Students and Teachers Forum

1. The cost of 7 wall clocks is Rs.1750. What is the cost of 13 wall clocks? How many wall clocks can be purchased for Rs.4000?

Here, Cost of 7 wall clocks = Rs 1750 Cost of 1 wall clock = Rs 1750 / 7 = Rs 250 Then, Cost of 13 wall clocks = Rs 250 * 13 = Rs 3250 Again, Number of clock that can be purchased for Rs 4000 = 4000 / 250 = 16 Hence, 16 clocks can be purchased .....

2. A trader cheats 10% on buying and again cheats 10% on selling. Find the total profit percentage gained by the trader.

Lets say the indicated weight is x . But the trader actually get x + 10% of x = 1.1x . Now he again cheats to the  customer 10% ,  that is, = 1.1x + 10% 0f 1.1x =   1.21x So,  profit % = (1.21x -x )/ x × 100% = .....

3. If 7 tanA = 1 and 3 tanB = 1, then prove that cos2A = sin4B.

Here,  7 tanA = 1  or, tanA = 1/7. LHS = cos2A = (1 - tan2A)/(1 + tan .....

4. If cos45o = 1/√2, provr that: tan22.5o = √(2 - √2).

We know, cosA = (1-tan2A/2)/(1 + tan2A/2) Put A =45o, we get cos45o = (1-tan222.5)/(1 + tan222.5) or, 1/√2 =  (1-tan222.5)/(1 + tan222.5) or,  (1+ tan222.5) = √2(1 - tan222.5) or, 1+ tan222.5 = .....

5. Prove that: Tan(A - B) + tan(B - C) + tan(C - A) = tan(A - B) tan(B - C) tan(C - A).

Let P = A - B, Q = B - C & R = C - A. Then,  P+Q+R = A- B + B- C + C - A = 0 or, P + Q = - R Operating both sides by tan we get or, tan( P + Q) = tan(-R) .....

6. Prove that: cot(A+B)/tan(A-B) = (sin2A - cos2B)/(cos2A - cos2B).

LHS = Cot (A+B) / tan (A-B)  Changing cot and tan into sin & cos, we get = {cos(A+B) cos(A-B)}/{sin(A+B)sin(A-B)} Using formula of sin(A+B)and so on we get = {(cosAcosB - sinA sinB)(cosA cosB + sinA sinB)}/{(sinA cosB + cosA sinB)(sinA .....

7. Prove that: { 1 + sin(A+B)}{1 - sin(A - B)} = (cosA - sinB)2.

In the question, LHS = [ 1 + sin(A+B)] [ 1 - sin(A-B)] = 1 + sin(A+B)  - sin(A-B) - sin (A+B)sin(A-B) Use formula, 2cosA.sinB= sin(A+B) - sin (A-B) [1st and 2nd term] 2sinA sinB= cos(A-B) - cos(A+B) [ Last term] You will get, cos2B and .....

8. If f(x) = 2x2 - 5x + 4, for what values of x is  2f(x) = f(2x)?

Here,  We have given,     2f(x) = f(2x) or, 2(2x2 - 5x + 4) = {2(2x)2 - 5(2x) + 4},    [ Since, f(x) = 2x2 .....

9. Prove that: sin6o.sin42o.sin66o.sin78o = 1/16.

We use the trigonometric rules :             2 Sin A  Sin B = Cos (A-B) - Cos (A+B)             2 Cos .....

10. न्युटनको बाल्यकाल किन संघर्षमय बन्न पुग्यो ? 

न्युटन जन्मनुभन्दा तीन महिनाअघि बुबाको मृत्यु भएको र न्युटन जन्मेपछि उनकी आमाले .....

11. What is pulakeshi?

Pulu kishi is the white elephant (the white elephant of Indra) dance during Indra jatra It is made out of bamboo and cloth and a face .....

12. Fill up the tables given below

a) 
y 1.99 1.999 2.001 2.0001 y → 2
f(y) = y-1 / y2 + 1         f(y)  → 1/3

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13. Argentina exports meat and wheat. Why?

Argentina exports meat and wheat in a large quantity. Argentina lies in the Temperate grassland region which is quite favorable for agriculture. Wheat cultivation is prominent in Temperate grassland as the climate is suitable for its .....

14. वायुपन्खि बिग्रह गर्नुहोस ।

वायुको जस्तो पंख छ .....

15. What actually is the Great Barrier Reef? Is it ocean, sea, bay or what? And before that what is reef?

A reef is a bar of rock, sand, coral or similar material, lying beneath the surface of the water. So, it is not the sea actually. The Great Barrier Reef contains an abundance of marine .....

