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. (1)
(b) माथिको जानकारीलाई भेनचित्रमा प्रस्तुत गर्नुहोस् ।
Present the above information in venn-diagram. (1)
(c) एउटा मात्र व्यवसाय गर्ने घरधुरीको सङ्ख्या निकाल्नुहोस् ।
Find the number of households doing only one business. (3)
(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. (1)
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. (1)
(b) रमेशले उक्त ऋण कति वर्षको लागि प्रयोग गरेछन् ? पत्ता लगाउनुहोस् ।
For how many years has Ramesh used the loan? Find it. (2)
(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. (1)
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. (1)
(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. (1)
(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. (2)
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. (1)
(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. (2)
(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. (2)
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.
(a) पिरामिडमा भएको सबै त्रिभुजाकार सतहहरूको क्षेत्रफल पत्ता लगाउने सूत्र लेख्नुहोस् ।
Write the formula for finding the area of all triangular surfaces of pyramid. (1)
(b) उक्त पिरामिडको आयतन पत्ता लगाउनुहोस् ।
Find the volume of the pyramid. (1)
(c) पिरामिडको पूरा सतहको क्षेत्रफल निकाल्नुहोस् ।
Find the total surface area of the pyramid. (2)
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.
(a) अर्धगोलाको उचाइ र अर्धव्यासको सम्बन्ध लेख्नुहोस् ।
Write the relation between height and radius of hemisphere. (1)
(b) उक्त ठोस वस्तुको पूरा सतहको क्षेत्रफल पत्ता लगाउनुहोस् ।
Find the total surface area of solid object. (3)
(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. (1)
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. (2)
(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. (2)
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.
| दिन (day) | पहिलो दिन (1st day) | दोश्रो दिन (2nd day) | तेश्रो दिन (3rd day) | चौथो दिन (4th day) | पाँचौ दिन (5th day) |
| जुत्ताको सङ्ख्या (No. of shoes) | 2 | 4 | 8 | 16 | ……… |
| चप्पलको सङ्ख्या (No. of slippers) | 3 | 6 | 9 | 12 | ……… |
(a) समानान्तरीय मध्यमा र गुणोत्तर मध्यमाको सम्बन्ध लेख्नुहोस् ।
Write the relationship between arithmetic mean and geometric mean. (1)
(b) 8 औँ दिनसम्म जम्मा चप्पलहरू कतिवटा बिक्री भएछन् ? पत्ता लगाउनुहोस् ।
How many slippers are sold up to 8th days? Find it. (2)
(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. (2)
एउटा आयताकार जग्गाको क्षेत्रफल र परिमिति क्रमशः 150 वर्ग.मि. र 50 मि. छन् ।
The area and perimeter of a rectangular field are 150 sq.m and 50 m respectively.
(a) उक्त जग्गाको लम्बाइ र चौडाइ कति हुन्छ ? वर्ग समीकरण बनाउ पत्ता लगाउनुहोस् ।
What is the length and breadth of the field? Find it by making quadratic equation. (3)
(b) उक्त जग्गाको लम्बाइ र चौडाइवाट कति बराबर भाग घटाउँदा क्षेत्रफल 84 वर्ग मिटर हुन्छ ? हल गर्नुहोस् ।
How much equal part should be subtracted from the length and breadth of the land to get the area 84 square meter? Solve it. (2)
(a) \(\frac{1}{x^{-6}}\) लाई \(x\) को धनात्मक घाताङ्कमा लेख्नुहोस् ।
Write \(\frac{1}{x^{-6}}\) in the positive index of \(x\). (1)
(b) सरल गर्नुहोस् (Simplify): \(\frac{a^2}{a-2b} + \frac{4b^2}{2b-a}\) (2)
(c) हल गर्नुहोस् (Solve): \(4^{x-2} = 0.25\) (2)
दिएको चित्रमा AE∥BD, ED∥AC र BE∥CD छन् ।
In the given figure, AE∥BD, ED∥AC and BE∥CD.
(a) एउटै आधार र उही समानान्तर रेखाहरू बीच रहेका समानान्तर चतुर्भुज र त्रिभुजको क्षेत्रफल बिचको सम्बन्ध लेख्नुहोस् ।
Write the relationship between the area of parallelogram and triangle standing on the same base and between the same parallel lines. (1)
(b) प्रमाणित गर्नुहोस् (Prove that): \(\triangle ABE = \triangle BCD\) (2)
(c) त्रिभुज ABE र समलम्व चतुर्भुज ACDE को क्षेत्रफलविच तुलना गर्नुहोस् ।
Compare between the area of triangle ABE and trapezium ACDE. (1)
दिइएको चित्रमा, एउटा चक्रिय चतुर्भुज PQRS छ । भुजा PQ लाई विन्दु T सम्म लम्ब्याइएको छ ।
In the given figure, PQRS is a cyclic quadrilateral. The side PQ is produced to the point T.
