ข้อสอบ A-Level คณิตประยุกต์ 1 ปี 2566 (หลักสูตรใหม่)

ข้อ 2

ให้ begin mathsize 12px style แสดงว ่ า space space space space space open square brackets 7 plus open parentheses negative 5 close parentheses close square brackets to the power of 6 space equals space sum from r equals 0 to 6 of open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times open parentheses negative 5 close parentheses to the power of r
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space sum from r equals 0 to 6 of open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times open parentheses negative 1 close parentheses to the power of r times 5 to the power of r
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space sum from r equals 0 to 6 of open parentheses negative 1 close parentheses to the power of r open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times 5 to the power of r

ด ั งน ั้ น space space space space space space space space space space sum from r equals 0 to 6 of open parentheses negative 1 close parentheses to the power of r open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times 5 to the power of r space equals space open square brackets 7 plus open parentheses negative 5 close parentheses close square brackets to the power of 6 space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open parentheses 7 minus 5 close parentheses to the power of 6 space equals space 2 to the power of 6
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 64 end style

และ begin mathsize 12px style แสดงว ่ า space space space space space open square brackets 7 plus open parentheses negative 5 close parentheses close square brackets to the power of 6 space equals space sum from r equals 0 to 6 of open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times open parentheses negative 5 close parentheses to the power of r
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space sum from r equals 0 to 6 of open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times open parentheses negative 1 close parentheses to the power of r times 5 to the power of r
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space sum from r equals 0 to 6 of open parentheses negative 1 close parentheses to the power of r open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times 5 to the power of r

ด ั งน ั้ น space space space space space space space space space space sum from r equals 0 to 6 of open parentheses negative 1 close parentheses to the power of r open parentheses table row 6 row r end table close parentheses times 7 to the power of 6 minus r end exponent times 5 to the power of r space equals space open square brackets 7 plus open parentheses negative 5 close parentheses close square brackets to the power of 6 space
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space open parentheses 7 minus 5 close parentheses to the power of 6 space equals space 2 to the power of 6
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 64 end style

พิจารณาข้อความต่อไปนี้

ก)  สมาชิกของเซต begin mathsize 16px style A end style ที่มีค่ามากที่สุด คือ begin mathsize 16px style 0 end style

ข)  begin mathsize 16px style A minus B end style เป็นเซตอนันต์

ค)  begin mathsize 16px style for all x open square brackets x element of A rightwards arrow x element of B close square brackets end style มีค่าความจริงเป็นเท็จ

จากข้อความ ก) ข) และ ค) ข้างต้น ข้อใดถูกต้อง

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