Students and Teachers Forum

1. Find the M.D. from mean: 8, 6, 2, 4, 5.

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2. Find the S.D. and its coefficient for: 1, 3, 5, 7, 9.

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3. Find the 10th term of the sequence 2, 6, 10, .........

Here, the given sequence is in AP in which, First term (a) = 2 Common difference (d) = 6 - 2 = 4 Now, the nth term of AP = tn = a + (n - 1)d So, t10 = 2 + (10 - 1) ⨉ 4 = .....

4. Prove that:1-tan2(450-A)1+tan2(450-A) = cos2A.

Taking, LHS  = 1- tan2450-A1+ tan2(450-A      (We have, 1-tan2A1+tan2A=cos2A) = cos2(450 - A) = cos( 90o - 2A) = sin2A  LHS = RHS proved  .....

5. M2x3 and N3x2 are the two matrixes. What will be the order of MN matrix.

When Ma⨉b  and Nb⨉c are multiplied, then the result MN will have order of a⨉c. Hence, the order of MN will be .....

6. If a man deposited Rs. 5000 rupees in a bank and the bank gave him 5% compound interest half yearly. How much money will he get after 2 years?

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7. If f(x) = (3x - 1) / 2, x belongs to n and p = {1, 2, 3} is the set of range of function then find its domain. Also represent the function in a venn-diagram. 

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8. Construct a 2 x 2 matrix A = [aij] whose elements are aij = (i+2j)2.

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9. Convert 0.0000065 into power of tens.

0.0000065 into power of tens. We know, 0.1 = 10-1 0.01 = 10-2 similarly, 0.0000001 = 10-7  0.0000001⨉ 65 = 65 ⨉ 10-7 0.0000001 = 65⨉ .....

10. Convert 0.00000000215 into power of tens.

 0.00,000,000,215 into power of tens. We know, 0.1 = 10-1 0.01 = 10-2 Similarly, 0.00,000,000,001 = 10-11 0.00,000,000,001 ⨉ 215 = 215 ⨉ 10-11 0.00,000,000,215 = 215 ⨉ 10-11  215 ⨉ 10-11 = 2.15 ⨉ .....

11. The present population of a town is 80,000. If the population increases 2% by birth and 3% by migration. What will be the population of the town after 2 years? (Ans: 88200)

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12. (a) A matrix has a 4 elements. Write the possible orders of the matrix.
(b) A  matrix has a 12 elements. Write the possible orders of the matrix.
(c) If a matrix has a 3 rows and 2 columns, what is the number of elements in the matrix?

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13. If the price of a record is Rs. 30, of a blade pocket Rs. 1.50 and of a soap cake Rs. 1.70, display the prices as a 3 × 1 matrix.

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14. The pupils in an algebra class marks score on the test as follows:
Solony: 77, 87, 92; Poonam: 95, 98, 91; Sita: 76, 88, 77. Display this information as a 3 × 3 matrix.

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15. Find the values of a.

 

i) a + 600 +300 = 180 (Sum of interior angles of triangle) or, a = 1800 - 900 or, a = 900 ii) Here, a = b (Being isosceles triangle) so, 2a + 900 = 1800 ( sum of interior angles of triangle) or, 2a = 900 or, a = .....

16. Name the fundamental units involved in the derived unit joule.

We  know that, Joule is the unit of energy or workdone. Workdone = Force x displacement The unit of force is N and displacement is m. So, J= Nm And again force = mass x acceleration = kgms-2= N So, J = kgm2s-2. So, the fundamental units .....

17. What is the SI unit of temperature?

The SI unit of temperature is Kelvin. It is denoted by .....

18. What is the standard unit used to measure mass?

The standard unit used to measure mass is kilogram .....

19. Underline the SI units from the given list of units.
   Minute, Kelvin, Mole, Bitta, Dharni, Metre

Answer: minute, Kelvin, mole, bitta, .....

20. When Sunayana purchased a video-game she paid Rs 162.50 as VAT at the rate of 13 %. Find its cost without levying VAT.

Here,    VAT amount = Rs.162.50     VAT rate = 13%     Cost without VAT = ? We know,          VAT% = VAT amount / Cost without VAT ⨉100%  or,    13 = Rs.162.50 .....

