Students and Teacher's Forum

Students and Teachers Forum

1. What points does a legislature have to consider while formulating laws ?

- The contribution and efforts made by the people for the betterment of their country should be respected. - The foreign policy of the neighbouring country should be analyzed. - The political structure of the country should be given due .....

2. Write in ascending order.
2√3, 3√4 and 6√27

Here, Given surds 2√3, 3√4 and 6√27 has same order of 2. So, by looking the number we can arrange them. And the answer is 2√3, 3√4 and .....

3. Compare > or <
√3 and 3√2

Alternatively, If a > b then a2 > b2 if a and b are positive real numbers greater than 1. Here, √3 and 3√2 are both greater than 1 as 2 > 1 and 3 > 1) Let's assume that √3 > 3√2. Squaring both .....

4. Find pure surd of x+yx-yx+y

.....

5. Solve:
1a+3+2aa2+9+4a3a4+81-8a7a8-6561=13-a

Here is an example. Replace x = 3 and do your problem. Question: 1a+x+2aa2 + x2 +4a3a4 + x4-8a7a8 – x8 = 1 / (x - .....

6. A flagstaff is fixed at one corner of a square room of side 30 m. The angle of elevation to the top flagstaff from the opposite corner of the room is found to be 60^o. Find the height of the flagstaff.

Please make correct; that is 30√2. Since, AB = √(302 + 302) = 30√2. [ Using pythagoras .....

7. A man of height P m observes the angle of elevation of the top of a pole situated in front of him and finds to be θ. If the height of the pole is 4P m and the distance between the pole and the man is 3√3 P m, find the value of θ.

Here, let AB be the pole with height 4P m and CD be the man with height P m. Distance between the pole and the man is 3√3P m. The angle of elevation of the top of a pole situated in front of the man is θ. From figure, OB = CD = P .....

8. Find pure surd of -43√5x

Definition of Pure Surd:

A surd in which the whole of the rational number is under the radical sign and makes the radicand, is called pure surd. In other words a surd having no rational factor except unity is called a pure surd or .....

9. If cos 300^o = √3/2, prove that sin 165^o = (√3 - 1)/2√2.

Here, Let A = 165o, then cos2A = 1 - 2sin2A [ Formula.] or, cos300o = 1 - 2sin2165o or, √3/2 = 1 - 2sin2165o [ Since, cos300o = √3/2.] or, 2sin2165o = 1 .....

10. Find the pure surd.
2√5

3a∛2

Definition of Pure Surd:

11. Find the HCF of:
x² + 2x - 3, x² - 1 and 4(x - 1)²

Here, 1st expression = x2 + 2x - 3 = x2 + (3 - 1)x - 3 [Splitting middle term] = x2 + 3x - x - 3 = x( x + 3) - 1(x + 3) = ( x + 3) (x - 1) 2nd expression = x2 - 1 = x2 - 12 = (x + 1)(x - 1) [ Using .....

12. Change the following sentences as indicated in the brackets.

a. Most of them have had their meal,...............? (Add question tag)
b. He did not see me on the way. (Into affirmative)
c. See! Who .. ... ..... (be) coming here? (Supply correct form of the verb)
d. Did Sita get anything? (Into negative)
e. The book will be bought by him. (Into active)
f. My mother said, "Go and do your homework. (Into indirect speech)

Answers a. haven't they? b. He saw me on the way. c. is coming? d. Didn't Sita get anything? e. He will buy the book. f. My mother ordered me to go and do my .....

13. solve the following equations.

2(2x+3)=15

Here, We have given, 2(2x + 3) = 15 Opening bracket we get or, 4x + 6 = 15 or, 4x = 15 - 6 or, 4x = 9 or, x = 9/4, which is required .....

14. If 3 sec²θ + 4 tan²θ = 3 then find the value of sec θ.

Here, 3 sec2θ + 4 tan2θ = 3 or, 3 sec2θ + 4( sec2θ - 1) - 3 = 0 [ Since, tan2A = sec2A - 1.] or, 3 sec2θ - 4 + 4 sec2θ - 3 = 0 or, 7sec2θ = .....

15. Define Human Resource Management.

It is a science as well because of the precision and rigorous application of the theory that is required. It is pervasive also because it is required in every department of the organization. It is a continuous process as there are numbers of .....

16. A(2, 0), B(3, 1) and C(1, 1) are the vertices of a ∆ABC. Find the coordinates of the vertices of the ∆ABC under the reflection on the line x = y followed by the enlargement E[(-3, -4), 2]. Present the ∆ABC and its image on the same graph paper.

Here, A(2, 0), B(3, 1) and C(1, 1) are the vertices of a ∆ABC. Now, the co-ordinates of the vertices a ∆ABC of under the reflection on the line x = y P(x, y) → P'(y, x) A(2, 0) → A'(0, 2) B(3, 1) .....

