Let x = 111.........11 (20 digits) y = 333........33 (10 digits) and z = 222.........22 (10 digits),

Question

Let x = 111.........11 (20 digits) y = 333........33 (10 digits) and z = 222.........22 (10 digits), (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x =(1/9)[999 ldots ldots . .99]=(1/9)[1020-1] ldots . .(1) y =(1/3)[999 ldots ldots . .99]=(1/3)[1010-1] z =(2/9)[1010-1] ∴ ( x - y 2/ z )=((1020-1)-(1010-1)2/2(1010-1))=((1010+1)-(1010-1)/2)=1

Q. Let x=111.........11 (20 digits) y=333........33 (10 digits) and z=222.........22 (10 digits),

x=91​[999……..99]=91​[1020−1]…..(1) y=31​[999……..99]=31​[1010−1] z=92​[1010−1] ∴zx−y2​=2(1010−1)(1020−1)−(1010−1)2​=2(1010+1)−(1010−1)​=1

Q. Let $x = 111.$ ........11 (20 digits)
$y = 333$ ........33 (10 digits)
and $z = 222$ .........22 (10 digits),