ASSEB Class IX Chapter 2 Polynomials Algebric Identities

{ "questions": [ { "question": "তলৰ কোনটো $(a+b)^2$ ৰ শুদ্ধ সূত্ৰ?", "options": [ "$a^2+ab+b^2$", "$a^2+2ab+b^2$", "$a^2-2ab+b^2$", "$a^2-b^2$" ], "answer": 1 }, { "question": "$(a-b)^2$ ৰ বাবে শুদ্ধ সূত্ৰটো হৈছে:", "options": [ "$a^2+2ab+b^2$", "$a^2-2ab-b^2$", "$a^2-2ab+b^2$", "$a^2-b^2$" ], "answer": 2 }, { "question": "কোনটো সূত্ৰই দুটা বৰ্গৰ প্ৰভেদক বুজায়?", "options": [ "$(a+b)(a-b)=a^2-b^2$", "$(a+b)(a-b)=a^2+b^2$", "$(a-b)^2=a^2-b^2$", "$(a+b)^2=a^2-b^2$" ], "answer": 0 }, { "question": "$(x+a)(x+b)$ ৰ সূত্ৰটো হৈছে:", "options": [ "$x^2+(a+b)x+ab$", "$x^2+(a-b)x-ab$", "$x^2+(a+b)x-ab$", "$x^2+(a-b)x+ab$" ], "answer": 0 }, { "question": "তলৰ কোনটো $(a+b+c)^2$ ৰ শুদ্ধ সূত্ৰ?", "options": [ "$a^2+b^2+c^2+ab+bc+ca$", "$a^2+b^2+c^2+2ab+2bc+2ca$", "$a^2+b^2+c^2-2ab-2bc-2ca$", "$a^2+b^2+c^2+3abc$" ], "answer": 1 }, { "question": "$(a+b)^3$ ৰ বাবে শুদ্ধ সূত্ৰটো হৈছে:", "options": [ "$a^3+b^3$", "$a^3+3a^2b+3ab^2+b^3$", "$a^3+2a^2b+2ab^2+b^3$", "$a^3-3a^2b+3ab^2-b^3$" ], "answer": 1 }, { "question": "$(a-b)^3$ ৰ বাবে শুদ্ধ সূত্ৰটো কোনটো?", "options": [ "$a^3-3a^2b+3ab^2-b^3$", "$a^3+3a^2b+3ab^2+b^3$", "$a^3-3a^2b-3ab^2-b^3$", "$a^3-b^3$" ], "answer": 0 }, { "question": "$a^3+b^3$ ৰ সূত্ৰটো হৈছে:", "options": [ "$(a+b)(a^2+ab+b^2)$", "$(a-b)(a^2-ab+b^2)$", "$(a+b)(a^2-ab+b^2)$", "$(a-b)(a^2+ab+b^2)$" ], "answer": 2 }, { "question": "কোনটো সূত্ৰই $a^3-b^3$ ক প্ৰকাশ কৰে?", "options": [ "$(a+b)(a^2-ab+b^2)$", "$(a-b)(a^2+ab+b^2)$", "$(a+b)(a^2+ab+b^2)$", "$(a-b)(a^2-ab+b^2)$" ], "answer": 1 }, { "question": "$a^2+2ab+b^2$ ৰ দ্বাৰা কোনটো অভেদ প্ৰকাশ পায়?", "options": [ "$(a-b)^2$", "$(a+b)^2$", "$(a+b)(a-b)$", "$a^2-b^2$" ], "answer": 1 }, { "question": "$a^2-2ab+b^2$ ৰ দ্বাৰা কোনটো অভেদ প্ৰকাশ পায়?", "options": [ "$(a+b)^2$", "$(a-b)^2$", "$(a+b)(a-b)$", "$(a+b)^3$" ], "answer": 1 }, { "question": "$a^2-b^2$ ৰাশিটোক কেনেকৈ লিখিব পাৰি?", "options": [ "$(a+b)^2$", "$(a-b)^2$", "$(a+b)(a-b)$", "$(a-b)(a-b)$" ], "answer": 2 }, { "question": "$(a+b)^2=a^2+2ab+b^2$ অভেদটোত মধ্য পদটো (middle term) কি?", "options": [ "$ab$", "$2ab$", "$a^2b^2$", "$2a^2b^2$" ], "answer": 1 }, { "question": "$(a-b)^3=a^3-3a^2b+3ab^2-b^3$ অভেদটোত $ab^2$ ৰ সহগ (coefficient) কিমান?", "options": [ "$-3$", "$-1$", "$1$", "$3$" ], "answer": 3 }, { "question": "তিনিটা পদৰ বৰ্গৰ বাবে কোনটো সূত্ৰ ব্যৱহাৰ কৰা হয়?", "options": [ "$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$", "$(a+b+c)^2=a^2+b^2+c^2+abc$", "$(a+b+c)^2=a^2+b^2+c^2+ab+bc+ca$", "$(a+b+c)^2=a^2+b^2+c^2-2abc$" ], "answer": 0 }, { "question": "দুটা ঘনৰ যোগফলৰ (sum of two cubes) বাবে কোনটো সূত্ৰ শুদ্ধ?", "options": [ "$a^3+b^3=(a+b)(a^2-ab+b^2)$", "$a^3+b^3=(a-b)(a^2+ab+b^2)$", "$a^3+b^3=(a+b)(a^2+ab+b^2)$", "$a^3+b^3=(a-b)(a^2-ab+b^2)$" ], "answer": 0 }, { "question": "দুটা ঘনৰ বিয়োগফলৰ (difference of two cubes) বাবে কোনটো সূত্ৰ শুদ্ধ?", "options": [ "$a^3-b^3=(a+b)(a^2-ab+b^2)$", "$a^3-b^3=(a-b)(a^2+ab+b^2)$", "$a^3-b^3=(a+b)(a^2+ab+b^2)$", "$a^3-b^3=(a-b)(a^2-ab+b^2)$" ], "answer": 1 }, { "question": "$a^3+b^3+c^3-3abc$ ৰ সূত্ৰটো হৈছে:", "options": [ "$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$", "$(a+b+c)(a^2+b^2+c^2+ab+bc+ca)$", "$(a-b-c)(a^2+b^2+c^2)$", "$(a+b-c)(a^2-b^2+c^2)$" ], "answer": 0 }, { "question": "যদি $a+b+c=0$ হয়, তেন্তে কোনটো সূত্ৰ শুদ্ধ?", "options": [ "$a^3+b^3+c^3=abc$", "$a^3+b^3+c^3=2abc$", "$a^3+b^3+c^3=3abc$", "$a^3+b^3+c^3=0$" ], "answer": 2 }, { "question": "বিয়োগফলৰ ঘনফলৰ (cube of a difference) বাবে তলৰ কোনটো শুদ্ধ সূত্ৰ?", "options": [ "$(a-b)^3=a^3-3a^2b+3ab^2-b^3$", "$(a-b)^3=a^3-3a^2b-3ab^2-b^3$", "$(a-b)^3=a^3+3a^2b+3ab^2+b^3$", "$(a-b)^3=a^3-b^3$" ], "answer": 0 }, { "question": "কোনটো অভেদ শুদ্ধ?", "options": [ "$(a+b)^2=a^2+ab+b^2$", "$(a+b)^2=a^2+2ab+b^2$", "$(a+b)^2=a^2-2ab+b^2$", "$(a+b)^2=a^2-b^2$" ], "answer": 1 }, { "question": "কোনটো অভেদৰ পৰা $a^2-2ab+b^2$ পোৱা যায়?", "options": [ "$(a+b)^2$", "$(a-b)^2$", "$(a+b)(a-b)$", "$(a-b)(a+b)^2$" ], "answer": 1 }, { "question": "$(a+b)^3$ অভেদটোত $a^2b$ ৰ সহগ (coefficient) কিমান?", "options": [ "$1$", "$2$", "$3$", "$4$" ], "answer": 2 }, { "question": "$(a-b)^3$ অভেদটোত $ab^2$ ৰ সহগ (coefficient) কিমান?", "options": [ "$-3$", "$3$", "$-2$", "$2$" ], "answer": 1 }, { "question": "কোনটো ৰাশি $a^3+b^3$ ৰ সমান?", "options": [ "$(a+b)(a^2-ab+b^2)$", "$(a-b)(a^2+ab+b^2)$", "$(a+b)(a^2+ab+b^2)$", "$(a-b)(a^2-ab+b^2)$" ], "answer": 0 }, { "question": "কোনটো ৰাশি $a^3-b^3$ ৰ সমান?", "options": [ "$(a+b)(a^2-ab+b^2)$", "$(a-b)(a^2+ab+b^2)$", "$(a+b)(a^2+ab+b^2)$", "$(a-b)(a^2-ab+b^2)$" ], "answer": 1 }, { "question": "$(a+b+c)^2$ ত $bc$ ৰ সহগ (coefficient) কিমান?", "options": [ "$1$", "$2$", "$3$", "$4$" ], "answer": 1 }, { "question": "কোনটো অভেদত $2ca$ পদটো থাকে?", "options": [ "$(a+b)^2$", "$(a-b)^2$", "$(a+b+c)^2$", "$(a+b)^3$" ], "answer": 2 }, { "question": "$a^2-b^2$ ৰ শুদ্ধ সূত্ৰটো কোনটো?", "options": [ "$(a+b)^2$", "$(a-b)^2$", "$(a+b)(a-b)$", "$(a-b)(a-b)$" ], "answer": 2 }, { "question": "$a+b+c=0$ হলে কোনটো অভেদ শুদ্ধ?", "options": [ "$a^3+b^3+c^3=abc$", "$a^3+b^3+c^3=2abc$", "$a^3+b^3+c^3=3abc$", "$a^3+b^3+c^3=-3abc$" ], "answer": 2 } ] }