Students and Teachers Forum

1. A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only 3 men got in all three games. How many medals did they receive in exactly two of three games?

Let x get exactly one mrdal and y get 2 medal and as stated 3 men get 3 medals. Therefore x+2y+3.3=38+15+20=73 or,  x+2y=64................(i) Also x+y+3=58= total no. of participants or,  x+y=55 ............(ii) Solving .....

2. In a survey of 2500 people in a village, the following data was found: 45% liked meat, 35% liked fish, 25% liked egg, 15% meat and fish, 10% fish and egg and those who liked meat did not like eggs. How many people didn't like all three food ?

Here given, n(U) = 2500 n(M) = 45% n(F) = 35% n(E) = 25% n(M∩F) = 15% n(F∩E) = 10% n(M∩E) = 0 n(M∩E∩F) = 0 [ Since people who like meat did not like eggs so there is no one who like all three items.]  Now, by using .....

3. What rights fall under the category of freedom of speech?

Freedom of speech is understood as a multi-faceted right. It includes not only the right to express, or disseminate, information and ideas but three further distinct aspects: - the right to seek information and ideas - the right to receive .....

4. What is the cause of killing pupa to produce silk?

The cocoons are kept in boiling water or in a hot  iven to destroy the glue of the cocoons.  Then the  silk fibre is unwoumd from them. The length of thread used in the formation of one cocoon is about 1000 .....

5. Prove that: cos5x = 16cos5x - 20cos3x + 5 cosx

Here, cos(5x) = cos(3x + 2x)   Expanding the above applying cos(A+ B),  cos5x = cos3x.cos2x - sin3x.sin2x  We knoiw, cos(3x) =4cos³x - 3cosx &  cos2x = 2cos²x - 1  So,  cos3x.cos2x = .....

6. Sinthia buys 20 pencils for Rs.100. She sold 3/5 of them at Rs.4 each and rest at Rs. 6 each . Find her gain or loss.

Here,  CP of 20 pencile = Rs.100 SP of 3/5 ⨯ 20 = 12 pencils = 12 ⨯ 4 = Rs.48 SP of remaining pencils ( 20 - 12 = 8) = 8 ⨯ 6 = Rs.48 Total SP = Rs.48 + Rs.48 = Rs.96. Here, SP<CP. Can you find the .....

7. मन भन्दा धन ठुलो वाद बिबाद ।

‘मनभन्दा धन  ठूलो’ भन्ने विषयको पक्षमा .....

8. मन भन्दा धन थुलो बाद बिवाद लेख्नुहोस । 

‘धनभन्दा विद्या ठूलो’ भन्ने विषयको विपक्षमा वादविवादः विपक्षबाट आदरणीय .....

9. Calculate the length of the unknown sides and find the area of the following figure.

Here,  Triamgles PQR and MNR are similar, since corresponding angles are equal. Now taking ratios of sides, MN/PQ = MR/PR = RN/ QR or, 7cm/15cm = 8cm/PR = RN/(RN+9cm) FInd PR & RQ from this relation. Then to find the area of PQR, use .....

10. कविताको मुख्य भाव के हो ?

मेरो घर’ कविता प्रभा भट्टराइ द्धारा रचिएको प्रतीकात्मक कविता हो । यहाँ मेरो घर .....

11. नेपाल्को प्रक्रिति छित्रन कसरि गरियेको छ ?

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12. Is silicon malleable and ductile? Why? Also show its pictures.

Silicon for example appears lustrous, but is not malleable or ductile (it is brittle - a characteristic of some nonmetals). It is a much poorer conductor of heat and electricity than the metals. Metalloids are useful in .....

13. What development works are seen in the field of education?

We know that education is the key to the development of a nation. It means if the people in the country are educated well, they contribute a lot for the betterment of the country. So, each nation has focused a lot in the development of the .....

14. What are different ways to diversify the trade?

You know that trade diversification is not satisfactory in Nepal. Due to this Nepal has been bearing trade loss for a long time. So Nepal should focus on effective ways on trade diversification. Some of the ways to diversify trade are mentioned .....

15. मन भन्दा धन ठुलो वाद बिवाद लेख्नुहोस । 

तरबारभन्दा कलम बलियो (वादविवाद)
कार्यक्रमका सभापति .....

16. What are the main objectives of the Tribhuvan University Teaching Hospital?

Tribhuvan University Teaching Hospital has been established to fulfill the following roles: - To provide a teaching base for the Institute of Medicine for all types of academic programs. - To provide tertiary level of health services to the .....

