Class 10 Compulsory Mathematicsकक्षा १० अनिवार्य गणित — SEE notes & solutions

कुनै गाउँको 120 घरधुरीमा गरिएको सर्वेक्षणमा 70 घरधुरीले होमस्टेको व्यवसाय र 50 घरधुरीले कृषि व्यवसाय गर्छन् । 30 घरधुरीले अन्य काम गर्छन् । होमस्टे र कृषि व्यवसाय गर्ने घरधुरीहरूको समूहलाई क्रमशः H र A ले जनाइएका छन् ।

In the survey conducted on 120 households of a village, 70 households are doing homestay business, 50 households are doing agriculture business and 30 households do other work. The sets of household doing homestay and agriculture business are denoted by H and A respectively.

(a) होमस्टे र कृषिमध्ये कुनै पनि व्यवसाय नगर्नेको संख्यालाई गणनात्मकता सङ्केतमा लेख्नुहोस् ।

Write the cardinality notation of the number of households who do not do any of the homestay and agriculture business.

(b) माथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् ।

Present the above information in venn-diagram.

(c) एउटा मात्र व्यवसाय गर्ने घरधुरीको सङ्ख्या निकाल्नुहोस् ।

Find the number of households doing only one business.

(d) अन्य काम गर्ने 10 घरधुरीले होमस्टे व्यवसाय सुरु गर्न थाले भने होमस्टे र कृषि व्यवसाय गर्ने घरधुरीको अनुपात निकाल्नुहोस् ।

If 10 households who do other work start home stay business, find the ratio of homestay and agriculture business households.

रमेशले बैङ्कवाट रु.2,00,000 प्रति वर्ष 7% का दरले वार्षिक चक्रीय व्याजमा ऋण लिएछन् । केही समयपछि साँवाँ र व्याज सहित रु. 2,28,980 बैङ्कमा बुभाएछन् ।

Ramesh borrowed the loan Rs.2,00,000 from the bank at annual compound interest rate of 7% per annum. After some time, he repaid Rs.2,28,980 including the principal and interest to the bank.

(a) रमेशले व्याजमात्र कति बुभाएछन् ? पत्ता लगाउनुहोस् ।

How much interest has Ramesh paid? Find it.

(b) रमेशले उक्त ऋण कति वर्षको लागि प्रयोग गरेछन् ? पत्ता लगाउनुहोस् ।

For how many years has Ramesh used the loan? Find it.

(c) यदि व्याजदर 1% ले घटायो भने रमेशले तिर्नुपर्ने मिश्रधन कति हुन्छ ? पत्ता लगाउनुहोस् ।

If the interest rate is reduced by 1%, how much amount would be paid by Ramesh? Find it.

गाउँ A को हालको जनसङ्ख्या 4500 र गाउँ B को 5000 छ । गाउँ A को वार्षिक जनसङ्ख्या वृद्धिदर 2% छ ।

The present population of village 'A' is 4500 and village B is 5000. The annual population growth rate of village A is 2%.

(a) T वर्षपछिको जनसङ्ख्या \(P_T = P\left(1 + \frac{R}{100}\right)^T\) मा P ले के जनाउँछ ? लेख्नुहोस् ।

What does P denote in the population after T years \(P_T = P\left(1 + \frac{R}{100}\right)^T\)? Write it.

(b) यदि गाउँ A मा 1 वर्ष पछि 200 जना बसाइँसराइ गरी थपिन आए भने, 1 वर्षपछि जनसङ्ख्या कति होला ? पत्ता लगाउनुहोस् ।

If 200 people are added by migration in the village 'A' after 1 year, what will be the population after 1 year? Find it.

(c) यदि गाउँ A कै वृद्धिदर बराबर गाउँ B को जनसंख्या घटेमा 2 वर्षपछि गाउँ B को जनसंख्या कति हुन्छ ? पत्ता लगाउनुहोस् ।

If the population of village B decreases by the same growth rate of village A, what will be the population of village B after 2 years? Find it.

रीता अमेरिकावाट नेपाल आउँदा साथमा 2500 अमेरिकी डलर ($) लिएर आएकी रहिछन् । उनी नेपाल आउँदा अमेरिकी डलरको विनिमयदर निम्नानुसार रहेको थियो ।

खरिद दर \$1 = NRs. 127.35 र विक्रीदर \$1 = NRs. 127.95

When Rita came to Nepal from America, she brought 2500 American dollars ($). When she came to Nepal, the exchange rate of American dollar was as follows.

\$1 = NRs. 127.35 buying rate and \$1 = NRs. 127.95 selling rate

(a) रीताले बैंकवाट नेपालमा रुपियाँ साट्दा कुन विनिमय दर प्रयोग हुन्छ ? लेख्नुहोस् ।

Which exchange rate is used to exchange Nepali currency by Rita from the bank? Write it.