21. When the VAT rate is 15 %, a customer pays Rs 1,610 to buy an electric iron . Find the cost of the iron without VAT.

Here, VAT rate = 15% Price after VAT = Rs.1610. SP( price without VAT) = ? We know,      Price with VAT = SP + VAT % of SP or, Rs.1610 = SP + 15/100 ⨉ SP or, Rs.1610 = 115SP /100 or, SP = Rs.1610 ⨉ .....

22. The price of an article is Rs 1200 and a customer pays Rs 1,380 with VAT. Find the rate of VAT.

Here, SP = Rs.1200 Price with VAT = Rs.1380 VAT% = ? We know, VAT  amount  = Price with VAT - SP                          = Rs.1380 - Rs.1200       .....

23. Solve : (36)34×1364

Here,      (36)3/4 ⨉ ∜(1/36) =  (36)3/4 ⨉ ∜36-1 = (36)3/4 ⨉ (36)-1/4 = (36)3/4 + (-1/4) = (36)3/4 - 1/4 =(36)2/4  = (36)1/2 = (62)1/2 = 62 x 1/2 = 61 = 6 .....

24. Write difference between SI system and CGS system. 

Differences between SI system and CGS system are as follows:   SI system CGS system 1. In SI system, the unit of length, mass and time are meter (m), kilogram (kg) and second (s) respectively. 2. SI system is .....

25. What are the two differences between fundamental units and derived units ?

Two differences between fundamental and derived units are: 1. Fundamental units are independent of each other and cannot be further expressed into any other units.     Derived units are expressed in terms of fundamental units. 2. .....

26. In the given figure, △ABC is an equilateral triangle. If AB ∥ CE, prove that ∠ACE = ∠ECD.

Here, in ∆ABC, 1.∡A = ∡B =∡C  [ since, ABC is an equilateral triangle.] 2.∡A = ∡ACE     [ Alternate angles.] 3.∡B = ∡ECD      [ Corresponding angles.] So, from 1,2& .....

27. Find the unknown sizes of angles.

Here, x = 65o       [ Alternate angles.] x + y + 60o = 180o      [ Angles of a triangle.] or, 65o + y + 60o = 180o or, y + 125o = 180o or, y = 180o - 125o or, y = .....

28. Factorise
1. x4 + 2x2 + 9
 

1)    x4 + 2x2 + 9 = x4 + 6x2 + 9 - 4x2 = (x2)2 + 2.x2 . 3 + 32 - (2x)2 = ( x2 + 3)2 - (2x)2 = ( x2 + 3 + 2x)( x2 + .....

29. Prove: sec2θ1-sin2θsin2θ=1-tan2θtan2θ

Here, LHS = sec2θ ( 1 - sin2θ /sin2θ)          = sec2θ (1 - 1 )          =  sec2θ . 0          = 0 RHS= 1 - tan2θ / .....

30. Resolve Into Factors: 
 a2b2+1+b2a2

Please mention the question .....

31. Why is computer called versatile machine?

Computer is the electronic device which perform the logical and mathematical calculation. Computer is known as the versatile machine because it is very fast in every field and it the part of life without it we cannot imagine life.

It can .....

32. Express the following Hindu Arabic numbers in Roman numbers.

378
429
897
984
1325
1664
2155
2518
3193
3745

Here, I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 Now, 378 = CCCLXXVIII 429 = CDXXIX 897 = DCCCXCVII 984 = CMLXXXIV 1325 = MCCCXX 1664 = MDCLXIV 2155 = MMCLV 2518 = MMDXVIII 3193 .....

33. Convert 378 in roman number.

Here, 100 = C So, 300 = CCC 50 = L And, 10 = X 20 = XX So, 70 = LXX Also,  8 = VIII Putting together we get,  378 .....

34. Fill in the blanks:
........ is the distance travelled in fix direction.

Displacement is the distance travelled in fix .....

35. उत्तर देउ:
कवितामा हाम्रा पुर्खाहरुले देश्का निम्ती दीएको योग्दानलाई के कसरी वणन गरिएको छ्, लेख ?


 

नेपाल कवितामा पुर्खाहरुको रगत, पसिना, त्याग तपस्याले देशको सृजना भएको चर्चा गरिएको छ .....

