Solution: Grade 10 : CDC Model Question.
Model Question Paper
2080
| Subject: Mathematics | Full Marks: 75 |
| Time: 3 hrs. | Grade:10 |
1. श्री शारदा माध्यमिक विद्यालयको कक्षा 10 मा अध्ययनरत विद्यार्थीहरुलाई 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 विद्यार्थीहरुले तीनै ओटा ठाँउ उपयुक्त हुने बताउँदा 5 जनाले कुनै राय नै व्यक्त गरेनन् ।
(क) P, L र I ले क्रमशः पोखरा, लुम्बिनी र इलाम उपयुक्त हुन्छ भन्ने विद्यार्थीहरुको समूहलाई जनाउँछ भने सबै ठाउँ उपयुक्त हुन्छ भन्ने विद्यार्थीको समूहलाई गणनात्मकता सङ्केतमा लेख्नुहोस् । [1K]
(ख) मााथिको जानकारीलाई भेन चित्रमा प्रस्तुत गर्नुहोस् ।[1U]
(ग) शारदा माध्यमिक विद्यालयमा कक्षा 10 मा कति जना विद्यार्थी अध्ययनरत रहेछन् ? गणना गर्नुहोस् ।[3A]
(घ) यदि सर्वेक्षणमा राय नै ब्यक्त नगरेका 5 जना विद्यार्थीले लुम्बिनी उपयुक्त स्थान हो भनेको भए पोखरा मात्र उपयुक्त स्थान भन्ने र लुम्बिनी मात्र उपयुक्त स्थान भन्ने विद्यार्थीहरुको अनुपात कति हुने थियो ?[1HA]
[ In a survey conducted to determine suitable educational trips for students studying in Class 10 at Shree Sharada Secondary School, 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. When 15 students from the class said that all three are suitable destinations, 5 students did not provide any opinion.
(a) 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]
(b) Show the above information in a Venn diagram.[1U]
(c) How many students are studying in Class 10 in Sarada Secondary School? Calculate.[1A]
(d) In a survey, suppose out of those five students who didn't express their opinion indicate Lumbini as a best place then what will be the ratio of students who consider only Pokhara to the students who consider only Lumbini as the suitable destination? [1HA] ]
1. (a) Solution:
1. (b) Solution:
Venn- Diagram
1. (c) Solution:
From Venn-diagram,
1. (d) Solution:
2. बिपिनले 2 वर्षका लागी रु 1,00,000 कुनै एउटा बैंकमा जम्मा गर्न चाहेका छन् । बैंकले प्रतिवर्ष 10% चक्रिय व्याजदरका दरले बिपिनलाई तीनओटा विकल्पहरु (बार्षिक चक्रीय ब्याज, अर्धबार्षिक चक्रीय ब्याज र त्रैमासिक चक्रीय ब्याज) दिएको छ ।
(क) माथिका तीन विकल्पमध्ये कुन विकल्प प्रयोग गर्दा बिपिनलाई बढी ब्याज प्राप्त हुन्छ ? लेख्नुहोस ।[1K]
(ख) उनले 2 वर्षको अन्त्यमा अर्धवार्षिक चक्रीय ब्याज अनुसार कति चक्रिय मिश्रधन प्राप्त गर्न सक्छन् ?[2U]
(ग) बिपिनले 1 वर्षको अन्त्यमा अर्धवार्षिक चक्रीय ब्याज अनुसार प्राप्त भएको जम्मा रकम झिकेर पुन त्रैमासिक चकीय ब्याज पाउने गरी बाँकी अवधिको लागि जम्मा गरेछन् भने अन्त्यमा कति रकम पाउँछन् ?[2A]
[ Bipin wants to deposit Rs 1,00,000 in a bank for 2 years. The bank has given Bipin three options (annual compound interest, half-yearly compound interest and quarterly compound interest) at the rate of 10% compound interest per year.
