Students and Teachers Forum

1. Discuss the major activities of social organizations.

The social organizations focus on the following things: - Empowering marginalize people, women, dalits, backward etc. - Helping people in natural calamities and disasters - To control social problems and evils like dowry system, gambling, .....

2. Prove that:
cos 28o - sin 58o = sin2o

Taking L.H.S. = cos28 - sin58                        = cos(30 - 2) - sin(60 - 2)                        = cos30.cos2 + sin30.sin2 .....

3. A number of two digits is equal to four times the sum of digits. If the product of the number is 18, find the number.

Here,     Let 10x + y be a two digits number where x and y are the digits in tenth and unit place respectively. now, In  first case,       10x + y = 4(x + y ) or,  10x + y = 4x + 4y or,  10x - 4x = 4y - .....

4. In ∆PQR, ∡P + ∡R = 160o and ∡Q + ∡R = 140o. Find the longest and the shortest side.
 

Given, ⋖P + ⋖R = 160 ⋖P = 160 - ⋖R ------------------ [ I ] ⋖Q + ⋖R = 140 ⋖Q = 140 - ⋖R -------------------- [ II ] We know, ⋖P + ⋖Q + ⋖R = 180 [ Sum of angles of a triangle ] 160 - ⋖R + .....

5. Prove that:
cos12A + cos4A = 2cos8A cos4A.

Taking L.H.S. = cos12A + cos4A                         = 2cos[(12A+4A) ∕ 2].cos[(12A-4A) ∕ 2]                       .....

6. Prove that :
 cos10-sin10cos10+sin10=tan35°

Here:  tan35°=tan⁡45°-10° Using: =tan45-tan101+tan45.tan10 =1-tan101+1.tan10       [ tan45° = 1 ] =1-sin10cos101+sin10cos10 =cos10-sin10cos10cos10+sin10cos10 =cos10-sin10cos10+sin10 = .....

7. A number consists of two digits whose product is 18. If 63 is subtracted from the number, the digits are interchanged. Find the number. 

Let the two digit number be (10x + y). By question, xy = 18  -------------------------- [ I ] (10x + y) - 63 = 10y + x 10x + y - 63 = 10y + x 10x - x = 10y - y + 63 9x = 9y + 63 9x - 9y = 63 9(x - y) = 63 x - y = 7  x = 7 + y .....

8. The altitude of a triangle is 3 cm greater than base and the area is 135 cm2. Find the altitude and base.

Let 'b' cm be the base of the triangle. According to the question, Height (altitude) of the triangle = (b + 3) cm Area of the triangle = 1/2 ⨉ base ⨉ altitude or, 135 = 1/2 ⨉ b ⨉ (b + 3) or, 270 = b2 + .....

9. The hypotenuse of a right angled triangle is 13 cm. If the difference between other two sides is 7 cm, find the length of remaining sides. 

Given, Hypotenuse of the right-angled triangle(h) = 13 cm Remaining two sides be 'b' and 'p', By question, b - p = 7 b = p + 7 ---------- [ I ] Using pythagoras theorem, h2 = p2 + b2 132 = p2 + ( p + 7 )2 169 = .....

10. The sum of the lengths of two sides containing the right angle in a right-angled triangle is 22 cm and the area of triangle is 60 cm2. Find the length of 3 sides.

Let the two sides of the right angled triangle be x and y. By question, x + y = 22  y = 22 - x ------------------ [I] Area of right angled triangle =( 1 ∕ 2 )∗ x ∗ y 60 = ( 1 ∕ 2 )∗ x ∗ y xy = .....

11. The perimeter of a right angled triangle is 12 cm2 and hypotenuse is 5 cm. Find the other two sides of triangle. (ans = 3cm, 4cm)

The perimeter of a right angled triangle is 60 cm. Its hypotenuse is 26 cm. Find the other two sides and area of the .....

12. A rectangular piece of land is 40m long and 25m wide. A path of uniform width and 426 m2 area surrounds the land from outside. Find the width of the path.

Let 'W' be the width of path. Length of field (L) = 40 m Breadth (B) = 25 m. We know, area of path outside field  = W ( L + B + W) or, 426 = W( 40 + 25 + W) or, 426 = 65W + W2 or, W2 +  65W - 426 = .....

13. Out of 65 people, 11 like tea only and 11 liked both tea and coffee. The number of people who like coffee is twice the number of people who like tea. By drawing a Venn-diagram find the number of people who like coffee only and who don't like both the drinks. 

Now, No. of people who like coffee only no(C) = n(C) - n(T ⋂C)                                                 .....

14. A broker sold a land of 214  ropani at the rate of Rs 32,00,000 per ropani. If the land owner reward Rs 1,38,96,000 then find the commission rate.

Here,  Total land = 9/4 ropani So, total selling price of land = 9/4 ⨯ Rs.32,00,000                                           .....

15. Write an essay on electricity and its importance (in about 200 words.)

Electricity is the greatest gift of science to mankind. We have reached a point of our civilization when electricity is used for all purposes. Without it, our existence will be impossible. Electricity is a source of .....

16. Imagine that one of your friends from Jhapa is coming to visit you. Write the short-cut directions to reach your home from nearest bus park.

Catch the bus from the station to Kathmandu.  You will be informed by the conductor after you reach Kalanki. You will be headed towards new bus park.   Get off the bus.  Make a phone call after your arrival.  Now, catch .....