(a) \(\angle PSQ\) र \(\angle PRQ\) को सम्बन्ध लेख्नुहोस् ।
Write the relation of \(\angle PSQ\) and \(\angle PRQ\). (1)
(b) \(\angle SPR\) र \(\angle SQR\) बराबर हुन्छन् भनी प्रयोगद्वारा प्रमाणित गर्नुहोस् । (कम्तीमा 3 से.मि. अर्धव्यास भएका दुईओटा वृत्तहरू अनिवार्य छन् ।)
Verify experimentally that \(\angle SPR\) and \(\angle SQR\) are equal. (Two circles with radii at least 3cm are necessary) (2)
(c) प्रमाणित गर्नुहोस् (Prove that): \(\angle RQT = \angle PSR\) (2)
चतुर्भुज PQRS मा PQ = 5 से.मि., QR = 4.5 से.मि., RS = SP = 6 से.मि. र QS = 6.5 से.मि. छन् ।
In a quadrilateral PQRS, PQ = 5 cm, QR = 4.5 cm, RS = SP = 6 cm and QS = 6.5 cm.
(a) माथिको नाप अनुसारको चतुर्भुज PQRS रचना गर्नुहोस् र उक्त चतुर्भुजको क्षेत्रफलसँग बराबर हुने गरी एउटा त्रिभुजको पनि रचना गर्नुहोस् ।
Construct a quadrilateral PQRS according to the above measurements and then construct a triangle which is equal to the quadrilateral in area. (3)
(b) यसरी बनेको चतुर्भुज र त्रिभुजको क्षेत्रफल किन बराबर हुन्छन् ? कारण दिनुहोस् ।
Why the area of the quadrilateral and triangle are equal? Give reason. (1)
चित्रमा टावरको उचाइ (CD) \(15\sqrt{3}\) मिटर र घरको उचाइ (AB) \(10\sqrt{3}\) मिटर छन् । घरको छतवाट टावरको टुप्पोमा हेर्दा \(30^\circ\) को कोण बन्दछ ।
In the figure, the height of tower (CD) is \(15\sqrt{3}\) meter and the height of house (AB) is \(10\sqrt{3}\) meter. The angle from the top of house to the top of tower is \(30^\circ\).
(a) घरको छतवाट टावरको टुप्पोमा हेर्दा बन्ने कोण कुन प्रकारको कोण हो ? लेख्नुहोस् ।
What type of angle is formed when the top of the tower is observed from the roof of the house? Write it. (1)
(b) टावरको भाग DE को उचाइ पत्ता लगाउनुहोस् ।
Find the height of part DE of the tower. (1)
(c) घर र टावरविचको दूरी निकाल्नुहोस् ।
Calculate the distance between house and tower. (1)
(d) घरको आधारवाट टावरको टुप्पोमा हेर्दा बन्ने कोण पत्ता लगाउनुहोस् ।
Find the angle of the top of the tower from the basement of the house. (1)
एउटा कक्षाका 50 जना विद्यार्थीहरूले गणित विषयको 60 पूर्णाङ्कको परीक्षामा प्राप्त गरेको प्राप्ताङ्कलाई तालिकामा दिइएको छ ।
The marks obtained by 50 students of a class in an exam of maths with full mark 60 are given in the table.
| प्राप्ताङ्क (Obtained marks) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| विद्यार्थी सङ्ख्या (Number of students) | 7 | 13 | 15 | 10 | 5 |
(a) रीत पर्ने श्रेणी लेख्नुहोस् ।
Write the class of mode. (1)
(b) दिइएको तथ्याङ्कवाट पहिलो चतुर्थांश \(Q_1\) को मान निकाल्नुहोस् ।
Find the value of first quartile \((Q_1)\) from the given data. (2)
(c) दिइएको तथ्याङ्कवाट औसत प्राप्ताङ्क गणना गर्नुहोस् ।
Calculate the average mark from the given data. (2)
(d) 40 वा 40 भन्दा बढी प्राप्ताङ्क ल्याउने विद्यार्थीहरूको औसत प्राप्ताङ्क कति छ ? पत्ता लगाउनुहोस् ।
What is the average mark of the students who obtained 40 or more than 40 marks? Find it. (1)
एउटा वाकसमा उत्रै र उस्तै आकारका 5 ओटा राता र 3 ओटा सेता वलहरू राखिएका छन् ।
In a box, 5 red and 3 white balls of same size and shape are kept.
(a) पारस्परिक निषेधक घटनाहरूको सम्भाव्यताको जोड नियम लेख्नुहोस् ।
Write the addition law of probability of mutually exclusive events. (1)
(b) वाकसमा राखिएका वलहरूवाट एकपछि अर्को गरेर दुईओटा वलहरू पुनः नराखी फिक्दा आउने सबै सम्भावित परिणामहरूको सम्भाव्यतालाई वृक्ष चित्रमा देखाउनुहोस् ।
Two balls are drawn one after another without replacement from the box. Show the probability of all the possible outcomes in a tree diagram. (2)
(c) वृक्ष चित्रवाट दुवै वल सेतो पर्ने सम्भाव्यता निकाल्नुहोस् ।
Find the probability of getting both white balls from the tree diagram. (1)
(d) दुवै वल पुनः राखी र पुनः नराखीकन फिक्दा दुवै वल सेतो पर्ने सम्भाव्यता विचको फरक निकाल्नुहोस् ।
Find the difference between the probability of both balls being white if two balls are drawn one after another with replacement and without replacement. (1)