17. The vertices of ∆ABC are A(-2, 1), B(4, 3) and C(0, -4). If the centre of enlargement is (1, 2) and scale factor -2, enlarge the ∆ABC and then rotate the enlarged ∆ABC by R[(0, 0) +90^o].

Here, The vertices of ∆ABC are A(-2, 1), B(4, 3) and C(0, -4). Now, under enlargement using E[(1, 2), - 2], we have, P (x, y) → [a + k(x - a) , b + k (y - b)] , where a = 1 and b = 2 are the centres of .....

18. Write a letter to your sister encouraging her to respect our national and nationality.

25th Nov. 2018 Chitwan, Nepal Sijuwa, Morang Dear Saru, I am very glad to receive your letter in which you have talked about your visit to Mustang. Saru, I would like to share you some important ideas to respect .....

19. तिनओटा बच्चाहरूका दिन कसरी बितेका थिए?

सिंह र स्यालको कथा मानवतावादी विचार प्रस्तुत भएको कथा हो । यसले मानवताको सन्देश .....

20. पोथी सिँहले स्यालको सिकार गर्न नमान्नुको कारण के हो?

शरणमा परेकालाई मरणमा पार्नु हुँदैन भनेको जो आफूसँग सहयोग खोज्दै आएको हुन्छ .....

21. show that (1+cos π/8)(1+cos3π/8)(1+cos5π/8)(1+cos7π/8) =1/8

.....

22. Show that :cos²(π/8) + cos²(3π/8) + cos²(5π/8) + cos²(7π/8) =2.

Here,: LHS = cos2(π/8)+cos2(3π/8)+cos2(5π/8)+cos2(7π/8) =cos2(π/8)+cos2(3π/8)+cos2(π−3π/8) + cos2(π−π/8) =cos2(π/8)+cos2(3π/8)+cos2(3π/8)+cos2(π/8) [ We know .....

23. A fruit seller purchased 20 kg of apples of Rs 80 per kg and sold them at Rs 85 per kg.
i. Find his /her profit.
ii. Find his /her profit percent.

Given, CP of 1 kg of apples = Rs 80 SP of 1 kg of apples = Rs 85 Since SP is greater than CP, the fruit seller gain profit. Profit = SP - CP = 85 - 80 = Rs 5 Hence, his / her .....

24. What happens when propene is reacted with sufficient amount of hydrogen?
so me clearly

C 3 H 6 ( g ) + H 2 ( g ) → C 3 H 8 ( g ) When propene is reacted with sufficient amount of hydrogen then propane is .....

25. If the circle center at origin and radius 2 units intercepts by the line x + y = 2 then find the length of the chord.

Let us make a diagram according to question. We have given equation of chord BC is x + y - 2 =0, compare this with Ax + By + C = 0, we get A = 1, B = 1 & C = -2. To find the distace OA, we use the formula OA = ∣(Ax1 + By1 + .....

26. Write down the applications of echo.

When a sound wave is produced in air, some of it is absorbed after hitting with a reflector while some of the sound wave is reflected back to the listener. This reflected sound is called echo. Applications of Echo: 1. Since bats cannot see .....

27. If 2 cos²θ + 4 sin²θ = 3 then what is the value of sin θ?

2cos2θ + 4sin2θ = 3 or, 2( 1- sin2θ ) + 4sin2θ = 3 [ sin2θ + cos2θ = 1 , cos2θ = 1 - sin2θ ] or, 2 - 2sin2θ + 4sin2θ = 3 or, 2 + 2sin2θ = 3 or, 2sin2θ = 3 - 2 or, .....

28. Find the equation of the circle which is concentric to the circle x² + y² - 6x - 8y + 9 = 0 and its area is double of it.

Here, We have given equation of circle is x2 + y2 - 6x - 8y + 9 = 0 Compare this with x2 + y2 + 2gx + 2fy + c = 0, we get g = - 3 , f = - 4 &c =9. So, centre = (h,k) = (-g, -f) =(3, 4) Radius r .....

29. What is veto?

The veto is a special power of the permanent members of the United Nations. The permanent members the USA, UK, France, Russia and China have the Veto power. If any of the permanent members use the veto power against any of the resolution, the .....

30. Solve ∆ABC if ∡B = 60^o, ∡A = 30^o and a = 20 .

We know, solve the triangle means we need to find the mesurement of remaining sides & angles. For this we use the trigonometric ratios. Let us make a diagram according to question. Then, ∡B = ?, b =? & c = ? In .....

31. Solve ∆ABC if ∡C = 90o, a = 5√2 and b = 5√2.

32. Solve ∆ABC if a = 2, b = √3 and c = 1

33. A man bought a camera for Rs 460 and sold it at 5% profit.
(i) Find the profit amount.
(ii) Find the selling price of the camera.

