Students and Teachers Forum

1. An AP has first term 'a' and common difference -1. The sum of the first n terms is equal to the sum of the first 3n terms.Express 'a' in terms of n.

Here, given first term (a) = a common difference (d) = -1 no. of terms in first case is 'n' and 2nd case is '3n' We know the sum of n terms of an AP is  Sn = n/2 [2a + (n-1) d]  Sn = n/2 [2a + (n-1) .....

2. Find the cost to galvanize a tank in US dollar given that the exchange rate £ 1=Rs 150 and $ 60=£ 40 if the cost is Rs 5000.

Here, £ 1=Rs 150  $ 60=£ 40 Rs.5000= $ x Using chain rule, £1 ⨯ $ 60 ⨯ Rs5000 =  Rs.150 ⨯ £40 ⨯ $x Find x, which is required .....

3. If selling rate and the buying rate of 1 pound sterling (£) are Rs 150 and Rs 148 respectively.Mr gorkhe bought pound sterling (£) for Rs 26000 and sold in the next day. What will be the profit percent of NC is devaluated by 10%?

Here is an example: Question: If the selling rate and the buying rate of 1 US dollar ar Rs. 62 and Rs. 61 respectively. Arjun bought US dollar for Rs. 24,000 and sold in the next day. What will be the profit percent if NC is devaluated by 10% .....

4. Explain the rural-urban population distribution in Nepal.

The information presented in the table above reveals that the population of rural areas is decreasing and the population of urban areas is increasing. The population of urban areas of Nepal is increasing rapidly in comparison to rural .....

5. What is chain rule?

Chain rule is an alternative and short method of unitary method and ratio & propertion method to find the value of unknown variable in a compound propertion, For example: If  A = B    B = C, then   C = A In chain .....

6. What do you mean by population composition? Also write about need to study population composition.

It is very important for the study of population. It provides detail information about the individual people. It helps to know about the total number pf people of a particular area belonging to different caste, religion, language, occupation, and .....

7. Find the  sum of the AP 1+ 4 + 7 + 10 + 13 + 16,......+ 1000. Every third term of the above progression is removed, i.e, 7, 16 etc. Find the sum of the remaining terms.

In the AP 1+ 4 + 7 + 10 + 13 + 16,......+ 1000,  First term (a) = 1,  last term (l) = 1000 and  common difference (d) = 3 We know,  l = a + (n - 1) d or, 1000 = 1 + (n - 1) 3 or, (1000 - 1) / 3 = (n - 1) or, 333 = n - .....

8. In the sequence 1.0, 1.1, 1.2........99.9, 1000 each number after the first is 0.1 greater than the preceding number, find:

i) How many numbers there are in the squence?
ii) The sum of all the number in the sequence.

Here, a  = 1, d  = 0.1  & tn = 100 n = ? We know, tn = a + (n - 1) d or, 100 = 1 + (n -1)0.1 or, 990 = n - 1 or, n = 1000. Again,  Sn = n/2[ a + l ]      = 1000/2 [ 1 + 1000] Find .....

9. The sum of the first 100 terms of an AP with first term -128 and common difference d is T. The sum of the first 50 odd numbered terms is (1/2T -1000). Find the value of d. 

Here,  first term of an AP (a) = -128 common difference = d the sum of the first 100 terms (S100) = T We know,  Sn = n/2 {2a + (n - 1)d} or, S100 = 100/2 {2 × (-128) + (100 - 1)d} or, T = 50 (99d - .....

10. Find the sum of the following series.
5+ 541+521+ 543+ …. +10 terms

Here, a  = 5 ,  t2 = 21/4 d = t2 - t1 = 1/4 n = 10 Sn = n/2[ 2a + (n - 1)d]      = 5[ 10 + 9 ⨯ 1/4] Calculate .....

11. Write any two difference between skeletal system and digestive system.

Skeletal System Digestive System 1. It gives strucutre to the body. 1. It helps to digest the food. 2. It is made of calcium and other substance 2. It is composed of .....

12. Heart and kidney are called organ. Why?
 

A part of an organism which is typically self-contained and has a specific vital function. So can you you tell me what are the function of heart and .....

13. Given that euro 1 is equal to Rs114.60 an article is sold at euro 120 and 35% profit is made.At what rupees should it be sold to get 40% profit?

