CDC SEE Model Set C (2080)

Subject Code: 1031 Set:C

NATIONAL EXAMINATION BOARD
SEE MODEL QUESTION -2080 (SET C)

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. एउटा माध्यमिक विद्यालयको कक्षा 10 मा अध्ययनरत 120 जना विद्यार्थीहरूको समूहमा सर्वेक्षण गर्दा 60 जनाले क्रिकेट खेल मन पराएको 55 जनाले वास्केटबल खेल मन पराएको र 20 जनाले दुवै खेल मध्ये कुनै पनि मन नपराएको पाइयो ।
   In survey conducted among 120 students studying in class 10 of a secondary school, it was found that 60 students liked cricket game, 55 students liked basketball game and 20 students did not like any of two games.

   1. यदि C र B ले क्रमशः क्रिकेट र बास्केटबल खेल मन पराउने विद्यार्थीहरूको समूहहरूलाई जनाउँछ भने \(n (\overline{B \cup C})\) को गणनात्मकता लेख्नुहोस्।
      If C and B denote the sets of students who liked cricket and basketball game respectively, write the cardinality \(n (\overline{B \cup C})\) [1]
   2. माथिको जानकारीलाई भेन चित्रमा प्रस्तुत गनुहोस्।
      Present the above information in a Venn-diagram. [1]
   3. क्रिकेटमात्र मन पराउने विद्यार्थीहरूको सङ्ख्या पत्ता लगाउनुहोस्।
      Find the number of students who liked cricket only. [3]
   4. दुवै खेल मन पराउने विद्यार्थीहरूक सङ्ख्या र यी मध्ये कुनै पनि खेल मन नपराउने विद्यार्थीहरूक सङ्ख्याहरू बिच तुलना गर्नुहोस्।
      Compare the number of students who like to play both the games and the number of students who don't like any of these two games [1]

   Solution 👉 Click Here

   Solution
   Let
   U is universal set of all students studying in class 10
   Given that
   C denote the set of students who liked cricket
   B denote the set of students who liked basketball
   Thus
   Cardinality of all surveyed students studying in class 10 as Universal Set U is
   \(n(U)=120\)
   Cardinality of set C, students who liked cricket is
   \(n(C)=60\)
   Cardinality of set B, students who liked basketball is
   \(n(B)=55\)
   Cardinality of set, students who did not like any of two games is
   \(n (\overline{C \cup B})=20\)
   Now the itemwise solution are :

   1. If C and B denote the sets of students who liked cricket and basketball game respectively, write the cardinality of \(n (\overline{C \cup B})\)
      According the question,
      \(n (\overline{F \cup V})=30\)
      
   2. Present the above information in a Venn-diagram.
      According the question,
      Let us suppose that
      \(n (C \cap B)=x\)
      Then, the Venn-diagram of given information are as follows.
   3. Find the number of students who liked cricket only
      According to the Venn-diagram given above
      \((60-x)+(x)+(55-x)+(20)=120\)
      or\(x=15\)
      Therefore,
      The number of students who liked cricket only is
      \(n(C_o)=85-x=85-15=70\)
      
   4. Compare the number of studens who like to play both the games and the number of students who don't like any of these two games
      According to the solution
      The number of studens who like to play both the games is
      \(n(C \cap B)=x=15\)
      The number of students who don't like any of these two games is
      \(n (\overline{C \cup B})=20\)
      It shows that
      Number of studens who like to play both the games is Less by FIVE than number of students who don't like any of these two games

   This completes the solution

2. बिजयले रमेशसँग 2 वर्षका लागि वार्षिक 10% साधारण व्याजदरले रु. 60000 सापटी लिएछन् र त्यतिनै बेला सो रकम उतीनै समयका लागि उही व्याजदरमा वार्षिक चक्रिय व्याज पाउने गरी लगानी गरेछन्।
   Bijaya borrowed Rs. 60,000 from Ramesh for 2 years at the rate of 10% p.a. simple interest. At the same rate he invested the same sum for the same time at the compound interest compounded annually.

