Question

. Match List-I with List-II.

List-I		List-II
I	The least square number which is divisible by 8, 12 and 16	P	48
II	If H.C.F and L.C.M of two numbers & are 16 and 192. If one of the number is 64 then other is	Q	40
III	HCF of 69 and 193 is	R	144
IV	No. of composite numbers between 150 to 200 (including both)	S	1

• A. I—Q; II—R; III—S; IV—P
• B. I—R; II—P; III—S; IV—Q
• C. I—P; II—Q; III—S; IV—R
• D. I—Q; II—P; III—R; IV—S

Answer 1

Answer: (B)

(I) $\mathrm{LCM}$ of $(8,12,16)=48$
But 48 is not a perfect square number
So, least square number will be multiple of 48
$\therefore 48\times 2=96$
(it is also not a perfect square)
$48\times 3=144$ (It is a perfect square)...(R)
(II) Given: H.C.F = 16, L.CM. = 192
One number $=64$
As, for two numbers
H.C.F $\times$ L.C.M $=$ Product of two numbers
$16\times 192=64\times x$
$\therefore x=\frac{16\times 192}{64}$
$\therefore x=48$....(P)
(III) As, 193 is a prime number.
$\therefore \mathrm{HCF}$ of $(69,193)=1$...(S)

$\therefore$ Prime numbers between 150 to 200 is 151 , $157,163,167,173,179,181,191,193,197,199$
$\therefore$ Total no. of prime number $=11$
Between 150 to 200
$\therefore$ Total number of composites $=51-11=40$
$\therefore$ Numbers between 150 to $200=40\dots (Q)$