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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Question 1

• 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, 6 students did not express any opinion.
  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. [1]
  2. Show the above information in a Venn diagram. [1]
  3. How many students are studying in grade 10 in the Sarada Secondary School? Calculate it. [3]
  4. If 6 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? [1]
  1. The cardinality notation for students for whom all places are suitable is
     \(n(P \cap L \cap I) = 15\)
  2. Venn-diagram representation
  3. To find total students \(n(U)\)
     From Venn-diagram, we see that
     n(U) = 25 + 15 + 30 + 0 + 0 + 0 + 15 + 6
     orn(U) = 91
     Thus, 91 students are studying in grade 10.
  4. New Ratio Calculation:
     If 6 students who expressed no opinion had preferred Lumbini:
     New Lumbini only \(n_o(L) = 15 + 6 = 21\)
     Pokhara only \(n_o(P) = 25\)
     Ratio \(n_o(P) : n_o(L) = 25 : 21\).
• 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 ।
  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 । [1]
  2. मााथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् । [1]
  3. शारदा माध्यमिक विद्यालयमा कक्षा 10 मा कति जना विद्यार्थी अध्ययनरत रहेछन् ? गणना गर्नुहोस् । [3]
  4. यदि सर्वेक्षणमा राय नै व्यक्त नगरेका 6 जना विद्यार्थीले लुम्बिनी उपयुक्त स्थान हो भनेको भए पोखरा मात्र उपयुक्त स्थान भन्ने र लुम्बिनी मात्र उपयुक्त स्थान भन्ने विद्यार्थीहरूको अनुपात कति हुने थियो ? [1]
  1. सबै ठाउँ उपयुक्त हुन्छ भन्ने विद्यार्थीको समूहको गणनात्मकता सङ्केत
     \(n(P \cap L \cap I) = 15\)
  2. भेनचित्रमा
  3. जम्मा विद्यार्थी संख्या \(n(U)\)
     भेनचित्रबाट
     n(U) = 25 + 15 + 30 + 0 + 0 + 0 + 15 + 6
     वाn(U) = 91
     त्यसैले, कक्षा १० मा जम्मा ९१ जना विद्यार्थी अध्ययनरत छन्।
  4. अनुपातको गणना
     यदि राय व्यक्त नगरेका ६ जनाले लुम्बिनी रोजेका भए:
     लुम्बिनी मात्र रोज्ने \(n_o(L) = 15 + 6 = 21\)
     पोखरा मात्र रोज्ने \(n_o(P) = 25\)
     अनुपात \(n_o(P) : n_o(L) = 25 : 21\) हुने थियो।