In the expansion of (2–3x3)20, if the ratio of 10th term to 11th term is 4522, then x is equal to
–23
–32
23-13
32-13
Explanation For The Correct Option:
Finding the value of x using the given information:
Given that
T10T11=4522T9+1T10+1=4522Weknowthatfor(a+b)n,nthtermisTr+1=nCran-rbr⇒20C9220-9-3x3920C10220-10-3x310=4522⇒20C9220-9-3x3920C10220-10-3x310=4522⇒20!9!11!211-39x2720!10!10!210-310x30=4522∵Crn=n!r!(n-r)!⇒10112-3x3=4522⇒3x3=-89⇒x3=-827⇒x=-23[takingcuberootbothsides]
Hence, option A is correct.
Find the value of x, if the ratio of 10th term to 11th term of the expansion (2−3x3)20 is 45 : 22.
Or
Find the value of a, so that the term independent of x in (√x+ax2)10 is 405.