^3+8 ) ( 4^3-8 4^3+8 ) \\ & ......... ( n^3-8 n^3+8 ) aligned array r = _ n [ (3-2) (3^2+2^2+3.2 ) (3+2) (3^2+2^2-3.2 ) ] [ (4-2) (4^2+2+4.2 ) (4+2) (4^2+2^2-4.2 ) ] \\ . . [ (n-2) (n^2+2^n+n .2 ) (n+2) (n^2+2^2-n .2 ) ] array gathered = _ n [ (3-2)(4-2) (n-2) (3+2)(4+2) (n+2) ] \\ [ (3^2+2^2+3.2 ) (4^2+2^2+4.2 ) . (n^2+2^2+n .2 ) (3^2+2^2-3.2 ) (4^2+2^2-4.2 ) . . (n^2+2^2-n .2 ) ] gathered = [ 1 2 3.4 .5 .6 . 5 6.7 .8 . . ] [ 19 28 39.52 .63 . . 7 12 19.28 .39 .52 . . ] = 2 7
Related: Mathematics — Definite Integration · All PYQ Banks