(a) From the above mentioned option which option is beneficial for Bipin to gain more interest? [1K]
(b) How much compound amount can he get at the end of 2 years at the rate of half yearly compound interest?[2U]
(c) At the end of 1 year, if Bipin withdraws the amount received according to semi-annual compound interest and then deposits it for the rest of the period to receive quarterly interest, how much amount will he get at the end? [2A] ]
2. (a) Solution:
Bipin will get more interest by selecting quarterly compound interest.
2. (b) Solution:
2. (c) Solution:
Case - II
3. साजनले आँफूसँग भएको रु 1,00,00,000 बाट रु. 30,00,000 को कार र रु. 70,00,000 को जग्गा किनेछन् । 2 वर्षसम्म कारको मूल्य वार्षिक 5% का दरले चक्रीय ह्रास हुँदै गएछ भने जग्गाको मूल्य निश्चित प्रतिशतले चक्रिय वृद्धि हुदै गएको छ ।
(क) चकीय ह्रास निकाल्ने सूत्र लेख्नुहोस् ।[1K]
(ख) 2 वर्षपछि उक्त कारको मूल्य कति पुग्छ, पत्ता लगाउनुहोस् ।[1U]
(ग) 2 वर्षपछि कार र जग्गाको जम्मा मूल्य रु. 1,05,72,700 भयो भने जग्गाको मूल्यमा कति प्रतिशतको चक्रीय बृद्धि भएको रहेछ ? गणना गर्नुहोस् ।[2HA]
[ Sajan has Rs 1,00,00,000 with him. Sajan purchased a car for Rs. 30,00,000 and land for Rs. 70,00,000. For 2 years, the price of the car has been decreasing at a compound rate of 5% per annum, while the price of land has been increasing at a certain compound rate .
(a) Write the formula to find out the compound depreciation.[1K]
(b) What will be the price of a car after two years ? Calculate.[1U]
(c) After 2 years the total value of car and land is Rs 1,05,72,700, what is the increase compound rate in the price of land? Calculate. [2HA] ]
3. (a) Solution:
3. (b) Solution:
3. (c) Solution:
For land
4. प्रविनले विदेश जानका लागि अमेरिकी डलर साट्न बैङ्क गयो । उक्त दिनको मुद्रा विनिमय दर अनुसार अमेरिकन डलर 1 को खरिद दर ने.रु. 131.05 र विकी दर ने.रु. 131.65 छ ।
(क) प्रविनले नेपाली रुपैयाँ 1,57,980 को अमेरिकी डलर साट्दा कति डलर पाउछन् ?[2A]
(ख) प्रविन घरायसी कारणले विदेश जान नसक्ने भएपछि सोही दिन उनीले साटेको डलरबाट कति नेपाली रुपैयाँ प्राप्त गर्दछन् ?[1A]
(ग) प्रविनले गरेको कारोवारबाट उनलाई कति रुपियाँ नाफा वा नोक्सान के हुन्छ कारण सहित पुष्टि गर्नुहोस् ।[1HA]
[ Pravin went to the bank to exchange US dollars in order to go abroad. According to the currency exchange rate of that day, the buying rate of 1 US dollar was Rs.131.05 and the selling rate was Rs. 131.65.
(a) How many dollars will he gets in exchange of Rs 1,57,980 ?[2A]
(b) How many Nepali rupees will he gets back from the exchanged dollars on the same day incase if he cannot go abroad due to family issue?[1A]
(c) How much profit or loss will he get from this transaction? Write with reason. [1HA] ]
4. (a) Solution:
Buying rate: $1 = Rs 131.05
Selling rate: $1=131.65
4. (b) Solution:
4. (c) Solution:
Thus, he will get Rs 720 loss from this transaction.