(b) रीताले उनीसँग भएको अमेरिकी डलरलाई नेपाली रुपैयामा साटी पुनः दुई दिन पछि नेपाली रुपैयालाई अमेरिकी डलरमा साट्दा उनलाई कति फाइदा वा घाटा हुन्छ ? पत्ता लगाउनुहोस् ।

What is the profit or loss for Rita if she exchanges the American dollars into Nepali currency and then exchanges Nepali currency into American dollars after two days? Find it.

(c) सोही दिन \$1 = ने.रु. 127.35 र ने.रु. 160 = भा.रु. 100 थियो भने भा.रु. 1,20,000 सँग कति डलर साट्न सकिन्छ ? निकाल्नुहोस् ।

On the same day, the exchange rate of \$1 = NRs. 127.35 and NRs. 160 = Indian Rs. 100. How many dollars can be exchanged with Indian Rs. 1,20,000? Calculate it.

संगैको चित्र, वर्ग आधार भएको एउटा पिरामिडको हो । त्यसको आधारको प्रत्येक भुजा 6 मिटर र ठाडो उचाई 4 मिटर छ ।

The diagram alongside is of a square based pyramid. Its each side of base is 6 meter and vertical height is 4 meter.

[Figure: Square based pyramid with base side 6m and vertical height 4m]

(a) पिरामिडमा भएको सबै त्रिभुजाकार सतहहरूको क्षेत्रफल पत्ता लगाउने सूत्र लेख्नुहोस् ।

Write the formula for finding the area of all triangular surfaces of pyramid.

(b) उक्त पिरामिडको आयतन पत्ता लगाउनुहोस् ।

Find the volume of the pyramid.

(c) पिरामिडको पूरा सतहको क्षेत्रफल निकाल्नुहोस् ।

Find the total surface area of the pyramid.

दिइएको ठोस वस्तु सोली र अर्धगोला मिली बनेको छ । सोली र अर्धगोलाका व्यासहरू बराबर छन् र ठोस वस्तुको जम्मा उचाई 17 से.मि. र आधारको व्यास 10 से.मि. छन् ।

Given solid object is made up of a cone and hemisphere. The diameters of the base of a cone and hemisphere are equal and the total height of object is 17 cm and diameter of base is 10 cm.

[Figure: Solid object made of cone on top of hemisphere, total height 17cm, base diameter 10cm]

(a) अर्धगोलाको उचाइ र अर्धव्यासको सम्बन्ध लेख्नुहोस् ।

Write the relation between height and radius of hemisphere.

(b) उक्त ठोस वस्तुको पूरा सतहको क्षेत्रफल पत्ता लगाउनुहोस् ।

Find the total surface area of solid object.

(c) उक्त ठोस वस्तुको सतहमा प्रति वर्ग सेन्टिमिटर 40 पैसाका दरले रङ लगाउँदा रु.150 पर्याप्त हुन्छ ? हिसाव गरी कारण दिनुहोस् ।

Will the amount of Rs. 150 be sufficient to color the surface of the solid object at the rate of 40 paisa per square cm? Give reason with calculation.

एउटा आयताकार कोठाको लम्बाइ 12 फिट, चौडाइ 8 फिट र उचाइ 9 फिट छन् । उक्त कोठामा 2.5 फिट × 3 फिटका दुईओटा भ्यालहरू र 6 फिट × 2 फिटका दुई ओटा ढोकाहरू छन् ।

A rectangular room has length 12 ft, breadth 8 ft and height 9 ft. There are two windows of size 2.5 ft × 3ft and two doors of size 6ft × 2ft.

(a) चार भित्ता, भुईँ र सिलिङको जम्मा क्षेत्रफल निकाल्नुहोस् ।

Find the total area of four walls, floor and ceiling.

(b) भ्याल ढोका बाहेक चार भित्तामा प्रति वर्ग फिट रु.175 का दरले रङ लगाउँदा रु. 50,000 भन्दा कति कम वा बढी खर्च लाग्ला ? पत्ता लगाउनुहोस् ।

How much less or more is the cost of coloring the four walls excluding the doors and windows at the rate of Rs. 175 per square feet than Rs. 50,000? Find it.

एउटा पसलले जाडोको बेलामा जुत्ता र चप्पल (जोडीमा) निम्नलिखित तालिका अनुसार बिक्री गरेको रहेछ ।

A shop sells shoes and slippers (in pairs) during winter season according to the following table.

(a) समानान्तरीय मध्यमा र गुणोत्तर मध्यमाको सम्बन्ध लेख्नुहोस् ।

Write the relationship between arithmetic mean and geometric mean.

(b) 8 औँ दिनसम्म जम्मा चप्पलहरू कतिवटा बिक्री भएछन् ? पत्ता लगाउनुहोस् ।

How many slippers are sold up to 8th days? Find it.

(c) 8 औँ दिनसम्म बिक्री भएका जम्मा जुत्ता र चप्पलको संख्या तुलना गर्नुहोस् ।

Compare the total number of shoes and slippers sold up to 8th days.