In this question we need to find selling price of an article by using the given conditions, In frist case, Profit=35% SP=Euro 120. Now we have formula,   SP=CP+profit % of CP or, 120=CP+35/100  CP Solve this and get CP= euro .....

14. Copper is used for making cooking utensils. Why?

Copper are good conductor of heat and give less resistance due to which less energy is wasted to heat copper vessels. So, copper is used for making .....

15. How much will be profit of an article bought for $4 is sold with £ 3 ? Given that $1=Rs 100 and £ 1=Rs150.

Here, CP = $4 = 4  x Rs 100 = Rs.400 SP = ₤3 =  3 x Rs. 150 = Rs.450 Profit = SP - CP           = Rs. 450 -  Rs 400 =  Rs .50 Profit % = Profit / CP X 100%      .....

16. The apparent depth of water in a pond appeares less then the real depth. Why?

Apparent depth of pond is less than real depth of pond due to the refraction of light. When rays travel from denser medium to rare medium it bends away from the normal and the actual depth appear to be .....

17. 400 nepali thanks bought for Rs400000 in nepali market is sold in britain after paying 10% export tax then 200% profit was made . Find the selling price of each cap in pound sterling. (£1 = Rs 155.63)

Here,  Cost price of 1 cap = Rs.400000/400 = Rs.1000 Price of a cap after 2% tax = Rs.1000 + 2% of 1000 = Rs.1020 SP of a cap after 200% profit = Rs.1020+ 200% of 1020                     .....

18. A student going to america for study need $2,500 .How much nepali rupees does he need if $1=Rs 100 and the bank charges 2% commission

Here, commission = 2% Commission amount = 2% of $ 2500 = (2/100) x 2500 = $ 50 Now, he need  $ 2500+ $50 = $ 2550. = 2550 x Rs.100 = Rs..............find .....

19. The plane fare of qatar airlines from kathmandu to the usa in kathmandu is Rs120000. If the ticket is bought in usa then it cost $1,400 which place is cheaper and by what percent find it ?($1=rs 110)

Here,  The plance fare bought from kathmandu = Rs. 120,000   The plane fare bought from USA = $ 1400 = 1400 ⨉ Rs. 110 = Rs. 1,45,000 So, the plane fare is cheaper from Kathmandu by,  =( Rs. 145000 - Rs. 120000) / Rs. .....

20. What are the different ways of forming the federal council of ministers according to the different conditions? Explain each each in brief.

(3) In cases where Prime Minister cannot be appointed under clause (2) no later than thirty days after the date of declaration of the final results of election to the House of Representatives or the Prime .....

21. Which part of Europe is very cold and why?

Europe is the second smallest continent. Europe extends from the island nation of Iceland in the west to the Ural Mountains of Russia in the east. Europe's northernmost point is the Svalbard archipelago of Norway, and it reaches as far south .....

22. वसन्त ऋतु भन्दा पहिले कोइली आफ्ना दिन कसरी बिताउँछन

उत्तर :   वसन्त ऋतुभन्दा पहिले कोइली दुःखी भएर लुकी लुकी दुःखका दिनहरु बिताउँथ्यो .....

23. Show the following pair of straight lines are perpendicular to eachother:
x2-y2+3x-3y=0.

We have given,  x2-y2+3x-3y=0 Compare this with ax2 + by2 + 2hxy + 2gx + 2fy + c = 0 we get, a = 1 , b = -1 Here,  a + b = 1 - 1 = 0 Thus, the given pair of straight lines are perpendicular to .....

24. Convert the following percentage into decimal.

20%

1.a) 20% We know, 20% = 20/100         = 2/10        = 0.2, which is required .....

25. In a survey among 460 people in a community, the number of people who drink tea is twice the number of people who drink coffee. If 140 people drink both and 150 drink neither, using Venn-diagram, find the number of people who drink tea, coffee and oly tea and who drink only coffee.

Here, Let, n(T), n(C), n(T∩C) and complement of n(T∪C) be the number of people who drink tea, coffee, who drink both and donot drink both respectively. Let, n(C) = x Then, n(T) = 2x n(T∩C) = 140 n(T∪C)' = .....

26. If the straight line represented by the equation (10p-1)x^2-(5p+3)xy-(1-p)y^2=0 are coincident ,find the values of p.