5. वर्ग आधार भएको पिरामिडको उचाइ 12 cm र आधार भुजाको नाप 10 cm छ ।
(क) वर्ग आधार भएको पिरामिडमा कतिओटा त्रिभुजाकार सतहहरु हुन्छन् ?[1K]
(ख) उक्त पिरामिडको आयतन कति हुन्छ, पत्ता लगाउनुहोस् ।[1U]
(ग) त्रिभुजाकार सतहहरुमा प्रतिवर्ग सेमी 1.50 पैसाका दरले रङ लगाउँदा जम्मा कति खर्च लाग्छ, पत्ता लगाउनुहोस् ।[2A]
[The height of the square based pyramid is 12 cm and the length of base is 10 cm.
(a) How many triangular faces does a square base pyramid have?[1K]
(b) Find the volume of the pyramid.[1U]
(c) Find the total cost of painting triangular surfaces at the rate of 1.50 paisa per square cm.[2A] ]
5. (a) Solution:
A square based pyramid have four triangular faces.
5. (b) Solution:
5. (c) Solution:
6. अर्धगोला र सोली मिलेर बनेको धातुको ठोस वस्तु दिइएको छ । सोलीको उचाइ 10 cm
र आधारको व्यास 6 cm छ । [ [π = 3.14]
[ A metallic solid made up of a hemisphere and a cone is given. The height of the cone is 10 cm and the diameter of the base is 6 cm. [ π = 3.14]
(क) सोलीको उचाइ र आधारको अर्धव्यास दिएको अवस्थामा छडके उचाइ कसरी पत्ता
लगाइन्छ ? लेख्नुहोस् । [1K]
[ How is the slant height of the cone found when the height of the cone and the radius of the base are given? Write.[1K] ]
(ख) उक्त ठोस वस्तुको आयतन पत्ता लगाउनुहोस् । [2U]
[ Find the volume of the solid object.[2U] ]
(ग) उक्त धातुको ठोस वस्तुलाई पगालेर 3 cm अर्धव्यास भएको बेलनाकार वस्तुमा
परिणत गरियो भने उक्त बेलनाको उचाइ कति हुन्छ ? गणना गर्नुहोस् ।[1HA]
[If a metallic solid is melted into a cylindrical object of radius 3 cm, what is the height of the cylinder ? Calculate. [1HA] ]
6. (a) Solution:
6. (b) Solution:
6. (c) Solution:
7. दुई परिवारले पानी पिउनका लागि बनाइएको आयतकार ट्याङ्कीको भित्री लम्बाइ, चौडाइ र उचाइ क्रमशः 3m, 1.5m र 1.6m छ ।
(क) उक्त ट्याङ्कीको भित्री चारओटा भित्तामा प्रति 3 वर्गमिटर रु. 100 का दरले रङ लगाउँदा जम्मा कति खर्च लाग्छ ? गणना गर्नुहोस् । [3A]
(ख) उक्त भरिएको ट्याङ्कीको पानी उपभोग गरेबापत दुवै परिवारले बराबर रकम तिर्छन् । प्रतिलिटर 50 पैसाका दरले एक परिवारले कति रकम तिर्नुपर्ला ? [2HA]
[The inner length, breadth and height of a rectangular tank made for drinking water by two families are 3 m, 1.5m and 1.6m respectively.
(a) What is the total cost of painting the inner four walls of the tank at the rate of 100 per 3 square metres? Calculate. [3A]
(b) Both families pay equal amounts for consuming water from a full tank. At the rate of 50 paisa per litre, how much will a family have to pay? [2HA] ]
7. (a) Solution:
7. (b) Solution:
8. अन्जुले छोरीको खुत्रुकेमा अघिल्लो दिनको दोब्बर हुने गरी रकम जम्मा गर्छिन् । उनीले पहिलो पाँच दिनमा जम्मा गरेको रकम तलको तालिकामा देखाइएको छ ।
[Anju deposits the double amount of money then the previous day in her daughter's piggy bank. The amount she collected in the first five days is shown in the table below.]