17. Why should we end misunderstanding at the bud? Write any five reasons of it.

Misunderstanding is a state failure to understand something correctly. In other words, misunderstanding may be defined as the wrong interpretation of any matter. Misunderstanding should be ended at the bud for the following reasons: - It may break .....

18. निबन्ध बन जङल

  नेपाली वनको महत्व 
वन घाँस दाउरा, काठ कृषि उपज .....

19. Prove that:sin∝ +sin2∝1+cos∝+cos2∝=tan∝

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20. If tanα = 5/6 and tanθ = 1/11, prove that: α + θ = πc/4.

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21. Solve:cos2⁡θ2-cosθ2+14=0  0o≤ θ≤180o

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22. Why is it considered better to grow a rose from a cutting rather than from a seed?

This method is called vegetative propagation. The main advantage of vegetative propagation methods is that the new plants contain the geneticmaterial of only one parent, so they are essentially clones of the parent plant. This means that, .....

23. Find the value of unknown angles.

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24. What are the main objectives of Mid-Hill highway? (6 points)

Mid-Hill Highway is one of the national pride projects. This is 1776 km long which extends from Chiyobhanjyang, Changthapu of Panchthar district to Jhulaghat of Baitadi district. It is under construction in the own investment of the Government of .....

25. What should be done to make human right more execution?

For the effective execution of human rights, the following things should be done: - The law and order should be maintained well in the country. - The judiciary should be kept free of any forms of political pressure. - The law, policies, acts, .....

26. Money is the key to bring progress in human life and nation. Justify.

Money is a medium which can be used for exchanging goods and services. Money has become the central phenomenon in today's economy. It is one of the fundamental invention made for the fulfilment of human needs. It was developed to solve the .....

27. Which matrix multiplies to matrix  1013 to get matrix 915 ? Find it.

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28. If A=3423 and B = 3-4-23 ,then prove that AB is an identity matrix.

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29. Why do animal curl into a ball during the winter?

Animals curl into a ball to keep themselves warm. Amount of heat loss is directly proportional to the surface area. Smaller the surface area less will be the heat loss. When animals curl into a ball the surface area of their body will be .....

30. Spread of 400 gm of sand homogeneously in one saucer and put 400gm of water in another saucer and place them under the sun.When the temperature is measured after 10 minute the temp. Of sand found to be more than that of water,why?

We know that the specific  heat capacity of water is 4200 J / kg °C, and the specific heat capacity of sand is 830 (J/kgoC). So can you tell which will heat first and .....

31. नेपाली वर्णमालामा कति वटा संयुक्त वर्णहरू हुन्छन् ?

नेपाली वर्णमालामा तीनवटा संयुक्त वर्ण हुन्छन् । जस्तैः क्ष, त्र, ज्ञ .....

32. Find the equation of a circle with the centre(2, 3) and passes through the point (-1, 1).

Here, centre C(h , k) = (2 , 3)  and any point R (x , y) = (-1 , 1) Radius (r) = √[( 2 +1)2 + (3 - 1)2] = √ [9 + 4] = √13 Now, using (x - h)2 + (y - k)2 = r2 or, (x - 2)2 + (y - 3)2 = .....

33. Find the equation of the circle touching both the axes with radius 2 units if it lies in the third quadrant.

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34. Find the value of x and y:

Here, x = 40 [ Circumference angle standing on same arc are equal ] Again, In triangle BCD, ⋖DBC + ⋖BCD + ⋖BDC = 180 [ Sum of angles of a triangle ] 40 + 100 + ⋖BDC = 180  ⋖BDC = 180 - 140 ⋖BDC = 40 y = ⋖BDC .....

35. Find the value.

Here, 65 + z = 180 [ Since PSTU is a cyclic quadrilateral ] z = 180 - 65 z = 115 Again, 95 + w = 180 [ Since PSTU is a cyclic quadrilateral ] w = 180 - 95 w = 85 Again, x + 95 = 180 [ Since PQRS is a cyclic quadrilateral ] x = 180 - 95 x = .....

36. Find the value.

Here,  ∠SPQ = 1/2 ∠SOQ  [The angle at the centre of a circle is twice the angle at the circumference standing on the sme arc.] ∠SPQ= 110⁰/2 = 55⁰ Now, ∠SPQ = ∠QBS = 55⁰  [ The angles at .....