We have given, (10p-1)x2-(5p+3)xy-(1-p)y2=0 Compare it with axx2 + 2hxy + by2 = 0, we get  a = 10p - 1, h = -(5p + 3)/2 & b = -(1 - p) If the lines are coincident, h2 = ab or, (5p + 3)2 / 4 = (10p - 1)(p - 1) or, .....

27. In a class, one third of the student like badminton, three fourth of the students like football, 5 ouy of 6 of the student like volleyball, 60 like football and volleyball. 65 like volleyball and badminton, 17 like badminton and football, 20% of the student like all three games and 8 students don't like any game. Draw a  Venn-diagram and find the total number of students in the class.

There is no question no. 14d in the .....

28. In a survey of 70 students, 24 liked only two of volleyball, football and basketball and 5 students liked all the three. If 10 did not like any of these games, find the ratio of students who liked only one and only two.

Here,  let, n0(F∩V),n0(V∩B), n0(F∩B) and complement of n(F∪V∪B) be the number of people who like only football and volleyball, volleyball and basketball, football  and basketball and who donot like any of the .....

29. In a class of 70 students, every student likes volleyball or football or cricket. If the ratio of students who like (volleyball or football) and only cricket is 6 : I. Find the number of students who like volleyball or football.

Here, Let, n(V∪F) and n0(C) be the number of people who like volley ball or football and n0 (c)  be the number of people who like only cricet Then according to question if n0(C) = x then n(V∪F) = 6x We have, .....

30. The following information was collected in an interview of 45 students in which 12 liked Mathematics only, 25 liked English or Science. How many students did not like any of the subjects?

Here, Let, n0(m) be the number of students who like only maths and complement of n(M∪E∪S) be the students did not like any of the subjects. Then,     n(U) = n(E∪S) +  .....

31. Of the total students in an examination, among the three subjects Math, Science and Health, 60% students passed in only one subject. If 30% passed in only two subjects, draw a Venn-diagram to show the above information. Calculate the percentage of students who passed in all the three. 

Here,  Let, n0(M), n0(S), n0(H) be the number of people who passed only in math, science and health respectively According to the questions,   n0(M) +  n0(S) +  n0(H) = 60%  n0(M∩S) +  n0(S∩H) + .....

32. A survey of a group of people showed that; 75 liked tea or coffee, 15 liked milk only, 10 did not like all the three. How many people were asked this question? Solve by drawing the Venn-diagram. 

Here,  Ler red colour above represents the number of people who liked tea or coffee,                n(T∪ C) = 75  Blue colour represents number of people who like only .....

33. In a survey of 200 people, 120 read the Kantipur or Gorakhapatra, 20 read the Himalaya Times only What percentage of people didn't read all three newspapers?

Here, Let, n0(H) be the number of  people who read himalaya times only and complement of n(H∪G∪K) be the people who do not read any. Then,   n(U) = n(K∪G) +  .....

34. Among examinees in an examination, 40% in Science, 45% in Maths and 55% in Social Studies obtained A + grades. Similarly, 10% in Maths and Science, 20% in Science and Social Studies and 15% in social studies and Maths obtained A + grades. If every student obtains at least A + in one subject,
i) I Show the above information in a Venn-diagram.
ii) Find the percentage of students who obtained A + grade in all the three subjects. 
iii) If 300 students were surveyed, how many students did obtain A+ grades in only one subject?

Here,  Let, n(S), n(M) and n(SO) be the number of strudents who obtained A+ in science, maths and social studies respectively. n(S) = 40% n(M) = 45% n(SO) = 55% n(S∩M) = 10% n(S∩SO) = 20% n(SO∩M) = .....

35. Among 200 students of a school, 60% are interested in English, 32% Maths and English, 20% Science and Maths, 22% Science and English, 15% Math only, 10% in Science only and 5% are interested in all the three subjects, using a Venn-diagram find the number of students who are interested in Math and English only.

n(U) = 200 n(E) = 60% n(M∩E) = 32% n(S∩M) = 20% n(S∩E) = 22% nₒ(M) = 15% nₒ(S) = 10% n(E∩M∩S) = 5% nₒ (M∩E) = ?  Now , representing above information in Venn-diagram. From the above diagram, nₒ (M∩E) = .....