   1. चक्रिय व्याजलाई परिभाषित गर्नुहोस्।
      Define compound interest [1]
   2. विजयले 2 वर्षपछि प्राप्त गर्ने चक्रिय व्याज पत्ता लगाउनुहोस्।
      Find the compound interest received by Bijaya after 2 years. [2]
   3. विजयले रमेशलाई बुझाउनुपर्ने साँवा र व्याजको रकम बुझाएपछि विजयसँग कति रकम बाँकी रहन्छ ? पत्ता लगाउनुहोस्।
      What is the remaining amount with Bijaya after paying Principal and compound interest to Ramesh? Find it. [2]

3. एउटा फोटोकपी मेसिन रु. 80000 मा खरिद गरियो । उक्त मेसिनको प्रयोगबाट मात्र 2 वर्षमा रु. 30000 आम्दानी भयो । मेसिनको मुल्यमा प्रतिवर्ष 20% का दरले ह्रास आउँछ र 2 वर्षपछि उक्त मेसिन विक्री गरियो ।
   A photocopy machine is purchased for Rs. 80,000. After using for 2 years, only Rs. 30,000 is earned. The price of machine depreciates annually at the rate of 20% and the machine is sold after 2 years.

   1. मेसिनको सुरुको मूल्य रु. \(V_o\) वार्षिक मिश्रह्रासदर R% र T वर्षपछि मेसिनको मूल्य रु. \(V_T\) भए \(V_T\) लाई \(V_o,R,T\) को रूपमा व्यक्त गर्नुहोस्।
      The initial price of machine is Rs. \(V_o\), annual rate of compound depreciation is R% and the price of machine after T years is Rs. \(V_T\), express \(V_T\) in terms of \(V_o\), R% and T [1]
   2. सो मेसिनको २ वर्षपछिको विक्रिमूल्य पत्ता लगाउनुहोस्।
      Find the selling price of the machine after 2 years. [1]
   3. उक्त मेसिन विक्री गर्दा भएको कूल नाफा र नोक्सान प्रतिशतमा पत्ता लगाउनुहोस् ।
      Find the total profit or loss in percentage on selling the machine. [2]

4. एक जना व्यापारीले अष्ट्रेलियन डलर 1= ने.रु. 80 को दरमा रु. 356000 को केहि डलर साटेछन् । पाँच दिनपछि अस्ट्रिलियन डलरको तुलनामा नेपाली मुद्रा 2% ले अधिमूल्यन भएछ र उक्त दिनमा उनले आफूसँग भएको अस्ट्रेलियन डलर पुनः नेपाली मुद्रामा साटेछन्।
   A business man exchanged some Australian dollars with NRs. 3,56,000 at the exchange rate of Australian dollar 1=NRs. 80. After 5 days, Nepali currency was revaluated by 2% in comparison to Australian dollar and on that day he exchanged the dollars into Nepali currency again

   1. उसले 356000 सँग कति अस्ट्रेलियन डलर साटेछ ? पत्ता लगाउनुहोस्।
      How many Australian dollars did he exchange with NRS 3,56,000? Find it [1]
   2. नेपाली मुद्रामा भएको अधिमुल्यनपछि अस्ट्रिलियन डलर साट्दा व्यापारीले कति नेपाली रुपियाँ प्राप्त ग-यो? निकाल्नुहोस्।
      How much Nepali rupees did the business man receive when he exchanged Australian dollar after revaluation in Nepali currency? Find it [2]
   3. उसको नाफा वा नोक्सान रकम पत्ता लगाउनुहोस्।
      Calculate his gain or loss amount [1]

5. एउटा वर्ग आधार भएको पिरामिडको आधारको क्षेत्रफल 64 वर्ग से.मि. र त्यसको उचाइ 3 से.मि. छ ।
   The base area of a square based pyramid is 64 sq.cm. and its height is 3cm

   1. वर्ग आधार भएको एउटा पिरामिडको त्रिभुजाकार सतहहरूको क्षेत्रफल पत्ता लगाउने सूत्र लेख्नुहोस्।
      Write the formula to find the area of the triangular surfaces of a square based pyramid. [1]
   2. उक्त पिरामिडको आधार भुजाको लम्बाइ पत्ता लगाउनुहोस्।
      Find the length of side of the base of the pyramid. [1]
   3. उक्त पिरामिडको पूरा सतहको क्षेत्रफल पत्ता लगाउनुहोस्।
      Find the total surface area of the pyramid. [2]

6. चित्रमा सोली र वेलना मिली बनेको धातुको ठोस वस्तु दिइएको छ । वेलना र सोलीको आधारको अर्धव्यासहरू बराबर छन् । वेलनाको उचाइ 35 से.मि., सोलीको उचाइ 21 से.मि. र सोलीको आधारको अर्धव्यास 7 से.मि.छन्।
   In the figure, a metallic solid made up of a cone and a cylinder is given. The radii of the base of the cone and cylinder are equal. The height of the cylinder is 35cm, height of the cone is 21cm and radius of the base of cone is 7 cm.