36. Solve :(36)34×1364

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37. What is the difference between kilogram and kilometer?

The difference between kilogram and kilometer is: - Kilogram (kg) is the unit to measure mass while,    Kilometer (km) is the unit to measure .....

38. Plants breathe through _________ .

Plants breathe through green leaves. Their leaves .....

39. Tick the correct statement and cross the wrong ones.
a.  Kg/m3 is a derived unit.
b. Weight is measured by using a physical balance.
c. The value of mass of a body is fixed everywhere.
d. Volume is not derived quantity. 

a. Kg/m3 is a derived unit.   ✓     b. Weight is measured by using a physical balance.    ✖            c. The value of mass of a body is fixed everywhere.    .....

40. Convert:
340 cm into m 

  100 cm = 1 m   1 cm = 1/100 m    340 cm = 340/100 m    340 cm = 3.4 .....

41. नेपाल कविताको मुख्य भाव लेख ।

नेपाल कविता युगकवि सिद्धिचरण श्रेष्ठ (१९६९ – २०४९) ले रचना गरेका हुन् । यस कवितामा कविले .....

42. Write the HTML codes for the following :
Write about yourself in 2 paragraphes by changing the paragraph, background colour as red, text aligned to center, font size 14, face as arial black, font style bold and italics, break the line as well, use horizontal rule to divide line between 2 paragraphs, set MARQEE behavior as scrool and align to the top.

<!doctype html> <html> <head> <title> my webpage </title> </head> <body style="background-color:red;color:black;text-align:center;font-family:arial .....

43. Find HCF
(a + b)2 - 4ab, a3 - b3,  a2 + ab - 2b2

Here,  First expression = (a + b)2 - 4ab                           = a2 + 2ab + b2 - 4ab                   .....

44. m3 - m2 - m + 1, 2m4 - 2m, 3m2 + 3m - 6

First expression = m3 - m2 - m + 1                            = m2( m - 1) - 1 ( m - 1)                       .....

45. Find the H.C.F.
5a3 - 20a, a3- 3a2 - 10a, a3 - a2 - 2a + 8

Here,  First expression = 5a3 - 20a                           = 5a( a2 - 4)                           .....

46. Ram Baral sold a pen to Kamala at 25% profit. Kamala sold the pen to Roshan at 10% loss. If Roshan paid Rs 72 to Kamala. How much did Ram pay to buy the pen?

Here,  For Ram, CP = x (say) Profit % = 25% Now, SP = CP +25% of CP               = x + 0.25x              = 1.25x For Kamala, CP = 1.25x Loss% = 10% SP = Rs. 72 ( .....

47. Bina Chand bought two kettles for Rs. 1,625. She sold one of them at 20% profit and the other at 20% profit and the other at 20% loss. If the selling price of both kettles are same, find the cost price of each kettles. Also calculate her gain or loss percent in the total transact.

Here, Let, the CP of kettle 1 be x. Then,  For, kettle 1st, CP = x profit% = 20% So,  SP = CP + 20% of CP      = CP +.2CP     = 1.2CP     = 1.2x For kettle 2nd , CP = (Rs. 1625 - x) loss% = .....

48. A wholesaler purched an electric item for Rs. 2,700 and sold to retailor at 10% profit. The retailer sold it at 20% profit to a consummer. How much did the consumer pay for it.

Here,  For wholesaller, CP = Rs. 2700 Profit% = 10% Now,  SP = CP + 10% of CP        = CP + 0.1CP          = 1.1CP        = 1.1 × Rs. 2700     .....

49. The selling price of a watch is Rs. 1800 and 13% VAT is levied on it. How much should a costomer pay for it?

a) Here,  Selling price of watch (SP)= Rs.1800 VAT % = 13% Price with VAT = ? We know,        VAT amount = 13% of SP                            .....

50. When 12percent discount is given a calculator is sold for Rs 1,760,find the marked price of calculator.

Here, Discount = 12% of MP SP = Rs 1760 Then, You may know, S.P = M.P - discount or, Rs 1760 = MP - 12% of MP or, Rs. 1760 = MP - 0.12MP or, Rs. 1760 = 0.88MP or MP = Rs. 1760/0.88         = Rs. .....