36. In a survey, it is found that 60 drink tea in the morning , 45 drink coffee, 40 drink milk. 25 drinkcoffee and tea, 20 drink tea and milk, 10 drink all the three tea, coffee and milk. If 5 do not drink all the three.

i) Show the above information inVenn- diagram.
ii) How many people drink at least on drink?
iii) How many people were surveyed?
iv) Find the number of people who drink only one drink.

Let, n(t), n(c) and n(m) represents the number of people who like tea, coffee and milk respectively. Showing in venn diagram people drink at least on drink = 25 + 15 + 17 + 10 + 10 + 3 + 17               .....

37. Among applicants inan advertisement 70 are expert in statistic, 60 are expert in computer, 50 are in English, 30 in statistics and computer, 20 in computer, 20 in computer and english, 25 in english  and statistic and 20 in all three subjects. If every applicant, 20 in computerand english, 25 in english and statistic and 20 in all three subjects. If every applicant is expert in atleast one subject them using Venn- diagram.

i) How many candidates are expert only in compute?
ii) How many did apply for the advertisement?

Here,  let, n(s), n(c) and n(E) be the number of people who are expert in science, computer and english respectively. n(s) =  70 n(c) = 60 n(E) = 50 n(s∩c) = 30 n(S∩ E) = 25 n(C∩ E) = 20 n(C∩ E∩ S) = .....

38. In a recent survey, it was found that 55% of customer want to use iphone mobile set, 35% want to use Samsung, 15% want to use Oppo only. 25% want to use iphone and Oppo, 20% want to use Oppo and Samsung, 15% want Iphone and samsung and 10% want all three. If 65 people do not want to use any mobile set, find the total number of cuutomer involved in the survey by using Venn-diagram.

n(I) = 55% n(S) = 35% nₒ(O) = 15% n(I∩O) = 25% n(O∩S) = 20% n(I∩S) = 15% n(I∩S∩O) =10% n(I∪S∪O)' = 65 n(U) = ? Now , representing above information in Venn-diagram. From the above diagram, From the above Venn- .....

39. In a group of people, 35% speak japanese, 30% speak English and 40% speak German language. If 7% speak japanese and English, 11% speak English and German, 10% speak japanese and German and 2% speak the entire three, find the percentage of people who speak exactly one language.

Here, Let n(J), n(E) and n(G) be the number of people who speaks japanese, english and german respectively. n(J) = 35% n(E) = 30%  n(G) = 40% n(J∩E) = 7% n(E∩G) = 11% n(J∩G) = 10% n(J∩E∩G) = .....

40. If cos 30 degree =√3/2 so that tan 15°=2-√3

We know, sin2θ=2sinθcosθ cos2θ=1−2sin2θ Then we can write the following equations: tanθ =sinθ/cosθ         =2sin2θ/ 2sinθcosθ       .....

41. In a survey concerning the percentage of consumers for three foods A, B and C, it was found that 60% liked food A, 50% liked B, 50% liked C, 30% liked A and B, 20 % liked B and C, 30% liked C and A and 10% liked all the three foods. Find the percentage of people who did not like any of the three foods.

Here, given n(U) = 100% n(A) = 60% n(B) = 50% n(C) = 50% n(A∩B) = 20% n(B∩C) = 20% n(C∩A) = 30% n(A∩B∩C) = 10% n(A∪B∪C)' = ? Now, by using formula, n(U) = n(A) + n(B) + n(C) - n(A∩B) .....

42. In an exam, 45% failed in Maths, 40% in Science, 35% in English, 15% in Maths and Science, 10% in Maths and English, 12% in Science and English and 5% failed in all three subjects. What percent passesd in all the three subjects?

Here, given n(U) = 100% n(M) = 45% n(S) = 40% n(E) = 35% n(M∩S) = 15% n(M∩E) = 10% n(S∩E) = 12% n(M∪S∪E)' = 5% n(M∩S∩E) = ? Now, by using formula, n(U) = n(M) + n(S) + n(E) - n(M∩S) .....

43. In a school result 20% students passed in all three subjects, 46% failed in Maths, 57% failed in English and 42% failed in dance, 35% failed in Maths and English, 25% failed in English and Dance, 15% failed in Dance and Maths. How many percent failed in all three subjects?