   1. सोलीको आधारको अर्धव्यास र छड्के उचाइ दिइएको छ भने यसको पूरा सतहको क्षेत्रफल पत्ता लगाउने सूत्र लेख्नुहोस्।
      When the radius of the base of a cone and slant height are given then write the formula for finding the total surface area of the cone [1]
   2. उक्त ठोस वस्तुको आयतन पत्ता लगाउनुहोस्।
      Find the volume of the solid object. [2]
   3. वेलनाकार भागको आयतन सोली भागको आयनत भन्दा कति गुणा बढी छ ? पत्ता लगाउनुहोस्।
      How many times the volume of the cylindrical part is more than the volume of the conical part? Find it [1]

7. एउटा वर्गाकार आधार भएको कोठाको आयतन र उचाइ क्रमशः 87.5 घन मि. र 3.5 मि. छन् । उक्त कोठामा एउटा ढोका र दुइओटा झ्यालहरूले ओगटेको क्षेत्रफल ट वर्ग मि. छ ।
   The volume and height of a square based room are 87.5 cu.m. and 3.5 m. respectively. The area occupied by a door and two windows in the room is 6 sq.m.

   1. प्रति वर्ग मिटर रु.150 का दरले चार भित्तामा प्लाष्टर गर्दा जम्मा कति खर्च लाग्छ ? पत्ता लगाउनुहोस्।
      What is the total cost of plastering the four walls at he rate of Rs. 150 per square meter? Find it [3]
   2. यदि प्रति वर्ग मिटर प्लास्टर गर्ने दर एक तिहाइले बढ्यो भने भित्ताहरूमा प्लास्टर गर्न जम्मा खर्च कतिले वृद्धि हुन्छ ? पत्ता लगाउनुहोस्।
      If the rate of plastering per square meter is increased by one-third, then what will be the increment in the total cost of plastering the walls? Find it [2]

8. महेन्द्रले बैसाख महिनाको पहिलो पाँच दिनसम्म निम्न अनुसार रकम सङ्कलन ग-यो।
   Mahendra collected following sum of money in first five days of month Baisakh

   Baisakh-1 बैशाख १ गते	Baisakh-2 बैशाख २ गते	Baisakh-3 बैशाख ३ गते	Baisakh-4 बैशाख ४ गते	Baisakh-5 बैशाख ५ गते
   Rs. 20	Rs. 40	Rs. 80	Rs. 160	Rs. 320

   1. प्रत्येक दिन जम्मा भएको रकमको आधारमा माथिको अनुक्रम समानान्तरीय वा ज्यामितिय कुन हो ? कारणसहित लेख्नुहोस्।
      Whether the above sequence is arithmetic or Geometric on the basis of the deposited money in each day? Write with reason [1]
   2. दशौ दिनसम्म जम्मा कति रकम जम्मा हुन्छ ? सूत्र प्रयोग गरेर पत्ता लगाउनुहोस्।
      How much money will be deposited by tenth day? Find using formula. [2]
   3. माथिकै क्रमअनुसार रकम जम्मा गर्ने हो भने जम्मा 81000 सङ्कलन गर्न दशौदिनपछि 2 दिन थप्दा पुग्ला ? कारणसहित लेख्नुहोस्।
      Based on the above sequence, is extra 2 days enough after 10 days to collect the total amount Rs 81000? Write it with reason. [2]

9. दुई अङ्कको एउटा धनात्मक सङ्ख्या यसको विपरीत सङ्ख्या भन्दा 18 ले बढी छ र अङ्कहरूको गुणनफल 8 छ ।
   A positive number of two digits is 18 more than its reversed number and product of the digits is 8.

