CDC SEE Model Set (2080)

Subject Code: 1031 Model Set

NATIONAL EXAMINATION BOARD
SEE MODEL QUESTION -2080 (Model Set)

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. श्री शारदा माध्यमिक विद्यालयको कक्षा 10 मा अध्ययनरत विद्यार्थीहरूलाई पोखरा, लुम्बिनी र इलाममध्ये कुन ठाउँमा शैक्षिक भ्रमण जान उपयुक्त हुन्छ भनी गरिएको सर्वेक्षणमा 40 जनाले पोखरा, 30 जनाले लुम्बिनी र 45 जनाले इलाम जान उपयुक्त हुने बताए । उक्त कक्षाका 15 जना विद्यार्थीहरूले तीनै ओटा ठाउँ उपयुक्त हुने बताउँदा छ जनाले कुनै राय नै व्यक्त गरेनन् ।
   In a survey conducted on students studying in grade 10 at Shree Sharada Secondary School to determine suitable place for educational trips among Pokhara, Lumbini and Ilam, it was found that 40 students considered Pokhara to be suitable, 30 students considered Lumbini to be suitable, and 45 students considered Ilam to be suitable. While 15 students of that grade said that all three places are suitable, 5 students did not express any opinion.

   1. P L र I ले क्रमश: पोखरा, लुम्बिनी र इलाम उपयुक्त हुन्छ भन्ने विद्यार्थीहरूको समूहलाई जनाउँछ भने सबै ठाउँ उपयुक्त हुन्छ भन्ने विद्यार्थीको समूहलाई गणनात्मकता सङ्केतमा लेख्नुहोस् ।
      If P, L and I denote the set of students who prefer Pokhara, Lumbini and Ilam respectively, write the cardinality notation of students for whom all places are suitable.[1K]
   2. मााथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् ।
      Show the above information in a Venn diagram. [1U]
   3. शारदा माध्यमिक विद्यालयमा कक्षा १० मा कति जना विद्यार्थी अध्ययनरत रहेछन् ? गणना गर्नुहोस् ।
      How many students are studying in grade 10 in the Sarada Secondary School? Calculate it. [3A]
   4. यदि सर्वेक्षणमा राय नै व्यक्त नगरेका छ जना विद्यार्थीले लुम्बिनी उपयुक्त स्थान हो भनेको भए पोखरा मात्र उपयुक्त स्थान भन्ने र लुम्बिनी मात्र उपयुक्त स्थान भन्ने विद्यार्थीहरूको अनुपात कति हुने थियो ?
      If 5 students, who did not express their opinion in the survey had said Lumbini as a suitable place, then what would have been the ratio of students who considered only Pokhara was the suitable place and only Lumbini was the suitable place? [1HA]

   Solution 👉 Click Here

   Solution
   Let
   U is universal set of all students studying in grade 10 at Shree Sharada Secondary School
   Given that
   P denote the set of students who prefer Pokhara
   L denote the set of students who prefer Lumbini
   I denote the set of students who prefer Ilam
   Thus
   Cardinality of all surveyed students studying in class 10 as Universal Set U is
   \(n(U)=?\)
   Cardinality of set P, students who prefer Pokhara is
   \(n(P)=40\)
   Cardinality of set L, students who prefer Lumbini is
   \(n(L)=30\)
   Cardinality of set I, students who prefer Ilam is
   \(n(I)=45\)
   Cardinality of set, students who prefer all three places is
   \(n(P \cap L \cap I)=15\)
   Cardinality of set, students who students did not express any opinion is
   \(n (\overline{P \cup L \cup I})=6\)
   Now the itemwise solution are :

   1. If P, L and I denote the set of students who prefer Pokhara, Lumbini and Ilam respectively, write the cardinality notation of students for whom all places are suitable.
      According the question,
      cardinality notation of students for whom all places are suitable is
      \(n(P \cap L \cap I)=15\)
      
   2. Present the above information in a Venn-diagram.
      According the question,
      The Venn-diagram of given information are as follows.
   3. How many students are studying in grade 10 in the Sarada Secondary School? Calculate it.
      According to the Venn-diagram given above
      \(n(U)=(40-15)+(30-15)+(45-15)+(0)+(0)+(0)+(15)+(6)\)
      or\(n(U)=91\)
      Therefore,
      The number of students studying in grade 10 in the Sarada Secondary School is
      \(n(U)=91\)
      
   4. If 5 students, who did not express their opinion in the survey had said Lumbini as a suitable place, then what would have been the ratio of students who considered only Pokhara was the suitable place and only Lumbini was the suitable place?
      According to the solution
      If 5 students, who did not express their opinion in the survey had said Lumbini as a suitable place, then
      \(n(L_o)=(30-15)+6=21\)
      \(n(P_o)=(40-15)=25\)
      Now, the ratio of students who considered only Pokhara was the suitable place and only Lumbini was the suitable place is
      \( \frac{n(P_o)}{n(L_o)}=\frac{25}{21} \)
      or the ratio is 25:21
      

   This completes the solution