Question

$S=(150-3x{)}^{20}(2x-50{)}^{30},(25\le -50{)}^{30},25\le \times \le 50$ which of the following could be the possible value of S

• A. $4^{50}\times {10}^{50}$
• B. $5^{50}\times {10}^{40}$
• C. $2^{50}\times {10}^{50}$
• D. $3^{50}\times {10}^{50}$

Answer 1

Answer: (C), (D)

The correct options are
C $2^{50}\times {10}^{50}$
D $3^{50}\times {10}^{50}$

$S={(150-3x)}^{20}{(2x-50)}^{30}$

$=3^{20}{(150-3x)}^{20}{(2x-50)}^{30}$

$25\le x\le 50$

For$x=25\to S=0$

For$x=30\to S=2^{30}\times 3^{20}\times {20}^{20}\times 5^{30}$

$=2^{40}\times 3^{20}\times 5^{50}$

For$x=35\to S=2^{30}\times 3^{20}\times {15}^{20}\times {10}^{30}$

$=2^{30}\times 3^{40}\times 5^{20}\times {10}^{30}$

For$x=40\to S=2^{30}\times 3^{20}\times {10}^{20}\times {15}^{30}$

$=2^{30}\times 3^{20}\times {10}^{20}\times 3^{30}\times 5^{30}$

$=(2\times {5)}^{30}\times {10}^{20}\times 3^{20+30}$

$={10}^{50}\times 3^{50}$

For$x=45\to S=2^{30}\times 3^{20}\times 5^{20}\times {20}^{30}$

$=2^{30}\times 3^{20}\times 5^{20}\times 2^{30}\times {10}^{30}$

$=2^{40}\times 3^{20}\times {10}^{50}$

$\therefore Ans.\to D>3^{50}\times {10}^{50}$.

OPTION : C & D.