Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 10MathematicsSetsVenn DiagramsHardLevel 13

In a class, n(A) = 74, n(B) = 68, and 86 students are in exactly one set. What is n(A ∩ B)?

Advertisement

Answer and explanation

Correct answer: 28

Let x = n(A ∩ B). The students in exactly one set are those in A only or B only. Their number is [n(A) − x] + [n(B) − x] = n(A) + n(B) − 2x. Therefore, 86 = 74 + 68 − 2x = 142 − 2x. Thus 2x = 56 and x = 28. Hence, the intersection contains 28 students, so option C is correct.

Tags

setsvenn diagramsexactly oneintersection equationMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

28

Why is this the correct answer?

Let x = n(A ∩ B). The students in exactly one set are those in A only or B only. Their number is [n(A) − x] + [n(B) − x] = n(A) + n(B) − 2x. Therefore, 86 = 74 + 68 − 2x = 142 − 2x. Thus 2x = 56 and x = 28. Hence, the intersection contains 28 students, so option C is correct.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.

Report question
Advertisement