| First day
| Second day | Third day | Forth day | Fifth day |
| Rs 5 | Rs 10 | Rs 20 | Rs 40 | Rs 80 |
(क) अन्जुले छोरीको खुत्रुकेमा जम्मा गरेको रकमबाट बनेको अनुक्रम समानान्तरीय वा गुणोत्तर कुन हो ? [1K]
[Which is the sequence, Arithmetic or Geometric, formed from the amount deposited by Anju in her daughter's piggy bank? [1K] ]
(ख) यही क्रममा रकम जम्मा गर्दै जाने हो भने 10 औं दिन सम्म खुत्रुकेमा कति रकम जम्मा हुन्छ ? [2U]
[ If the amount is deposited in this order, how much will be deposited in the Piggy bank till the 10th day? [2U] ]
(ग) माथिकै अनुक्रम अनुसार रकम जम्मा गर्ने हो भने खुत्रुकेमा रु. 20000 पुर्याउन 10 औं दिनपछि थप 2 दिन भए पुग्ला ? कारण सहित लेख्नुहोस् । [2HA]
[If she deposits the amount according to the sequence to reach Rs 20000, will 2 more days after the 10th day be enough? Write with reasons. [2HA] ]
8. (a) Solution:
Geometric sequence is formed from the amount deposited by Anju in her daughter's piggy bank.
8. (b) Solution:
8. (c) Solution:
9. एउटा आयताकार खेतको लम्बाइ चौडाइको दोब्बर छ र त्यसको क्षेत्रफल 72 वर्ग मिटर छ।
(क) वर्ग समिकरणको स्तरीय स्वरुप लेख्नुहोस् । [1K]
(ख) उक्त खेतको लम्बाइ र चौडाइ पत्ता लगाउनुहोस् ।[3A]
(ग) उक्त आयताकार खेतमा (6x3) वर्ग मिटरका कति ओटा टुक्राहरु तयार गर्न सकिएला ? गणना गर्नुहोस् ।[1A]
[ The length of a rectangular field is twice the width and its area is 72 square metres.
(a) Write the quadratic equation in standard form.[1K]
(b) Find the length and width of the field.[3A]
(c) How many plots of (6x3) square metres can be prepared in a rectangular field? Calculate [1A] ]
9. (a) Solution:
The standard form of quadratic equation is ( )
9. (b) Solution:
9. (c) Solution:
10. (क) हल गर्नुहोस् (Solve): [3A]
Solution:
(ख) सरल गर्नुहोस् ( Simplify):[2U]
Solution:
11. सँगैको चित्रमा त्रिभुज LMZ, समानान्तर चतुर्भुजहरु XYZM र NLZM एउटै आधार MZ र उही समानान्तर रेखाहरु MZ र XL का बीचमा बनेका छन् ।
[In the given figure, triangle LMZ, parallelograms XYZM and NLZM are standing on the same base MZ and between same parallel lines MZ and XL]
(क) समानान्तर चतुर्भुज XYZM र समानान्तर चतुर्भुज NLZM को क्षेत्रफल बीचको सम्बन्ध लेख्नुहोस् | [1K]
[Write the relationship between the area of Parallelogram XYZM and parallelogram NLZM [1K] ]
(ख) त्रिभुज MLZ को क्षेत्रफल समानान्तर चतुर्भुज NLZM को क्षेत्रफलको आधा हुन्छ भनी प्रमाणित गर्नुहोस् । [2U]
[Prove that the area of triangle MLZ is half the area of parallelogram NLZM. [2U] ]
(ग) सँगैको चित्रमा AB //CE र AC // DE छ । यदि AB को मध्यबिन्दु D छ भने △DBC को क्षेत्रफल △CDE को क्षेत्रफलसँग बराबर हुन्छ भनी प्रमाणित गर्नुहोस् ।[2HA]
[AB //CE and AC // DE are in the given figure. If D is the midpoint of AB , Prove that the area of △DBC is equal to the area of △CDE [2HA] ]
11. (a) Solution:
Area of parm. XYZM = Area of Parm.NLZM
11. (b) Solution:
Area of triangle MLZ Area of parallelogram NLZM. [ Diagonal ML bisects the parallelogram. ]
11. (c) Solution:
12. केन्द्रविन्दु O भएको वृत्तमा एउटै चाप LP मा आधारित केन्द्रिय कोण ∠LOP, परिधिका कोणहरु ∠LMP र ∠LNP छन् ।
(क) परिधिका कोणहरु ∠LMP र ∠LNP बिचको सम्बन्ध लेख्नुहोस् । [1K]
(ख) केन्द्रिय कोणको नाप ( 9x + 2 )° र परिधि कोणको नाप (4x + 5) ° भए x को मान पत्ता लगाउनुहोस् । [1U]
(ग) परिधिका कोणहरु ∠LMP र ∠LNP बिचको सम्बन्ध प्रयोगात्मक रुपमा पुष्टि गर्नुहोस् ।( कम्तिमा 3 cm अर्धव्यास भएका दुईओटा वृत्तहरु आवश्यक छन् ।) [2A]
[ In a circle with centre O, the central angle ∠LOP, the circumcircle angles are ∠LMP and ∠LNP are standing on same arc LP.
