Students and Teacher's Forum

Students and Teachers Forum

1. Show that the line 2x + 4y = 3 is penpendicular to the line passing through the points (7, 3) and (0, -11).

Here, Slope of line 2x + 4y = 8 is m1 = - 2/4 = -1/2 Slope of line passing through (7,3) & (0 , -11) m2 = (y2 - y1) / (x2 - x1) = (-11 - 3)/(0 -7) = .....

2. Find the value of k so that the following two straight lines :
a. x + 3y = 7 and 2x + ky + 8 = 0 are parallel.

Here, If the given lines are //, slope of x + 3y = 7 is equal to slope of 2x + ky + 8 =0 or, -1/3 = -2/k or, k = 6. Hence, k = .....

3. tan(A + B) + tan(A - B) = sin2B / ( cos²A - sin²B)

= sin2B / ( 1 - sin2B - 1 + cos2A) = sin2B / ( cos2A - sin2B) = .....

4. A firm invests Rs. 2500000 to establish itself. After one year it makes a profit of 32%. If 5% of the profit is decided to be distributed as bonus among 80 employees, find the bonus given to each employee. (Ans: 500)

Here, Profit amount = 32 % of Rs. 2500000 = 0.32 ⨉ Rs. 2500000 =Rs. 800000 Now, Bonus = 5% of Profit amoutn = 0.05 ⨉ Rs. 800000 .....

5. A hotel raised its profit up to 5000000 in a year. It distributed to its 60 workers the bonus at the rate of Rs. 12000 each. Find what % of the profit was distributed among the workers. If the per head bonus is raised to Rs. 15000, find the new% of the profit distributed. (Ans 14.4% next 18%)

Here, Total bonus = Rs. 12000 ⨉ 60 =Rs. 720000 Now, % of the profit distributed = Rs. 720000 / Rs. 5000000 ⨉ 100% = 14.4 % Now, New Bonus For Each worker = Rs. 15000 Bonus to all workers = Rs. 15000 x 60 = Rs. 900000 Now, .....

6. A departmental store earned Rs 1200000 as profit and distributed Rs 4800 as bonus to each of its 20 salesman. Find what % of the profit was distributed among them. If it is increased by 2%, what amount will each salesman get as bonus? (Ans 6000)

Here, Total bonus = Rs. 4800 ⨉ 20 =Rs. 96000 Now, % of the profit distributed = Rs. 96000 / Rs. 1200000 ⨉ 100% = 8 % When 2 % is increased, the bonus% = 8% + 2% = 10% Now, Bonus = 10% of 1200000 = Rs. 120000 Bonus to each salesman .....

7. An agent is paid commission of 2% on the total sales and a bonus of 0.5% on the excess of sales over Rs 450000. Find how much he recieves as commission if the bonus amounts to Rs 1500. (Ans 15000)

Let, The sales above the Rs. 450000 = Rs. x Now, 0.5% of x = Rs. 1500 or, 0.005x = Rs. 1500 So, x = Rs. 1500 / 0.005 = Rs. 300000 Now, Total sales = Rs. 450000 + Rs. 300000 = Rs. 75000 Commission amount = 2% of Total sales .....

8. How many types of angle are there?

Is your question .....

9. When age of Rita was equal to present age of Shova , she was thrice as old as shova was . If the sum of their present age is 40 years , find their ages.

Let the present ages of Rita and Shova be x and y. By question, y = 3 [y + ( y - x ) ] y = 3 [ y + y - x ] y = 3 [ 2y - x ] y = 6y - 3x 3x = 6y - y 3x = 5y x = ( 5 ∕ 3 ) y --------- [ I ] Again, x + y = 40 Placing the value of x .....

10. In 2010, Sali was two times as old as Kedar was . If the ratio of their ages will be 5:3 in 2015.Find their years of birth.

Let in 2010 age of Sali was x and age of Kedar was y. From the first case, x = 2y ..........i) From the second case, ( x+ 5)/ ( y + 5) = 5/3 or, 3x + 15 = 5y + 25 or, 6y - 5y = 25 - 15 .....

11. Mr. Gurung was four times as old as his son was in 2002 but he was only three times as old as her son on 2007. What is the year of son's birth?

Let ages of Gurung be x and son be y in 2002. From the first condition, x = 4y ....................i) From the second condition in 2007,there ages will be x + 5 & y + 5. So, x + 5 = 3( y+ .....

12. The present age of the mother is 4 times the age of daughter. If the age of daughter after 20 years is equal to the age of mother before 25 years. Find present ages.

Let the present age of the mother be 'm' and the present age of the daughter be 'd' . According to the question, m = 4d, After 20 years, d + 20 = m - 25 or, m - d = 20 + 25 or, 4d - d = 45 ∴ d = 15 m = .....

13. cosA/sec2A - sinA/cosec2A = 1/ sec3A

Here, LHS = cosA/sec2A - sinA/cosec2A = cosA.cos2A - sinA.sin2A = Cos(A + 2A) = cos3A = 1/ sec3A .....