37. Find the value of x and y.

Here, from the above figure, ∠ABD = 90⁰    [The angle in the circumference of a semi circle is one right angle.] ∠ABD + ∠BDA + ∠BAD = 180⁰             [sum of angles of .....

38. Find the value of x and y from the following:

Here, x + 115 = 180 [ Since PQRS is a cyclic quadrilateral ] x = 180 - 115 x = 65 Then, ⋖POR = 2 ∗ x [ Relation between central and the inscribed angle standing on the same arc ] ⋖POR = 2 ∗ 65 ⋖POR = 130 Then, ⋖POR .....

39. Discuss the ways to make national information commission active.

The National Information Commission (NIC) was established in 2008. It was established as an independent body for the implementation of Right to Information. It is responsible for the protection, promotion and practice of RTI in Nepal. The .....

40. If sina = (a - 1)/(a + 1), prove that tan a = (a - 1)/(2√a)

Here, sin a =a-1a+1= ph Therefore, p = a - 1 and h = a +1   Now, by using pythagoras theorem find the value of 'b'. Then, find cos a = b/h Then, find the value of tan a = sin a /cos .....

41. If C.P = Rs 320, S.P = Rs 352, find the profit and profit percent.

Given by the question, C.P = Rs. 320 S.P = Rs 352 Profit = ? Profit precentage = ? By using formula, Profit = S.P - C.P             = 352 -320            = Rs. 32 Profit .....

42. Prove that:
1+ tan2A1+ cot2A = 1-⁡tanAcotA-1

From LHS SinACos A = tan A Now, solve from RHS by changing tan A and cot A into sin A and cos A and simplify it You will get .....

43. Give reasons
more iron fillings are attracted at the two ends of a magnet than in the middle.

The closer together the field lines are, the stronger the field. As you can see the field is very strong in the center of the magnet, but because they are mostly contained in the magnet itself, the field is very weak in the air near the .....

44. Give reason
a magnet attracts steel but does not attract plastic.

Magnets attract iron due to the influence of their magnetic field upon the iron. Before a piece of iron enters the magnbetic field of a magnet, the polariztion of the iron's atom is random. When exposed to the magnetic field, the atoms beign .....

45. A line segment AB is increased along its length by 25% by producing it to C on side of B. If A and B have the co-ordinates (l , 2) and (5, 6) respectively then find the co-ordinates of C. 
 

We can do it by using section formula. Here, AC =AB + 25% of AB or, AC = 125/ 100 of AB or, AC/ AB = 5/4    So,  m1 : m2 = 5:1. [ Since, m1:m2 = AC : BC & BC = AC - AB = 5 - 4 = 1.] Let (x1,y1) = A(1, .....

46. भ्रष्टचार भनेको के हो? यसको निराकरणका उपायहरु लेख्नुहोस।

सदाचार विपरीतको आचरण तथा ऐन , कानुन र नैतिकतालाई तोडेर आफुलाई फाईदा हुने गरी गरीने भ्रष्ट .....

47. If coseca= ( m2+n2)/ (m2-n2),prove that m2+n2=2mn×seca

Here, CosecA = (m2 + n2)/(m2 - n2) = h/p Thus, b = √[ h2 - p2]             = √[ (m2 + n2)2 - (m2 - n2)2]             = √[ (m2 + .....

48. The vertices of triangle trs are t(-2,2) r(2,2)and s(2,6)respectively. The vector t1ot2 translates it and triangle t'r's' is formed. Coordinate of the vertices of t'r's' are t'(1,0) r'(5,0) and s'(5,4).Find the translation vector

Here,  T(-2, 2) is translated to T'(1, 0) by translation vector T1oT2. So, the translation vector T1oT2 = OT' - OT            =  10 - -22           = 1 + 20 - .....

49.  Prove that: 
(sin5θ + sin4θ + sin2θ + sinθ ) / ( cos5θ + cos4θ + cos2θ + cosθ) = tan3θ.

 

Here, LHS = (sin5θ + sin4θ + sin2θ + sinθ ) / ( cos5θ + cos4θ + cos2θ + cosθ) Arrainging we get        =[ (sin5θ + sinθ) + ( sin4θ + sin2θ )] / [( .....

50. Prove that :
⁡sinα+β- 2 sinα-sinα-β⁡cosα+β- 2cosα+cosα-β=tanα

Here, LHS = ⁡sinα+β- 2 sinα-sinα-β⁡cosα+β- 2cosα+cosα-β          = ⁡sinα+β-  sin(α-β )- .....