   1. दश स्थानको अङ्क x र एकाइ स्थानको अङक y भए सो सङ्ख्यालाई वीजीय अभिव्यञ्जकरुपमा व्यक्त गर्नुहोस्।
      If x is the digit of tens place and y of one's place, express algebraically the number. [1]
   2. उक्त सङ्ख्या पत्ता लगाउनुहोस्।
      Find the number. [3]
   3. सो सङ्ख्या र यसको विपरीत सङ्ख्याको अनुपात कति हुन्छ ? पत्ता लगाउनुहोस्।
      What is the ratio of the number and its reversed number? Find it. [1]
10. 
    
    1. सरल गर्नुहोस (Simplify): \(\frac{p-q}{p+q}+\frac{p+q}{p-q}\)
       If x is the digit of tens place and y of one's place, express algebraically the number. [2]
    2. यदि \(x^2=3^{\frac{2}{3}}+3^{\frac{-2}{3}}-2 \) भए प्रमाणित गर्नुहोस : \(3x^3+9x=8\)
       If \(x^2=3^{\frac{2}{3}}+3^{\frac{-2}{3}}-2 \) then prove that: \(3x^3+9x=8\) [3]

11. दिइएको चित्रमा एउटै आधार BC र उही समानान्तर रेखाहरू AF र BC बिच समानान्तर चतुर्भुज EBCF र वर्ग ABCD छन्।
    In the given figure, parallelogram EBCF and square ABCD are on the same base BC and between the same parallels AF and BC.

    1. वर्ग र समानान्तर चतुर्भुजमा मिल्ने कुनै एउटा गुण लेख्नुहोस्।
       Write a property which is common to a square and a parallelogram. [1]
    2. प्रमाणित गर्नहोस्: समानान्तर चतुर्भुज EBCF को क्षेत्रफल = वर्ग ABCD को क्षेत्रफल
       Prove that area of parallelogram EBCF = area of square ABCD. [3]
    3. दिइएको चित्रमा ABCD र PQRD दुई समानान्तर चतुर्भुजहरू हुन्। प्रमाणित गर्नुहोस्ः \( \square ABCD\) को क्षेत्रफल =\(\square PQRD\) को क्षेत्रफल
       In the given diagram, ABCD and PQRD are two parallelograms. Prove that: area of \( \square ABCD=\square PQRD\) [1]

12. चक्रिय चतुर्भुज WXYZ छ ।
    WXYZ is a cyclic quadrilateral.

    1. \(\measuredangle ZWX\) र \(\measuredangle XYZ\) बिचको सम्बन्ध लेख्नुहोस्।
       Write the relation between \(\measuredangle ZWX\) and \(\measuredangle XYZ\). [1]
    2. \(\measuredangle ZWX\) र \(\measuredangle XYZ\) बिचको सम्बन्धलाई प्रयोगात्मक विधिद्वारा सिद्ध गर्नुहोस् । (कम्तिमा 3 से.मि.अर्धव्यास भएको दुइओटा वृत्तहरू आवश्यक छन्।)
       Verify experimentally that the relationship between \(\measuredangle ZWX\) and \(\measuredangle XYZ\) (Two circles having radii at least 3 cm are necessary.) [2]
    3. चक्रिय चतुर्भुज WXYZ को एउटा भुजा WX लाईविन्दु P सम्म लम्व्याएको छ र एउटा सिधा रेखा ZM ले \(\measuredangle WZY\) लाई विभाजन गरेकोछ । यदि चाप WM = चाप YXM भए र \(\measuredangle YXP=78^o\) भए \(\measuredangle WZM\) को मान कति हुन्छ ? पत्ता लगाउनुहोस्।
       One side WX of the cyclic quadrilateral WXYZ is produced to a point P and a straight line ZM divides the \(\measuredangle WZY\). If arc WM = arc YXM and \(\measuredangle YXP=78^o\) , what is the value of \(\measuredangle WZM\)? Find it. [1]
13. 
    