14. cotA/(cotA - cot3A) - tanA/(tan3A - tanA) = 1

LHS = cotA/(cotA - cot3A) - tanA/(tan3A - tanA) = (1/tanA)/ [ 1/ tanA - 1/ tan3A] - tanA/(tan3A - tanA) = tan3A/ (tan3A - tanA) - tanA/(tan3A - tanA) .....

15. Prove that:
cot θ - cot 2θ = cosec 2θ

LHS = cot θ - cot 2θ = cosθ/sinθ - cos2θ/sin2θ = cosθ/sinθ - ( 2cos2θ - 1) / ( .....

16. If cot α = 1 2 and sec β = 1 2 where 90⁰ < β < 180⁰, ten find value of tan ( α + β)

Here, Cotα = 1/2 ⟹ tanα = 2. & secβ = 1/2 ⟹ tanβ = √[ (1/2)2 - 1] = √(-3/2), which is impossible . Please check .....

17. If cos A = 12 13 and cot B = 24 7
[where A lies in second quadrant and B in third quadrant], then find the value of

(a) sin (A + B) (b) tan (A + B)

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18. If tan θ + tan ϕ = a, and cot θ+ cot ϕ = b, then prove that:
cot (ϕ+θ) = (1 a - 1 b)

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19. Prove that:
tan 20⁰ + 4 sin 20⁰ = √3

LHS = tan 20⁰ + 4 sin 20⁰ = Sin20 / cos20 + 4sin20 = [sin20 + 4sin20.cos20] / cos20 = [ sin20 + 2sin40] / cos20 = [ sin( 60 - 40) + 2sin40] / cos20 .....

20. मलाई अधुनिक प्रविधी को बारेमा लेख्नुछ

आधुनिक प्रविधि वर्तमानमा जे भइरहेको छ, त्यो आधुनिक हो । आधुनिकले नयाँ भन्ने बुझाउँछ .....

21. एक वाक्यमा उत्तर भन:
देवकुमारीको जन्म कहाँ र कहिले भएको थियो ?
देवकुमारी थापाले किन बाल साहित्यको पुस्तक लेख्न थलिन ?
देवकुमारीले आफ्नै खर्चमा कुन संस्था स्थापना गरिन ?
देवकुमारी थापा कुन कुन छेत्रमा उदाहरण बनेकी छिन ?

(क) देवकुमारी थापाको जन्म भारतको दार्जिलिङ क्षेत्र अन्तर्गत खरसाङमा वि. सं.१९८५ वैशाख २ गते .....

22. चित्रकलाको बिकासमा ग्रन्थचित्रको कस्तो भूमिका छ, बिबेचना गर् ।

मानव सभ्यताको विकाससँगै विविध क्षेत्र, विधा, संस्कार र संस्कृति हुँदै चित्रकला अगाडि बढेको छ .....

23. Find the Selling price with VAT from the table given below.

S.No.	S.P. without VAT	VAT%	S.P. with VAT
(i)	Rs. 1,500	13%	?
(ii)	Rs, 7,200	13%	?
(iii)	Rs, 25,000	15%	?

iii) S.P with Vat = S.P + Vat % of S.P = 25000 + 13 % of 25000 .....

24. Prove that:
cosec 2A + cosec 4A + cosec 8A = cot A - cot 8A

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25. Simplify: x + 1x – 1+x² – 1x + 1

Here, = ( x + 1)/( x – 1) + (x 2 – 1)/( x + 1) = ( x + 1)/( x – 1) + (x – 1)(x + 1)/( x + 1) = ( x + 1)/( x – 1) + (x – 1) .....

26. Find the H.C.F. and L.C.M of the following expressions.
x³ - 9x, x⁴ - 2x³ - 3x², x³ - 27

First expression = x3 - 9x = x ( x2 - 9 ) = x ( x2 - 32 ) = x ( x - 3 ) ( x + 3 ) Second expression = x4 - 2x3 - 3x2 = x2 ( x2 - 2x - 3 ) = x2 ( x2 - 3x + x - 3 ) = x2 { .....

27. Find the L.C.M. of the following expression.
(a - 3)², a² - 9, a³ + 27

1st expression = (a - 3)2 = (a - 3) (a - 3) 2nd expression = a2 - 9 .....

28. Find the L.C.M. of the following expressions.
x² + 3x + 2, x² + 5x + 6, x² + 4x + 3

1st expression = x2 + 3x + 2 = x2 + 2x+ x + 2 = x( .....

29. Find the L.C.M. of the following expressions.
x³ - 2x²y + 2xy² - y³, x⁴ - y⁴, x³ + y³

1st expression = x3 - 2x2y + 2xy2 - y3 = x3 - y3 - 2x2y + 2xy2 [a3 - b3 = (a - b) (a2 + ab + .....

30. Find the L. C. M of the following expression.
a³ - 4a, a⁴ - a³ - 2a², a³ - 8

Here, First expression = a3 - 4a = a(a2 - 22) = a(a + 2)( .....

