SEE Model Set 1 (2080)_MEAN

Subject Code: 1031 Set:1[MEAN]

NATIONAL EXAMINATION BOARD
SEE MODEL QUESTION -2080 (SET 1)[MEAN]

Subject: C. Maths
Time: 3 hours Full Marks:75

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दिइएका निर्देशनका आधारमा आफ्नै शैलीमा सिर्जनात्मक उत्तर दिनुहोस् ।
सबै प्रश्नहरुको उत्तर दिनुहोस् (Answer all the questions)

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1. Eight blood types are shown by the eight regions of the Venn diagram shown here. Each circle represents one of three antigens: A, B or Rh. If A and B are both absent, the blood type is O. If Rh is present, the blood type is positive (+); otherwise, it is negative (-). The following table represents the blood types of 150 people.
   
   

   Antigens	Number of people
   A	60
   B	27
   Rh	123
   A and B	12
   A and Rh	46
   B and Rh	17
   A and B and Rh	9

   1. If A,B and Rh denote the set of people who have A, B र Rh Antigens in their blood respectively, write the cardinality notation of people for all groups.[1K]
   2. Show the above information in a Venn diagram. [1U]
   3. How many people are having O negative blood? Calculate it. [3A]
   4. When receiving a blood, the recipient must have all the antigens of the donor. If a person has O positive, to how many people he can donate the blood?[1HA]
   Solution
   Let
   U is universal set of all antigens
   Given that
   A denote the set of people having A antigens
   B denote the set of people having B antigens
   Rh denote the set of people having Rh antigens
   Thus
   Cardinality of all surveyed people as Universal Set U is
   \(n(U)=150\)
   Now the itemwise solution are :

   1. If A,B and Rh denote the set of people who have A, B र Rh Antigens in their blood respectively, write the cardinality notation of people for all blood groups.
      According the question,
      Cardinality of set, people having A, B and Rh antigens is
      \(n(A \cap B \cap Rh )=n(AB+)=9\)
      Cardinality of set, people having A and Rh antigens only is
      \(n_o(A \cap Rh )=n(A+)=46-9=37\)
      Cardinality of set, people having B and Rh antigens only is
      \(n_o(B \cap Rh )=n(B+)=17-9=8\)
      Cardinality of set, people having A and B antigens only is
      \(n_o(A \cap B )=n(AB-)=12-9=3\)
      Cardinality of set A, people having A antigens only is
      \(n_o(A)=n(A-)=60-37-9-3=11\)
      Cardinality of set B, people having B antigens only is
      \(n_o(B)=n(B-)=27-8-9-3=7\)
      Cardinality of set Rh, people having Rh antigens only is
      \(n_o(Rh)=n(O+)=123-37-9-8=69\)
      
   2. Present the above information in a Venn-diagram.
      According the question,
      The Venn-diagram of given information are as follows.
   3. How many people are having O negative blood? Calculate it.
      According to the Venn-diagram given above
      \(n(U)=150\)
      or\(69+11+7+37+3+8+9+x=150\)
      or\(x=6\)
      Therefore,
      The number of people having O negative blood is
      \(n \overline{(A \cup B \cup Rh)}=6\)
      
   4. When receiving a blood, the recipient must have all the antigens of the donor. If a person has O+, to how many people he can donate the blood?
      According to the solution
      A person having O+ blood, can donate blood to
      people having Rh antigens
      people having O+,A+,B+, AB+ blood groups
      Which is
      \(n(Rh)=123\)
      Thus, A person having O+ blood, can donate blood to 123 people
      

   This completes the solution
यहाँ प्रस्तुत गरिएको भेनचित्रका आठवटा क्षेत्रहरूले रगतका आठ प्रकारहरूलाई जनाउँछन्। प्रत्येक वृत्तले तीनवटा एन्टिजेनहरू मध्ये एउटालाई जनाउँछ: A, B वा Rh। यदि A र B दुवै अनुपस्थित छन् भने, रगतको प्रकार O हुन्छ। यदि Rh उपस्थित छ भने, रगतको प्रकार पोजेटिभ (+) हुन्छ; अन्यथा, यो नेगेटिभ (-) हुन्छ। तलको तालिकाले 150 जना मानिसको रगतको प्रकारलाई प्रतिनिधित्व गर्दछ।



Antigens	Number of people
A	60
B	27
Rh	123
A and B	12
A and Rh	46
B and Rh	17
A and B and Rh	9

1. A,B र Rh ले क्रमश: A, B र Rh एन्टीजेनलाई जनाउँछ भने सबै समुहलाई गणनात्मकता सङ्केतमा लेख्नुहोस् ।[1K]
2. मााथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् । [1U]
3. कति जना मानिसहरुमा ओ नेगेटिभ रगत समुह रहेछन् ? गणना गर्नुहोस् । [3A]
4. रगत प्राप्त गर्दा, प्राप्तकर्तासँग दाताको सबै एन्टिजेनहरू हुनुपर्छ। अब, ओ पोजेटिभ भएको व्यक्तीले कति जना मानिसलाई रगत दान गर्न सक्दछ? [1HA]
1. समूहहरूको गणनात्मकता सङ्केत:
   \(n(A \cap B \cap Rh) = 9\) (AB+)
   \(n_o(A \cap Rh) = 37\) (A+)
   \(n_o(B \cap Rh) = 8\) (B+)
   \(n_o(A \cap B) = 3\) (AB-)
   \(n_o(A) = 11\) (A-)
   \(n_o(B) = 7\) (B-)
   \(n_o(Rh) = 69\) (O+)
2. भेनचित्रमा प्रस्तुतीकरण
3. O नेगेटिभ (\(x\)) पत्ता लगाउन:
   \(69 + 11 + 7 + 37 + 3 + 8 + 9 + x = 150\)
   वा\(144 + x = 150\)
   वा\(x = 6\)
   त्यसैले, 6 जना मानिसको रगत समूह O नेगेटिभ छ।
4. दाताको रगत समूह O पोजेटिभ (O+) हुनुको अर्थ उसँग केवल Rh एन्टिजेन छ। नियम अनुसार प्राप्तकर्तासँग दाताको सबै एन्टिजेन हुनुपर्छ, त्यसैले Rh एन्टिजेन भएका सबै (O+, A+, B+, AB+) ले रगत लिन सक्छन्।
   जम्मा मानिस संख्या = \(n(Rh) = 123\)।