16. Prove that:
sinθ + sin5θ = sin3θ [ 0 ≤ θ ≤ 360]

I think we need to solve it! sinθ + sin5θ = sin3θ or, 2sin(θ + 5θ)/2 . cos(θ - 5θ)/2 = sin3θ  or, 2sin3θ . cos2θ - sin3θ = 0 or, sin3θ( 2cos2θ - 1) = 0 Either, .....

17. The centre of circle having radius 5 units lies in the third quadrant. If the circle touches the y-axis at (0, -4), find the equation of the circle.

h = - r =  -5 not h = 0. Please look answere .....

18. In the given figure, A' is the image of A(1, -2) when translated by the translation vector (2, 4). A" ia the image of A' when translated by (-5, -1). Find the coordinates of A' and A'' and the single translation vector which translates A to A".

Here,  A' is the image of A (1, -2) when translated by the translation vector (2,4).  So, we have formula,  P(x, y)------------T(a, b)------------>P'(x + a, y+b). A (1, .....

19. Prove that: sin(x +1)A . sin(x + 2)A + cos(x + 1)A.cos(x + 2)A = cosA.

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20. Prove that: tan8o + tan52o = √3 - √3tan8o tan52o      

We know, 8o + 52o = 60o  Operating both sides by tan we get,       tan(8 + 52) = tan60 or, (tan8o + tan52o)/(1 - tan8o tan52o) = √3   [ .....

21. If cotα =1/2 and secβ = 5/3, find the value of tan(α + β).

Here,  Cotα = 1/2  ⟹ tanα = 1/ cotα = 2. &  secβ = 5/3  ⟹ tanβ = √( sec .....

22. Tan (A -B) + TanB / 1- tan (A - B) tan B = tanA

Here,  LHS = {tan(A-B) + tanB}/{1 - tan(A-B) tanB} = tan{(A - B) + B}    [Since, letting A-B = A and using formula of tan(A+B).] = tan(A - B + B) =tanA = .....

23. Derive the equation of the circle whose centre lies on the fourth quadrant and on the line 2x + y -1 =0, area 25π sq.units and the circle passes through (4, 3).

Hre, let r be the radius of the required circle. Then Area  =25π  or, π r2 = 25π  or, r = 5 .....

24. Find the equation of stright line orthogonal to 2x + 3y + 7 = 0 and makong X-intercept 5.

Here, equation of given st line is 2x + 3y + 7=0 Slope (m1) = - coeff.of x / coeff. of y = -2/3 Let m2 be .....

25. If (ay - bx)/p = (cx - az)/q = (bz - cy)/r, prove that  x/a = y/b = z/c.

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26. A boat is being right away from the from a cliff 150 m high at the top of the cliff the angle of depression of the boat changes from 60 ° to 45° in 2 minutes find the speed of the boat

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27. What can we understand about Prithvi Narayan Shah as a person from the fact that he respected common people's view like Bise Nagarchi and others?

The following things can be understood by the character of Prithvi Narayan Shah who would give more priority to people's opinion. - He was a democratic king in the history of Shah Dynasty in Nepal. - He was a very practical person in .....

28. Why was it necessary to cooperate with people for unification?

People had played a great role in the unification campaign. People volunteered in the war from each family. Every family sent their member in the war. They also donated money for making .....

29. Prove that: cos2π/7 + cos4π/7 + cos8π/7 = -1/2.

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30. If a + b = 4 and ab=3, prove that a-2 + b-2 = 10/9.

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31. Find the equation of the remaining sides of the equilateral triangle whose vertex is (-1, 2) and base y = 0.

Here, one point = ( -1, 2) = (x1, y1) Since itis an equilateral triangle and one side is parallel to the x- axis, The angle its arm makes with the horizontal is 60o and 120o. From the angle, you can calculate the slope of the lines. Slope .....

32. Find the single equation of the stright line passes through the origion and perpendicular to the line represented by the equation ax2 + 2hxy + by2 = 0.

Here is an easy and short method: Let ax2 + 2hxy + by2 = 0 represent two linear  l1x + m1y = 0 --------(i)   and   l2x + m2y = 0 --------(ii)  Combine these two .....

33. Prove that: cosπ/8 + cos3π/8 +cos5π/8 +cos7π/8 = 0.

L.H.S. = cosπ/8 + cos3π/8 +cos5π/8 +cos7π/8  Arranging we get,             = cos7π/8 + cosπ/8+ cos5π/8 + cos3π/8 .....

34. Mention any three partial knowledge which can be learned by human society from honey bee.

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35. Why is the necessary to study the life cycle of the honeybee? Clarify with two reasons.

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36. १. दिइएको गद्यांश राम्ररी पढी अन्त्यमा सोधिएका प्रश्नको उत्तर दिनुहोस् :
त्यो दिन मलाई राम्ररी सम्झना छ, सूर्यका लालीकिरणहरू धर्तीलाई आलिङ्गन गर्न निकै आतुर देखिन्थे । पोखराको सराङ्कोटबाट झुलुक्क झुल्किएको सूर्यले जब आफ्ना किरणहरू माछापुच्छेको शिरमा हुत्याए, तब सिङ्गो हिमाल मुसुक्क मुस्कुरायो । हो, त्यहीबेला चाँदीको शिर, हरियो सारी र पहेंला घुँगुरा लगाएकी पृथ्वी मेरा आँखा अगाडि छमछम नाच्न थालिन् । दर्शकले ताली बजाए । मेरा लाली ओठ मुस्कुराए । सूर्यमुखी फुलले पूर्वतर्फ फर्किएर सूर्यलाई आलिङ्गन गरे अनि कसरी हो कुन्नि, धर्तीको कोखमा सेती नदी जन्मिन् । अझै बग्दै छिन् र कहिलेसम्म बग्छिन्, कसैलाई केही थाहा छैन । मेरा आँखाका नजर र मुस्कानका अधरहरूका ती घटना अझै ताजै छन् ।

प्रश्नहरू :
क) माथि उल्लिखित ‘धर्तीलाई’ शब्दको कारक र विभक्ति पहिचान गरी लेख्नु्होस् ।
ख) रेखाङ्कित वाक्यलाई सरल वाक्यमा परिवर्तन गर्नुहोस् ।
ग) अनुच्छेदबाट ‘पुष्प’ र ‘रवि’ शब्दका पर्यायवाची शब्द पहिचान गरी वाक्यमा प्रयोग गर्नुहोस् ।
घ) सिङ्गो हिमाल किन मुसुक्क मुस्कुरायो ?
ङ) ‘दुग्धधारा’ र ‘अधर’ शब्दको अर्थ लेख्नुहोस् ?

अनुच्छेदबाट भेटिने दुइटा प्रश्नको उत्तर चाहिँ आफैँ लेख्नुहोस् है त .....

37. ८. कोष्ठकमा दिइएको निर्देशनअनुसार तलका वाक्य परिवर्तन गर्नुहोस् :
क) आफू त किवता लेखिन्छ । (कर्तृवाच्य)
ख) तपाईं कहिल्यै हार्नुभएको छैन । (सामान्य आदर)
ग) मिहिनेत गरे हामी सफल बन्छौँ । (वाक्य विश्लेषण)
घ) कुशल घर जान्छ । (प्रेरणार्थक)

८. (क) म त कविता लेख्छु । (ख) तिमीले कहिल्यै हारेका छैनौ । (ग) हामी मिहिनेत गर्छौँ । हामी सफल बन्छौँ .....

38. ७. कोष्ठकमा दिइएको धातु र सङ्केतका सहायताले वाक्य पुरा गर्नुहोस् :
क) हामी तपाईंको खबर पुर्याउन .......... । (जाः अपूर्ण वर्तमान)
ख) तीर्थयात्रीहरू सधैं मन्दिर .......... । (घुम्ः अभ्यस्त भूत)
ग) भिखारीहरू भिक्षा .......... । (मागः इच्छार्थक)
घ) सबै योद्धाहरू विजयी .......... । (हुः सम्भावनार्थक)

७. (क) जाँदै छौँ । (ख) घुम्थे । (ग) मागून् । (घ) होलान् .....

39. ६.
क) तलका उपसर्ग र प्रत्यय लगाई एक एक ओटा शब्द बनाउनुहोस् :
उपसर्ग बे, वि
प्रत्यय आन, आइ

ख) तलका गद्यांशबाट एउटा समस्त शब्द र विग्रहको अवस्था पहिचान गरी विग्रह वा समास गर्नुहोस् ।
टेलिभिजनको लोकप्रिय कार्यक्रम हेरिसकेपछि हजुरबा पूजा गर्न पूजाको कोठामा पस्नुभयो ।

६.(क) उपसर्ग बेकाम, विज्ञान प्रत्यय कटान, बसाइ (ख)  लोकमा प्रिय छ जो, .....

40. ५. रेखाङ्कित शब्दको शब्दवर्ग पहिचान गर्नुहोस् :
दुलहीसित सल्लाह नगर्नाले सबैले दुःख पाए, तसर्थ छोराछोरीका बारेमा निर्णय गर्दा बाबुआमाले आफ्नो पुरानो सोचाइ बदल्नु जरुरी भएको छ ।

५. सितः नामयोगी सल्लाहः नामपद सबैः सर्वनाम तसर्थः संयोजक पुरानोः विशेषण भएको छः .....

41. ४.
क) तल दिइएका शब्द समूहबाट शुद्ध शब्द छानी लेख्नुहोस् :
अ) विद्वद्वर्ग, बिद्वद्वर्ग, विद्वद्वर्ग, बिद्वद्बर्ग
आ) सस्त्र, शास्त्र, शाष्त्र, साश्त्र

ख) तल दिइएको वाक्यलाई शुद्ध पारी सार्नुहोस् :
कमानसिंहले भने त्यसो त नेपाल मा नोकरि नपाएर देश पसेको होइन ।

४.(क) अ. विद्वद्वर्ग आ. शास्त्र (ख) कमानसिंहले भने, ‘त्यसो त नेपालमा नोकरी नपाएर देश पसेको होइन .....

42. २. कोष्ठकबाट मिल्ने शब्द छानी तलका खाली ठाउँ भर्नुहोस् :
क) .......... अनेकार्थी शब्द हो । (हाल, बेहाल, नहाल)
ख) ‘भ्रमण’ को पर्यायवाची शब्द .......... हो । (ग्रहण, जात्रा, यात्रा)
ग) ‘जोर’ को विपरीतार्थक शब्द .......... हो । (जार, बिजोर, चोर)
घ) दिन–दीन .......... शब्द हुन् । (अनेकार्थक, श्रुतिसमभिन्नार्थी, लघुवाची)

२. (क) हाल (ख) यात्रा (ग) विजोर (घ) .....

43. १. तल समूह ‘क’ मा दिइएका शब्दहरूका अर्थ समूह ‘ख’ बाट पहिचान गरी जोडा मिलाउनुहोस् :

समूह ‘क’                  समूह ‘ख’
परिष्कार                   बाढी
भेल                          एक भएको
एकाकार                   समूह
श्रीहीन                      शुद्ध पारिएको
                               शक्ति नभएको
                               सम्पत्ति नभएको

१. परिष्कारः शुद्ध पारिएको भेलः बाढी एकाकारः एक भएको श्रीहीनः सम्पत्ति .....

44. An automatic device from a control tower observes the vechicles to check their speed, the speed-limit for the high way is 60km/hr. From a position on the tower 50meter above the ground the device records the angle of depressions of a car at the time of initial observation as 30o and after 1 second the angle of depression increases to 60o . Find the speed of the vehicle. Does the vehicle cross the speed limit?

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45. Find the equation of stright line l Ias shown in the figure) that passes through the mid-point of the portion of the stright line 2x + 3y = 6 interceped between the coordiante axes and is perpendicular to the line 2x + 3y = 6.

Here, we have given,  2x + 3y = 6 or, x/3 + y/2 = 1 Compare it with x/a + y/b = 1, we get a = 3 & b = 2. Thus, the line 2x + 3y = 6 intercepets at points (3, 0) and (0,2) Mid-point of .....

46. Find the single transformation for the rotation through a positive quarter turn about the origin followed by the reflection in X-axis. Also use this single transformation to find the image of the point ( 6,2 ).

For the rotation through a positive quarter turn about the origin, P( x,y ) = P'( -y,x ) Again, For the reflection in X-axis, P( -y,x ) = P'( -y,-x ) For the single transformation, reflection in the line y=-x. which is, P( x,y ) = P'( .....

47. Solve for x: (0o ≤ x ≤ 360o) 
√3cotx = sin30o.sec60o. 

Here, √3cotx = sin30o.sec60o.  Using value of sin30o & sec60 .....

48. What must be added to the polynomial p(x) = 2x3 - 7x2 + 8x + 7 to get remainder 10, when divided by (x + 3)?

Here, compare x + 3 with x - a, we get a = -3. Then,  p(-3) = 2(-3)3 - 7(-3)2 + 8(-3) + 7 =  -131. So, to get remainder 10, we must add 131 + 10 = .....

49. Let f(3x + 1) = 3x - 2 is a function under the domain of all real numbers, then find ff(-2).

Here,  f(3x + 1) = 3x - 2 f(3x + 1) = (3x + 1)  - 2 - 1 Put x = 3x + 1, we get f(x) = x - 3. Now,  ff(-2) = f{f(-2)} = f(- 2 - 3) = f(-5) = - 5 - 3 = - .....

50. How to convert 1/2 and 6/9 into like fraction?

Here,  1/2 = 1/2 ⨯ 9/9 = 9/18 And 6/9 = 6/9 ⨯ 2/2 = 12/18 Here both fraction has same denominator. So they are like .....