31. Find the L.C.M. of the following expressions.
a² - 4, a³ - 8, (a + 2)²

Here, first expression = a2 - 4 = a2 - 22 .....

32. Find HCF
X² - 9, 3X³+ 81

Here, 1st expression = x2 - 9 = x2 - 32 = ( x + 3) ( x .....

33. Find HCF of:
ax² + ax, ax² - a

Here, First expression = ax2 + ax = ax( x + 1) Second expression = ax2 - a .....

34. Find the L.C.M. of the following expression
x² + 5x + 6, x² - 4

Here, First expression = x2 + 5x +6, = x2 + 3x + 2x+6, .....

35. Find the L.C.M. of the following expression
3x² + 6x, 2x³ + 4x²

1st expression = 3x2 + 6x = 3x( x + 2) 2nd expression = 2x3 + 4x2 .....

36. Find the L.C.M of :
8a²b (a-b) (a²+ab+b²) and 12ab²(a-b) (a+b)

Here, First expression = 8a2b (a-b) (a2+ab+b2) = 2.2.2.a.a.b(a-b) (a2+ab+b2) Second expression = 12ab2 (a-b) .....

37. Find the L.C.M of :
3x (x+1) (x-1) and 2x²(x-1) (x+3)

1st expression = 3x (x+1) (x-1) 2nd expression = 2x2 (x-1) (x+3) so, LCM = 3x 2x2 (x+1) (x-1) (x+3) = 6x2(x+1) (x-1) .....

38. Find the L.C.M. of the following expressions.
x² - 18x - 19 + 20y - y², x² + x - y² + y, x² - y² + 2y - 1

1st expression = x2 - 18x - 19 + 20y - y2 = x2 - 2. x.9 + 92 - 100 .....

39. Find the H.C.F of:
x³ -1 , x⁴ + x²+1 , x³+1+2x²+ 2x

1st expression = x3 -1 = (x - 1) ( x2 + x +1) 2nd .....

40. Find the H.C.F of :
x³ - 64y³ ,x² -6xy + 8y² , x² -16y²

1st expression = x3 - 64y3 = x3 - (4y)3 .....

41. Find the H.C.F. of the following expressions.
m³ - m² - m + 1, 2m⁴ - 2m, 3m² + 3m - 6

(a + b)² - 4ab, a³ - b³, a² + ab - 2b²

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

42. Find the H.C.F of the following expressions :
3x² - 8x + 4, 2x² - 5x + 2, x⁴ - 8x

Here, First expression = 3x2 - 8x + 4 = 3x2 - 6x - 2x + 4 .....

43. In a survey of 825 farmers, 125 of them were not using any type of fertilizers in their vegetable farming. 150 of them were using chemical as well as organic fertilizers. That ratio of the number of only chemical fertilizers users to that of only organic fertilizers users is 5:6.
(i) Find the number of chemical fertilizer users.
(ii) How many of them were using only type of fertilzers?.
(iii) How many of them were not using organic fertilizer?
(iv) Represent the above information in Venn-diagram.

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44. In a survey of a group of people, 50 % liked to listen radio and 60% liked to watch television. If 30 % of them neither listen radio nor watch television, then
(i) Represent the above information in a Venn-diagram.
(ii) Find the percent of people who like to listen radion as well as watch television.

Here, Total % of people in survey = n(U) = 100% % of people like to listen radio = n(R) = 50% % of people like to watch TV = n(T) = 60% % of people do not likeboth = n(R U T)' = 30%. i) .....

45. In a class of 60 students, 15 students liked maths only, 20 liked English only and 5 didn't like any subject.
(i) Represent the above information in a Venn-diagram.
(ii) Find the number of students who liked both the subjects.
(iii) How many students liked maths?

Here, Total no.of students = n(U) = 60 No.of students liked maths only = no(M) = 15 No.of students liked english only = no(E) = 20 No.of students did not liked any of them = n(MUE)' = .....

46. In a group of 120 people, 90 play volleyball, 72 play football and 10 play neither of games.
(i) Draw a Venn-diagram to represent the given information.
(ii) How many people play only one game?

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47. What is ssdp? What are it's mangoal?

Could you please revisit the question and post the question in full so we may help .....

48. In a survey of 900 students in a school, it was found that 600 students liked tea, 500 liked coffee and 125 did not like both the drinks.
(i) Draw a Venn-diagram to illustrate the above information.
(iii) Find the number of students who liked both the drinks.
(iii) Find the number of students who didn,t like tea only.

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49. In a school, every student has to participate at least one of the activities, atheletics or music. In a class of 50 students 30 participated in atheletics and 25 participated in music.
(i) Draw a Venn- diagram to illustrate the above information.
(ii) How many students participated in only one activity?

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50. Among 1,200 Chinese tourists who are visiting Nepal, 45% of them have already visited India, 40% have visited Pakistan and 15% have visited both the countries.
(i) Illustrate this information in a Venn - Diagram
(ii) How many Tourists have not visited any of these two countries?

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