(a) Write the relationship between the circumcircle angles ∠LMP and ∠LNP.[1K]
(b) Find the value of x if the measure of the central angle is (9x + 2)° and the measure of the circumference angle is (4x + 5)°. [1U]
(c) Verify experimentally the relationship between the circumcircle angles ∠LMP and ∠LNP. (Two circles with a radius of at least 3 cm are required.) [2A] ]
12. (a) Solution:
[ They are standing on same arc LP ]
12. (b) Solution:
12. (c) Solution:
Experimental Verification:
Measurement Table:
Conclusion: The inscribed angles standing on same arc are equal.
13. (क) भुजा PQ= 7 cm, QR = 5 cm र ∠PQR = 120° हुने त्रिभुज PQR को रचना गरी उक्त त्रिभुजको क्षेत्रफलसँग बराबर क्षेत्रफल हुने त्रिभुज SQR को रचना गर्नुहोस् । [3A]
[ Construct a triangle PQR with side PQ = 7 cm, QR = 5 cm and ∠PQR = 120° and construct a triangle SQR whose area is equal to the area of the triangle. [3A] ]
(ख) दिइएको चित्रमा BC = CD र AE // BD छ भने त्रिभुज ABC
र त्रिभुज BDE बिचको सम्बन्ध कारण सहित लेख्नुहोस् ।[1HA]
[In the given figure, if BC = CD and AE // BD, Write the relationship between triangle ABC and triangle BDE with reasons. [1HA] ]
13. (a) Solution:
Here, Area of triangle PQR is equal to the area of triangle SQR.
13. (b) Solution:
Construction: Let's join A and D.
14. चित्रमा देखाएअनुसार AB = 10.45m उचाइमा रहेको बाँदरले CD = 1.45m उचाइ भएको केटालाई हेर्दा अवनती कोण 45° बनेको छ ।
[ As shown in the figure, a monkey whose height AB = 10.45m looks at a boy whose height is CD = 1.45m makes an angle of depression of 45°.]
(क) केटाले बाँदरको दृष्टिबिन्दुमा हेर्दा उन्नतांश कोण कति पाउँछ ? [1K]
[What is the angle of elevation of the monkey's point of view from the boy ?[1K]]
(ख) बाँदरको दृष्टिबिन्दु केटाको उचाइ भन्दा कति मिटरले माथि छ, पत्ता लगाउनुहोस् ।[1U]
[ By how many metres is the monkey's point of view above the boy's height, find out.[1U]]
(ग) रुखदेखि केटासम्मको दुरी पत्ता लगाउनुहोस् ।[1A]
[Find the distance between the boy and the tree. [1A] ]
(घ) बाँदरले केटालाई हेर्दा अवनतीकोण 30° बनाउन बाँदर अहिलेको स्थानबाट कति मिटर तल वा माथी जानु पर्छ ? [1HA]
[ When the monkey looks at the boy, how many metres down or up must the monkey go from its current position to make the angle of depression 30°? [1HA] ]
14. (a) Solution:
Thus the angle of elevation of the monkey's point of view from the boy is .
