Q.
Let $\log _{10} 2= a$ and $\log _{10} 3= b$ then
Column I
Column II
A
$\log _{10}\left(\sin ^2 \frac{5 \pi}{3}\right)$ equals
P
$\frac{4(2 a+b)}{1-a+2 b}$
B
$\log _{100} 4+2 \log _{100} 27$ equals
Q
$\frac{2 b ^2+3 a ^2}{ ab }$
C
$\log _2 9+\log _3 8$ equals
R
$a+3 b$
D
$\log _{\sqrt{45}} 144$ equals
S
$b -2 a$
| Column I | Column II | ||
|---|---|---|---|
| A | $\log _{10}\left(\sin ^2 \frac{5 \pi}{3}\right)$ equals | P | $\frac{4(2 a+b)}{1-a+2 b}$ |
| B | $\log _{100} 4+2 \log _{100} 27$ equals | Q | $\frac{2 b ^2+3 a ^2}{ ab }$ |
| C | $\log _2 9+\log _3 8$ equals | R | $a+3 b$ |
| D | $\log _{\sqrt{45}} 144$ equals | S | $b -2 a$ |
Continuity and Differentiability
Solution: