Students and Teachers Forum

1. If A + B + C = πc then prove that: (sin2A + sin2B - sin2C)/4sin(C/2) cos(C/2) = 2cosA cosB

Here, Numerator of LHS = Sin2A + sin2B - Sin2C                                 = sin2A + sin 2B -sin2C                 .....

2. Prove that:
3(sinx/2 - cosx/2)4 + 6(sinx/2 + cosx/2)2 + 4(sin6x/2 + cos6x/2) = 13

Here, Taking LHS, = 3(sin x/2 – cos x/2)4 + 6(sin x/2 + cos x/2)2 + 4(sin6 x/2 + cos6 x/2)

= 3 [(sin x/2 – cos x/2)2]2 + 6(sin2x/2 + cos2x/2 + 2 sin x/2 cos x/2) + 4 [(sin2x/2)3 + .....

3. Write about the composition of the Nepalese parliament and How the member are elected?

The upper house is called the National Assembly. It has 59 members. Out of 59, 56 are elected by an electoral college. The electoral college consists of state assembly members, chairmen and vice chairmen of village executive and mayors and deputy .....

4. Prove that:
cos(150o + x) + cos(150o - x) = -√2 cos x.

L.H.S. = cos(150+x) + cos(150-x) = cos150.cosx - sin150.sinx + cos150.cosx + sin150.sinx = 2.cos150.cosx = 2.cos(180-30).cosx = 2. -cos30.cosx =2.-√3∕2. cosx = -√3cosx The R.H.S. must be -√3cosx instead of .....

5. Why are frogs only seen in the rainy seasons?

Frog love to come out in the rain because they prefer a wet, dark environment. After a steady rain, the area is usually cloudy, cool and moist. This means that the conditions are right for the animal to roam around without drying out. If .....

6. Write the components of population.

Birth rate is the number of live births per thousand persons in a year. Death rate is the number of deaths per thousand persons in a year. Migration is the movement of people across rregions and .....

7. Is time travel possible?

It’s one of the greatest topic in movies, literature, and television shows: the idea that we could travel back in time to alter the past. From the time turner in Harry Potter to Back To The Future to Groundhog Day, traveling back in time .....

8. अर्थ स्पष्ट हुने गरी वाक्यमा प्रयोग गर:
पर्यटन, लगनशील, हस्तान्तरण, छात्रवृत्ति

पर्यटनः नेपालमा भौगोलिक तथा प्राकृतिक विविधता रहेकाले पर्यटन व्यवसायको राम्रो सम्भावना .....

9. While taking blood out of your bleeding nose what should you do?

6. Use a pinch. Pinch the soft part of your nose shut for 10 minutes. Use a clock to keep track of time. Resist the urge to peek after a few minutes to see if your nose has stopped bleeding. 7. Observe and react. After 10 minutes, let go of your .....

10. तलका शब्दको अर्थ लेख:
निकुञ्ज, अनुकरणीय, सजीव, जाज्वल्यमान, उपत्यका

निकुञ्जः वन सुरक्षाका लागि छुट्याइएको क्षेत्र अनुकरणीयः नक्कल गर्न वा सिको गर्न लायक सजीवः .....

11. Simplify:
 √x + √(a + x) = 3a/√(a + n)

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12. Prove that the matrix 3211 transforms the unit square to the parallelogram 0301  5221
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13. The volume of the given solid object is 38808 cm3.
(i) Find the radius of the base.
(ii) Find the volume of the cone.

Given, Volume of solid object = 38808 cm3 Height of cylinder(h1) = 240 cm Volume of cylinder(v1) = πr2h1                                       = .....

14. The curved surface area of given figure is 4686 cm2. Find the common radius.

Curved surface area = curved surface area of cone + curved surface area of hemisphere  4686 = πrl + 2πr2 or, 4686 = π.r.29 + 2πr2 now simplify and find value of .....

15. If the water filled in the cone is poured into the cylinder, to what height will the surface of the water reach such that the cone will be full of water?

First find volume of cone since cone is completely filled volume of water v1=  1/3 x  πr2h                                 = 1/3 x 22/7 x 62 x .....

16. From human trafficking chapter "Unlike common people, victim's life is different ." Justify it with an example.

It is obvious that, unlike common people, victims' life is different. Common people can enjoy so many types of freedoms but victims can't. The victims have different types of problems that are unresolved. We .....

17. Highlight the importance of skilled manpower.

Dear student, a dialogue between two friends Dilmaya and Manmaya on the importance of skilled manpower is presented below. So, you are requested to note down the importance of skilled manpower from the dialogue. Dilmaya   : Hi, good .....

18. एउटा x  मि. अग्लो खम्बामाथि एउट ध्वजदण्ड खडा गरी रखिएको छ। यदि खम्बा र  ध्वजदण्डले खम्बाको फेददेखि y  मि. परको दुरिमा बराबर् कोणहरु ध्वजदण्डको उचाइ xx2+y2y2-x2 हुन्छ भनी प्रमणित गर्नुहोस्

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19. A(3, 4), B(-2, 6) and C(1, -5) form a triangle. Find the image of triangle under enlargement with (1, 2) as the centre and scale factor -2 and present them on a graph.

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20. If a(-1, 2), b(2, 2) and c(2, 6) are the vertices of a triangle abc. Find the image of triangle abc under negative quarter turn about the origin and represent them in the graph paper.

   After negative quarter turn we get ( x , y )       →     ( y , -x ) so we get  A ( -1 , 2 )      →   A' ( 2 , 1 ) B ( 2 , 2 )        → .....

21. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}.
Verify: n(u) = n(A) + n(B) - n(A∩B) + n(A∪B).

Here's n( U ) = 10 n ( A ) = 5 n ( B ) = 4 A U B = 1 , 2 ,3 , 4 , 5 , 6 , 8 so n ( A U B ) = 7            _______ and n  ( A U B )  = 3 and n  A ∩ B = 2 , 4 so n ( A ∩ B ) = .....

22. Find the images of points A(2, 3), B(-5, 8) and C(4, -3) under the rotation about the origin through -90o, 180o, -270o.

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23. The image of points (3a, 7) under the translation vector -13 is (8, 3b + 4). Find the values of a and b.

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24. A(2, 3), B(-2, 4), C(1, 8) and D(5, 7) are the vertices of a parallelogram ABCD.
i. Find AC⃗ ii. Using AC⃗ as the translation component, find the images of the vertices of the parallelogram ABCD and show them on a graph.

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25. Using the translation component T 1-2, find the images of the vertices A(2, 6), B(-1, 4) and C(5,1) of the ∆ABC under the translation. Show ∆ABC and its image  ∆A'B'C' on a graph. 

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26. P(4, 2) and Q(-2, 6) are two points. Translate the points P and Q using the translation vector  21. Also show the line PQ and its image on a graph.

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27. A(4, 3), B(6, 4), C(5, 6) and D(3, 5, ) are the vertices of a parallelogram ABCD. If the square ABCD is  reflected about the line y = 0, find its image and present ABCD and its image in a graph.

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28. A(2, 3), B(-2, 4), C(1, 8) and D(5, 7) are the vertices of a parallelogram ABCD. find the image of the parallelogram ABCD when it is reflected about the line y = - x.

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29. Under the reflection, ∆ABC is mapped to ∆A'B'C' where A'(3,1), B'(5,1), and C'(5,2) are the vertices of the image ∆A'B'C. Find the axis of thereflection if A is the point (1,3) and also find the coordinates of the remainingvertices of ∆ABC.

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30. P(-1, 0), Q(3, 1), R(2, 2) and S(-2, 1) are the vertices of parallelogram. Show that parallelogram PQRS on the graph paper. Find the reflection of the parallelogram PQRS about the line Y = X. Present the image P'Q'R'S' on the same graph paper.

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31. A translation T maps the points A(3, 7) to A'(-8, 10). what are the components of  T?

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32. The vertices of  ∆ABC are A(3, 4), B(7, 6) and C(9, 2) respectively. The triangle ABC is translated by the vector -4-3. Write down the coordinates of the vertices of the image ∆A'B'C' so formed and draw it on a gaph.

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33. The vertices of ∆ABC are A(2, 3), B(4, 5) and C(6,2). Reflected it in X-axis and Y-axis and then write down the coordinates of the images.

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34. When a point P is reflected about Y-axis, its image is P'(-4, 2). Find the coordinates of P and also find the image of P under the reflection about X-axis.

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35. List any 10 festival

5. Ramadan 6. .....

36. If A + B + C = π and cosA = cosB . cosC, then prove that  tanA = tanB + tanC.

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37. Prove that: cos15o - sin15o = 12

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38. Prove that(without using calculator or table): cos15o = 2 + 3

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39. Prove that(without using calculator or table): cos105o 1 - 325

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40. Prove that: sin2 2 (π/6+ θ) - sin2 2 (π/6- θ) = √3/2 sin2θ

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41. Prove that: cos10o- sin10ocos10o+ sin10o=tan35o

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42. Prove that: sin(x + y) + sin(x  - y) = 2sinx . cosy

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43. Prove that: tan9A - tan6A - tan3A = tan9A . tan6A . tan3A.

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44. Prove that: tan55o - tan35o = 2tan20o.

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45. NH3 is a covalent compound and MgCl2 is an electrovalant compound. Why?
 

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46. Define covalent bond and explain the formation of CH4?

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47. Give reason why oxygen has valancy two and aluminum has three.

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48. What is covalent bond? Explain with one example.

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49. Explain about the octet with one example.

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50. If tanθ= 3- 13+ 1, prove that cosθ=3+ 122

Here,  Tanθ = (√3 - 1) / (√3 + 1)  = p/b So, p = (√3 - 1)  & b = (√3 + 1) . So, by Pythagorus theorem,    h = √[ p2 + b2 ]       .....