17. विश्वकप फुटबल २०१८ शिर्षकमा निबन्ध लेख्नुहोस

विश्वकप फुटबल २०१८ विश्वकप फुटबल प्रतियोगिता सन् २०१८ जुन १४ देखि सन् २०१८ जुलाई .....

18. Write an essay on "Waste management in Panauti" with effective solutions.

Panauti is a relatively small municipality in the Kavre Palanchowk district of Bagmati Zone of the Central Development Region. The municipality lies 32 Km east of Kathmandu and immediately south of Banepa .....

19. What is wetland?

Wetlands are areas where water covers the soil or is present either at or near the surface of the soil all year or for varying periods of time during the year, including during the growing .....

20. The supreme court is also called the ' court of record'. Give reason

The supreme court is the highest court of the land. It is also referred to as the court of record. A court of record is a court whose acts and proceedings are recorded safely for perpetual memory and testimony. These records are used with high .....

21. At present the product of the ages of a mother and daughter is 100. After 10 years, mother's age will be twice the age of daughter. Find their present ages.

Here, Let the present age of mother be y and daughter be x. According to 1st condition,  xy = 100  or, x = 100/y ..............(i) According to 2nd condition,  y + 10 = 2 ( x + 10)  or, y + 10 = 2x + 20 or, y + 10 = .....

22. When a number is added to its square, the sum becomes 56. Find the numbers.

Let the number be a The square of the number be a2 The sum of the number is 56. ∴ a2 + a = 56  We now solve the equation: or, a2  + a = 56 or, a2 + (8-7)a - 56 = 0 or, a2 + 8a - 7a - 56 = 0 or, a(a + 8) - .....

23. If the product of two consecutive natural numbers is 240 find numbers.

Let the consecutive even numbers are y and y + 1 According to question, y ( y +1 ) = 240 or, y2 + y - 240 = 0  or, y2  + 16y -15 y - 240 = 0 or, y ( y + 16 ) - 15 ( y + 16) = 0 or, ( y - 15) ( y + 16) = 0 Either, y - .....

24. Find the value of x if 
xcos(90o +  θ) . cos(90o - θ) + tan(180o - θ) . cot(90o + θ) = sinθ . sin(180o - θ)

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25. Find the value of θ if sec2θ = cosec8θ.

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26. Find the value of θ if tan3θ = cot2θ.

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27. Find the value of A if sin4A = cosA.

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28. If A, B and C are the angles of a triangles, prove that:
tan(A + B) + tanC = 0

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29. If A, B and C are the angles of a triangles, prove that:
sin(A + B) = sinC

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30. Simplify: tan180o- θ . cot90o- θ.cos(360o- θ)tan180o+ θ. tan90o+ θ.sin(- θ)

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31. Prove that: tan32o - cot53o + cosec80o = tan37o + cot58o - sec10o.

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32. Prove that: sin65o + cos35o = cos25o + sin55o.

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33. Find the value of cos290o + cos2120o + cos2135o + cos2150o + cos2180o.

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34. Find the value of cos150o + sin120o + sin2150o + cos2120o.

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35. Find the value of tan9o . cot27o - cot81o . tan63o.

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36. Find the value of tan675o.

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37. Find the value of cos(-690o).

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38. Find the value of sin(-1650o).

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39. Table for the value of trigonometric rario of complementary and supplementary angle. 

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40. Claculate the area of the folowing trapeziums.

Here,  In right angled triangle  BEC,  CE = √[BC2 - BE2]          = √[132 - 122]          = 5cm Now,  Area of trap.ABCD = 1/2 ⨯ .....

41. Table for trigonometri ratio of any angle:

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42. Calculate the area of the following trapeziums.

Here,  PT = PQ - TQ = 17cm - 7cm = 10cm In right angled triangle PTS,  ST = √[SP2 - PT2]       = √[262 - 102]        = 24cm. Now,  Area of trap.PQRS = .....

43. Prove that :
cosecθ+cotθcosecθ-cotθ=cosecθ+cotθ2

LHS = ( cosecθ + cotθ) / ( cosecθ - cotθ) = ( cosecθ + cotθ) ( cosecθ + cotθ) / [( cosecθ - cotθ)( cosecθ + cotθ) ] = ( cosecθ + cotθ)2 / ( .....

44. Prove that:
 tanθ-cotθsinθ cosθ=⁡sec2θ-cosec2θ

3.  Here,  LHS = (tanθ - cotθ) / sinθcosθ         = [ sinθ/cosθ - cosθ/sinθ] / sinθcosθ  [ Since, tan = sin/cos & cot = cos/sin]     .....

45. Find the value of x.

Here,  ∡BAD = 90o,     [ Since, angle in semi-circle.] ∡BAC = ∡BAD - ∡ CAD = 90o - 26o = 64o Finally, x = ∡ BAC           [ Angle in alternate segment.] Can you write the .....

46. Find the value of x.

Here,       ∡ P + ∡ R = 180o              [ Opposite angles od cyclic qd. are supplementary.] Or, ∡R = 180o - 110o    Again,   x = ∡R    .....

47. The mid-points of theree sides of a triangles are (1, 1), (2, -3) and (3, 4). Find the coordinates of the vertices and centroid of thr triangle.

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48. Find the coordinates of the points of  trisection of the line joining (1, 8) and (4, 2).

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49. Find the ratio in which point (2, 1) divides the line joining (1, -2) and (4, 7) internally.

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50. Centroid of a triangle:

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