a=240!
b=80^240
Which is it large

B = 80^240

logB = 240log80 ~ 456

No. Of digits = 457



Using Stirling approximation

log(n!) ~ log(√2πn) + nlog(n/e)

log(n!) ~ 468

No. Of digits = 469

So A > B.

(C+1)(c+3)/(c+7)
C+1)(c+3) should be Minimum
C+7>0. C>-7 maximum infinity
But we want whole fraction
Negative will give minimum
(C+1)(c+3) is negative
For -1<c<-3
At c =-1. Fraction 0
At c=-3. Fraction 0
At c=-1.5. (-.5)(1.5)/5.5
=-1.5/11=-3/22
At c=-2. (-1)(1)/5=-1/5 minimum
Or


F(c)=c^2+4c+3
F'(c)=0. C=-2
F(-2)=4-8+3=-1
Minimum value of fraction
-1/-2+7=-1/5

2

4 more

56 h ans please solve

15a+7=21b+10
5a=7b+1
5a=5b+(2b+1)
b=7,12,17,22,....
At b=7. 21*7+10=157 Frist number
At b=237 21*282+10=5932
(277-7)/10 +(282-12)/10 +2
27+27+2=56

Let m along the length
N along the width
At edges total tiles=2m+2n-4
Interior=(m-2)(n-2)
Mn-2(m+n)+4=2m+2n-4
Mn-4(m+n)+8=0
Factorise or see which option is giving integer
If m=12
12n-4(12+n)+8=0
8n=40 n=5 yes
5*12 types