14. (b) Solution:
Thus, the monkey's point of view is 9 m above the boy's height.
14. (c) Solution:
Thus the distance between the boy and the tree is 9 m.
14. (d) Solution:
Thus, the monkey must go down 3.8m from its current position to make the angle of depression 30°
15. जनता माध्यमिक विद्यालयका 40 जना विद्यार्थीले गणित विषयमा प्राप्त गरेको प्राप्ताङ्कलाई तलको तालिकामा दिइएको छ ।
[The marks obtained by 40 students of Janata Secondary School in Mathematics are given in the table below.]
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| No. of Students | 4 | 6 | 8 | 5 | 7 | 10 |
(क) मध्यिका पत्ता लगाउने सूत्र मा ले के जनाउँछ । [1K]
[What does i represent in the formula for finding the median (Md). [1K] ]
(ख) दिइएको तथ्याङ्कबाट मध्यिका पत्ता लगाउनुहोस् । [2U]
[Find the median from the given data.[2U] ]
(ग) दिइएको तथ्याङ्कबाट औषत प्राप्ताङ्क गणना गर्नुहोस् । [2A]
[Calculate the average score from the given data. [2A] ]
(घ) विद्यार्थीहरुको औसत प्राप्ताङ्क 30 बनाउन 50-60 वर्गान्तरका विद्यार्थी सङ्ख्या कति हुनु पर्छ ? गणना गरी लेख्नुहोस् । [ 1HA ]
[What should be the number of students in class 50-60 in order to make 30 as the average score of students? Calculate and write. [ 1HA ]
15. Solution:
15. (a) Solution:
represents the class interval.
15. (b) Solution:
15. (c) Solution:
15. (d) Solution:
16. राम्रोसँग फिटिएको 52 पत्ती तासको गड्डीबाट नहेरिकन दुईओटा तासहरु एकपछि अर्को गरी पुन: नराखीकन झिकिएको छ ।
(क) यदि A र B दुई ओटा अनाश्रित घटनाहरू हुन् भने P (A∩B) पत्ता लगाउने सूत्र के हुन्छ, लेख्नुहोस् । [1K]
(ख) दुवै तास अनुहार भएको पर्ने सम्भाव्यता कति हुन्छ, पत्ता लगाउनुहोस् ।[1U]
(ग) अनुहार भएको तास पर्ने र नपर्ने सबै सम्भावित परिणामहरुको सम्भाब्यतालाई वृक्षचित्रमा देखाउनुहोस् ।[2A]
(घ) यदि दुईओटा तासहरु एकपछि अर्को गरी पुन: राख्दा दुवै तास अनुहार भएको पर्ने सम्भाव्यता दुवै तास एक्का पर्ने सम्भाव्यता भन्दा कति गुणा बढी हुन्छ ? [1HA]
[Two cards are drawn randomly from a well shuffled deck of 52 playing cards.
(a) If A and B are two independent events, then write down the formula to find P(A∩B). [1K]
(b) Find the probability of getting both faced cards. [1U]
(c) Show the probabilities of all possible outcomes of getting and not getting faced cards in a tree diagram. [2A]
(d) If two cards are drawn randomly one after another with replacement, how many times more is the probability that both are faced cards than the probability that both cards are ace?[1HA] ]
16. (a) Solution:
16. (b) Solution:
Let be the event of getting faced card in first draw and be the event of getting faced card in second draw.
Then, and
16. (c) Solution:
Let be the event of getting faced cards and be the event of not getting faced cards.
16. (d) Solution:
Thus, the probability of getting both faced cards is 9 times more than the probability of getting both ace.
Let and be the event of getting an ace in first and second draw respectively.
Let and be the event of getting faced cards in first and second draw respectively.
Therefore, the probability of getting both faced cards is 9 times the probability of getting both ace.
Thus, the probability of getting both faced cards is 8 times more than the probability of getting both ace.
Thank You