Here, given n(U) = 100% n(M) = 46% n(E) = 57% n(D) = 42% n(M∩E) = 35% n(D∩E) = 25% n(D∩M) = 15% n(M∪E∪D)' = 20% n(M∩E∩D) = ? Now, by using formula, n(U) = n(M) + n(E) + n(D) - n(M∩E) .....

44. In a survey of 200 students, 70 are fond of playing cricket, 80 football and 100 basketball. Similarly 20 are fond of playing cricket and football only, 30 cricket and basket ball only, 40 are fond of playing basketball only. If 20 students are fond of playing football and basketball only, by drawing Venn-diagrm find:
i. Number of students who play all the above games.
ii. How many student don't play any game?

n(U) = 200 n(F) = 80 n(C) = 70 n(B) = 100 nₒ(C∩F) = 20 nₒ(C∩B) = 30 nₒ(B) = 40 nₒ(B∩F) = 20 n(C∩F∩B)= x (say) n(C∪F∪B)' =y (say) Representing above information in Venn-diagram. From above Venn-diagram From .....

45. In a survey of people, 48 liked Nepali films, 40 liked English films, 31 liked Hindi films, 24 liked Nepali and English films, 19 liked Nepali and Hindi films, 13 liked Hindi and English , 11 liked Nepali only and 21 people were found not interested in any films. Find.
i. How many people liked all the three films?
ii. How many people were asked this question?

Here given, n(N) = 48 n(E) = 40  n(H) = 31 n(N∩E) = 24 n(N∩H) = 19 n(H∩E) = 13 nₒ(N) = 11 n(N∪E∪H)' = 21 i ) n(N∩E∩H ) = ? Here,  nₒ(N) = n(N) - n(N∩E) - n(N∩H) .....

46. In a group of students, 20 study Account, 21 study Mathematics, 18 study History, 7 study Account only, 10 study Mathematics only, 6 study Account and Mathematics only and 3 study Mathematics and History only.
 (i) How many students study all the subjects?
 (ii) How many students are there altogether?

Here given, n(A) = 20 n(M) = 21  n(H) = 18 nₒ(A) = 7 nₒ(M) = 10 nₒ(A∩M) = 6 nₒ(H∩M) =3 n(H∩A∩M ) = x (say) n(U) = ? Now solving it by using Venn- diagram. Now, from the above Venn- diagram From set M 6+10+x+3 = 21 x .....

47. Out of 100 students in an examination, 42 offered Mathematics, 35 offered Physics and 30 offered Chemistry, 20 offered none of these subjects, 9 offered Maths and Chemistry, 10 offered Physics and Chemistry and 11 offered Maths and Physics. What's the number of students offering all three subjects? 

Here given, n(U) = 100 n(M) = 42 n(P) = 35  n(C) = 30 n(M∩C) = 9 n(P∩C) = 10 n(M∩P) = 11 n(M∪P∪C)' = 20 n(M∩P∩C ) = ? Now, using formula, n (U) =  n(M) +n(P) + n(C) - n(M∩C) - n(P∩C) .....

48. In a village of 140 houses, 70 believe in Hindu religion, 60 believe in Buddhism and 45 in other religion. Among them 17 houses don't find any difference in Hindu and Buddhism, 18 houses don't find any difference in Hindu and other religion. While 16 houses don't find any difference between Buddhism and other religions. If 6 houses don't believe in any religion, find how many houses do not find any difference in any religion. Show it in a Venn-diagram.

Here given, n(U) = 140 n(H) = 70 n(B) = 60  n(O) = 45 n(H∩B) = 17 n(H∩O) = 18 n(B∩O) = 16 n(N∪E∪H)' = 6 n(N∩E∩H ) = ? Now, using formula, n (U) =  n(H) +n(B) + n(O) - n(H∩B) - n(H∩O) .....

49. A, B and C are the subsets of the universe set. If n(A) = 60, n(B) = 45, n(C) = 30 n(A ∩ B) = 25, n(B ∩ C) = 20. n(C ∩A) = 15 and n( A∪ B  ∪ C) = 85, find the n(A  ∩ B  ∩C).

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50. Set A, B and C are the subsets of the universal set. If n(A) = 100, n(B) =90, n(A∩ B) = 60 n(B ∩ C) = 40, n(C∩A) = 45 and n( A ∪ B ∪C) = 200, find the n( A ∩ B ∩ C)

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