Given, CP of the camera = Rs 460 Profit percent = 5% We know, Profit amount = Profit% of CP = 5% of 460 = ( 5/100 ) * 460 = Rs 23 Hence, the profit amount is Rs 23. Again, SP of the camera = CP of the camera + Profit amount = 460 + 23 = Rs .....

34. A shopkeeper bought an electric item for Rs 1520 and sold it at 10% loss.
(i) Find the loss amount.
(ii) Find the selling price of the item.

Given, CP of the electric item = Rs 1520 Loss percent = 10% Then, Loss amount = Loss % of CP = 10% of 1520 = ( 10 / 100 ) * 1520 = Rs 152 Hence, the loss amount is Rs 152. Again, SP of the item = CP of the item - Loss amount = 1520 - 152 = Rs .....

35. In the triangle ad is perpendicular bisector to bc .Find equation of adand bc .Where vertices are a(1,5) ,b(-1,2),c(3,2)

Here, using mid-point formula, D(x, y) = {(x1 + x2)/2, (y1 + y2)/2} = {(-1 + 3)/2, (2 + 2)/2} or, D(x, y) = (1, 2) Now equation of the median, AD is (y - y1) = {(y2 - y1)/(x2 - x1)}(x - x1) or, y - 5 = {(2 - .....

36. Find the equation of medians of the triangle having vertices (2,4),(2,6),and (-4,-8)

Take one vertex A( -2,0)= (x1,y1) Now, take the remaining two vertices B(2,4) and C(4,2). and find the mid-point of the two points. i.e; mid - point = D(3,3) = (x2,y2) Now, you have two points, so you can find the equation of median .....

37. In the figure, the equations of the sides AB, BC and CA are x + y = 2, 3x - y = 5 and 3x + y = 8 respectively, find the
(a) coordinates of the vertices of A, B and C.
(b) length of perpendiculars AP, BQ and CR.

Here, to find coordinates of A, we need to solve the equations of AB & AC. i,e; solving equation x + y = 2 & 3x + y = 8, x + y = 2 3x + y = 8 - - - _________ -2x = - 6 or, x = 3. Put x .....

38. Mrs. Rai buys a radio for Rs. 1880 and sells it to Mrs. Shrestha at 20% profit. How much does Mrs. Shrestha pay for it?

Here, CP of radio = Rs.1880 Profit % = 20% We know, Profit amount = Profit% of CP = 20% of Rs.1880 .....

39. Solve ∆ABC if ∡C = 90^o, ∡B = 30^o and a = 4√3.

40. What are the benefits we gets from the scale of map?

A map is a pictorial representation of the place on a piece of paper. A map does not exactly represent a location since spherical earth is almost impossible to be presented in a two dimensional map without some form of distortion. A map scale .....

41. What do you mean by the scale on map?

42. Why do we need to learn the drawing of the map of our country ? Give four reasons

A map is a pictorial representation of the place on a piece of paper. Nepal is a South Asian nation between Asian giants, India and China. We need to learn how to draw the map of Nepal. It will give us an idea about out nation. The .....

43. How is twister caused?

Tornadoes and twisters are the same. The term “twister” is just slang for “tornado” because of how it acts. First and foremost, a twister is a spinning pillar of air formed when cold air from the sky meets the warm air on .....

44. What precautions should we take during windy seasons?

Wind flow is the natural phenomenon due to difference between atmospheric pressure. Wind usually flows from high-pressure region to the low-pressure region. Despite of being natural phenomenon, precautions need to be taken to save life and .....

45. What type of wind is common in Nepal?

Nepal is a South Asian nation between India and China. Wind that dominates over Nepal is monsoon wind rising as high pressure develops over bay of bengal. As result of which the hot moist air rises from bay of bengal and move towards .....

46. What is wind? What causes wind?

Wind is perceptible natural movement of the air, especially in the form of a current of air blowing from a particular direction. Wind is caused by air flowing from high pressure to low pressure. Since the Earth is rotating the air does not flow .....

47. Make a list of valuable minerals found in Africa

Africa has the world's richest concentration of minerals and gems. In South Africa, the Bushveld Complex, one of the largest masses of igneous rock on Earth, contains major deposits of strategic metals such .....

48. What are the major four types of climate found in Africa?

Due to Africa's unique position across equatorial and subtropical latitudes in both the northern and southern hemisphere, different climate types can be found within it. The continent mainly lies within the intertropical zone between the Tropic .....

49. Find out the reasons for the high development of the USA and Canada. What should Nepal learn from them?

Nepal is the least developed nation in the world. The development of infrastructure is in pathetic condition. The problems like illiteracy, poverty, unemployment, etc. are everywhere there in the country. So, Nepal should learn the following .....

50. Which part of North America is called ' breadbasket of North America '?

The breadbasket is the regions in the world that produce food, particularly grains to feed their people as well as for export to other places. The region invests heavily in agricultural practices as well as agricultural based industries to process .....