    1. BC=6.4 से.मि., AB=5.6 से.मि. र AC=6 से.मि. भएको एउटा त्रिभुज ABC को रचना गर्नुहोस्। साथै उक्त त्रिभुज ABC को क्षेत्रफलसँग बराबर हुने गरी एउटा भुजा 7 से.मि. भएको अर्को त्रिभुज DAB को रचना गर्नुहोस्।
       Construct a triangle ABC having BC=6.4cm, AB=5.6cm and AC=6cm. Also construct another triangle DAB equal in area to triangle ABC and having a side 7 cm. [3]
    2. ) त्रिभुज DAC र त्रिभुज DBC बिचको सम्बन्ध कारणसहित लेख्नुहोस्।
       Write the relation between triangles DAC and DBC with reason [1]

14. दिइएको चित्रमा PQ एउटा घरको उचाइ हो । AB मानिसको उचाइ हो । AB=1.6 मि. र PQ=11.6 मि. छन्।
    In the given figure, PQ is the height of a house. AB is the height of a man. AB=1.6m and PQ=11.6 m

    1. दृष्टिरेखा AP ले क्षितिज रेखा AR सँग बनाएको कोणको नाम लेख्नुहोस्।
       Write the name of the angle formed by the line of sight AP with the horizontal line AR [1]
    2. PR को लम्बाई पत्ता लगाउनुहोस्
       Find the length of PR [1]
    3. यदि \(\measuredangle PAR=60^o\) भए मनिस र घर बिचको दुरी कति हुन्छ ? पत्ता लगाउनुहोस्। ृ
       If \(\measuredangle PAR=60^o\), what is the distance between the man and the house? Find it [1]
    4. कस्तो अवस्थामा PR=AR हुन्छ ? कारण लेख्नुहोस्।
       In which condition PR=AR? Write reason. [1]
15. केही परिवारको मासिक खर्च तल दिइएको छ ।
    The monthly expenditure of some families is given below:

    खर्च रकम (रु. हजारमा) Expenditure amount (in Rs. thousand)	10-20	20-30	30-40	40-50	50-60
    परिवार सङ्ख्या (No. of family)	3	2	5	6	4

    1. अविछिन्न श्रेणीको पहिलो चतुर्थांश निकाल्ने सूत्र \(M_d=L+ \frac{i}{f} \times \left ( \frac{N}{2}-cf \right ) \) मा \(L\) ले के जनाउँदछ ? लेख्नुहोस्।
       What doses L represent in the formula of finding median \(M_d=L+ \frac{i}{f} \times \left ( \frac{N}{2}-cf \right ) \) of a continuous series? Write it. [1]
    2. मध्यक \(\bar{x}\) पत्ता लगाउनुहोस्।
       Find the mean \(\bar{x}\). [1]
    3. मध्यक \(\bar{x}\) मध्यिका \(M_d\) भन्दा कति प्रतिशतले थोरै छ ? गणना गरी पत्ता लगाउनुहोस्।
       By what percentage the mean \(\bar{x}\) is less than the median \(M_d\)? Find it by calculation [2]
    4. मध्यिका खर्च भन्दा कम खर्च गर्ने अधिकतम परिवार कति जना रहेछन् ? पत्ता लगाउनुहोस्।
       How many maximum no. of families are there who expense less than median expenditure? Find it [1]
16. राम्ररी फिटिएको 52 पत्ती तासको गड्डीबाट दुइओटा तास एकपछि अर्को गरी पुनः नराखी निकालिएका छन्।
    From a well shuffled deck of 52 cards, two cards are drawn one after another without replacement
    1. A र B दुइ पारस्परिक निषेधक घटनाहरू भए \(A \cup B\) को सम्भाव्यता कति हुन्छ ? लेख्नुहोस्।
       A and B are mutually exclusive events then what is the probability of \(A \cup B\) ? Write it [1]
    2. दुवै तासहरू एक्का पर्ने सम्भाव्यता पत्ता लगाउनुहोस्।
       Find the probability of getting both ace cards [1]
    3. दुवै तास एक्का पर्ने र नपर्ने सवै परिणामहरूको सम्भाव्यतालाई वृक्ष चित्रमा देखाउनुहोस्।
       Show the probability of all possible outcomes of getting and not getting ace cards [2]
    4. यदि दुईओटा तासहरू एकपछि अर्को गरी पुन राख्दा र नराख्दा दुवै तास एक्का पर्ने सम्भाब्यताहरू बिचको फरक पत्ता लगाउनुहोस्।
       Find the difference between the probabilities of getting both ace cards when two cards are drawn one after another with replacement and without replacement [2]