Students and Teachers Forum

1. Find the value of x :

In this fihure,  ∡D = ∡ABE            [ Interior angle is equal to opposite exterior angle in a cyclic qd.] Thus,  x = .....

2. Find the value  of  x:


 

Here,  Angles AQB & APB are standing on same arc AB. So,   ∡AQB (x) = ∡APB Thus, x = .................write .....

3. In the adjoining figure, find the value of :

Here, ∡D = 90o   [ Since, anhle at semi-circle.] So,  In triangle ADB. ∡A +∡C +  D = 180o or, x + y + 90o = 180o Complete .....

4. Which angles are supplementary in the given figure?

In the given figure, 1. ∡A & ∡C are supplementary. 2. ∡B & ∡D are supplementary.    Since, they are the opposite angles of a cyclic .....

5. In the given figure,find the value of ∢SPR. 

Here, ∡SPR = 1/2 of ∡SOR          [ Since, inscribed angle is half of central angle on same arc .] Thus, ∡SPR  = 1/2 of 120o. Calculate .....

6. In the given figure, find the value of ∡ AOB.

Here, ∡AOB = 2 of ∡ACB          [ Since, central  angle is half of inscribed angle on same arc .] Thus, ∡AOB  = 2 of 55o. Calculate .....

7. In the figure, find the value of ∡ADB.

 

Here, ∡ADB = ∡ACB          [ Since, they are standing on same arc AB.] Can you write the result .....

8. Find the value of x:

 

Here, ABCD is a cyclic qd. So,  ∡A + ∡C = 180o or, x + 130o = 180o Find .....

9. Find the value of x:

 

Here, ∡ABD = 1/2 of ∡AOD          [ Since, inscribed angle is half of central angle on same arc .] Thus,  x  = 2 of 32o. Calculate .....

10. From the adjoining figure, find the value of x.

Here, ∡BAC= 1/2 of ∡BOC        [ Since, inscribed angle is half of central angle on same arc .] Thus, ∡x  = 1/2 of 140o. Calculate .....

11. From the adjoining figure, find the value of  x.

Here,   ∡A = 90o          [ Angle at semicircle.] Thus,  x + 90o + 40o = 180o Find .....

12. In the given figure, ∡ BAC + ∡ ACB = 900. what AC is called?

Here,  We have given,  ∡A + ∡C = 90o So,  ∡A + ∡B + ∡C = 180o or, ∡B= 90o Thus, AC is diameter, as ∡B = .....

13. In the adjoining figure, which angles are equal?

In thr given figure,  ∡A = ∡DCN               [ since, interior angle is equal to opposite .....

14. In the adjoining figure, If arc AB = arc BC then which angles are equal?

In the given figure, arc AB = arc BC. We know, Equal arc makes equal angle at the curcumference. So, ∡A .....

15. In the adjoining figure, ∡AOB = ∡COD, which arc are equal? 

Here, As we know,  Equal angles makes equal arcs. So, if ∡AOB = ∡ COD, Then Arc AB = Arc .....

16. Write the relation between ∡ AOB and ∡COD in the figure.

Here,  Arc AB = Arc CD. Thus,  ∡AOB = ∡ COD.               [ Equal arcs makes equal angle at the .....

17. If ac and bd are two equal chords on the opposite sides of diameter ab of a circle with center o,prove that ac// bd.

Here, AC = BD. Join B & C. Now,  Show arc AB = arc CD Then  1/2 of ∡ACB = 1/2 of ∡DBC      [ Relation between arc and inscribed angle.] or,  ∡ACB .....

18. In the adjoining figure, O is the centre of the circle, AB the tangent and D the point of  contact, write the relation between OD and AB.

Here, AB is tangent  and OD is radius. We know that radius is perpendicular to tangent. Thus,  OD ⊥ .....

19. भूत कालको पूर्ण पक्षको तीन ओटा कृयापद प्रयोग गरी धरहराको बारेमा वर्णन गर्नुहोस्।

धरहरा
मैले धरहरा देखेको थिएँ । मैले धरहरामा फोटो खिचेको थिएँ । .....

20. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:
क)मेरो प्रार्थना सुनियोस्।(कतृवाच्य)
ख)राजेन्द्रलाई चिठी लेख्छ।(प्रेरणार्थक)
ग)आज पटक्कै जाडो छैना। (अकरण)
घ) रिसाएको भाइल्पहाडतिर हेर्यो। (संयुक्त वाच्य)

(क) तपाईं मेरो प्रार्थना सुन्नुहोस् । (ख) म राजेन्द्रलाई चिठी लेखाउँछु । (ग) आज असाध्यै जाडो छ .....

21. कोष्ठकमा दिइएका निर्देशनअनुसार तलका वाक्य परिवर्तन गर्नुहोस्:
(क) म मस्तसँग सुतेँ। (भाववाच्य)
(ख) ऊ हिमाल चढ्दै हुनेछ। (प्रेरणार्थक)
(ग) त्यो केटो धेरै बाठो छ। (बहुवचन)
(घ) राम हिमाल चढ्छ। श्याम हिमाल चढ्छ। (वाक्य संश्लेषण)

(क) मस्तसँग सुतियो । (ख) पथप्रदर्शकले उसलाई हिमाल चढाउँदै हुनेछन् ।  (ग) ति केटाहरु धेरै बाठा .....

22. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस: क)उनीहरु भकुन्डो खेल्लान्।(कर्मवाच्य)
ख)चालकले मोटर हाँक्यो।(प्रेरणार्थक)
ग)उनीहरु कविता लेख्छन्। (द्र्तीय पुरुष)
घ) वृक्षरोपण गरिएन त्यसैले पहिरो गयो।(संयुक्त वाक्य)

(क) उनीहरुद्वारा भकुन्डो खेलिएला । (ख) मैले चालकलाई मोटर हाँक्न लगाएँ । (ग) तिमीहरु कविता लेख्छौ .....

23. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:
(क) दाइले बहिनीलाई रुवाउनुभयो ।(कर्मवाच्य)

(ख) हामी धेरै प्रगति गर्नेछौँ।(प्रेरणार्थक)

(ग) उ भात खान्छ ।(अति उच्च आदर)

(घ) मेघ गर्जेर पानी पर्यो ।(मिश्र वाक्य)

(क) दाइद्वारा बहिनी रुवाइई । (ख) उसले हामीलाई धेरै प्रगति गर्न लगाउनेछ । (ग) उहाँ भात खानुहुन्छ .....

24. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:

(क) तिमीहरु खुब हाँसेछौ र नाचेछौ ।(भवाच्य)

(ख) रीता गीत गाउँछिन्।(प्रेरणार्थक)

(ग) पृथ्वी गोलो भएको कुरा सबै मान्छन् । (अकरण)

(घ) रवि घर पुगेर खाजा खान्छ ।(संयुक्त वाक्य) 

(क) तिमीहरुद्वारा खुब हाँसिएछ र नाचिएछ । (ख) म रीतालाई गीत गाउन लगाउँछु । (ग) पृथ्वी गोलो नभएको .....

25. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:

(क) म त धेरै डुल्दिन ।(भवाच्य)

(ख)राम चिया पिउँछ लगाउँछु । (प्रेरणार्थक)

(ग) नेपाल वीरहरुको देश हो ।(स्त्रीलिङग)

(घ)  ऊ सुते पनि उसलाई निद्रा लाग्दैन ।(मिश्र वाक्य)

(क) आफू त धेरै डुलिँदैन । (ख) म रामलाई चिया पिउन लगाउँछु । (ग) नेपाल वीराङ्गनाहरुको देश हो । (घ) जब ऊ .....

26. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:
(क) म त आज निकै थाकेँ ।(भाववाच्य)

(ख) विद्यार्थीहरु खेल्दै थिए ।(प्रेरणार्थक)

(ग) यो किताब कसका हो? (बहुवचन)

(घ) पानी परेकाले म तिम्रो घरमा ओत लाग्न आएँ ।(संयुक्त वाक्य)

 (क) आफू त आज निकै थाकियो । (ख) तिमी विद्यार्थीहरुलाई खेलाउँदै थियौ । (ग) यी किताबहरु कसका हुन् .....

27. कोष्ठकमा दिएको निर्देशन् अनुसार तलका वाक्य परिवर्तन गर्नुहोस:

(क) ऊ कापी र कलम किन्ला ।(कर्मवाच्य) 

(ख) तिमी कविता लेख्छौ ।(प्रेरणार्थक)

(ग) ऊ कत्ति मिहिनेत गर्दैन। (करण) 

(घ) ऊ प्रथम हुन्छ किनभने मिहिनेत गर्छ ।(सरल वाक्य)

(क) ऊद्वारा कापी र कलम किनिएलान् ।    (ख) म तिमीलाई कविता लेखाउँछु ।    (ग) ऊ असाध्यै मिहिनेत .....

28. कोष्ठकमा दिएको धातु र सङकेतका सहायताले  वाक्य पुरा गर्नुहोस:

(क) रोपारहरुले रमाउँदै धान____ । ( रोप्:पुर्ण भूत)
(ख) सबै युवाहरु स्वदेशमै काम ____  । ( गर्:पुर्ण भूत)
(ग) यस वर्ष सबै विद्यार्थीहरु उत्तीर्ण ____। (हु: सम्भावनार्थ)
(घ) ऊ कथा ____।( रच्: सामान्यार्थ)

(क) रोपारहरुले रमाउँदै धान रोपेका थिए । (ख) सबै युवाहरु स्वदेशमै काम गर्नेछन् ।  (ग) यस वर्ष सबै .....

29. कोष्ठकमा दिएको धातु र सङकेतका सहायताले  वाक्य पुरा गर्नुहोस:
(क) किसानहरु धान ____ । (काट् :अपूर्ण भविष्यत्)
(ख) उ गुरुले सोधेकाे प्रश्नको जवाफ ____  । (दि :अज्ञात भूत) 
(ग) तँ शत्रुबाट ____  (जोगि: आज्ञार्थ)
(घ) म विद्यालयको पोशाक ____।( धु: सामान्यार्थ) 

स्याबास .....

30. कोष्ठकमा दिएको धातु र सङकेतका सहायताले  वाक्य पुरा गर्नुहोस:
(क) म बाटो भुसुक्कै  ____  । (बिर्स:अभ्यस्त भूत)
(ख) बहिनी चिठी ____।(लेख्: सामान्य बर्तमान)
(ग) ऊ बिहान सबेरै ____।(हिँड्: इच्छार्थक)
(घ) तिमी छिट्टै घर  ____।(आउ: आज्ञार्थक)

(क) म बाटो भुसुक्कै बिर्सन्थेँ । (ख) बहिनी चिठी लेख्छे । (ग) ऊ बिहान सबेरै हिडोस् । (घ) तिमी छिट्टै .....

31. कोष्ठकमा दिएको धातु र सङकेतका सहायताले  वाक्य पुरा गर्नुहोस:
(क) म पोखरामा हिमाल ____। (देख्:अज्ञात भूत)
(ख) यिनीहरु घुम्न ____  । (जा:अपूण भविष्यत)
(ग) भगवानले आशिर्वाद ____।(दि: इच्छार्थक)
(घ) तिमी राम्रो कथा  ____।(लेख्: सम्भावनार्थ)

(क) मैले पोखरामा हिमाल देखेछु । (ख) यिनीहरु घुम्न जाँदै हुनेछन्  । (ग) भगवानले आशिर्वाद दिउन् .....

32. कोष्ठकमा दिएको धातु र सङकेतका सहायताले  वाक्य पुरा गर्नुहोस:
(क) सानीले मिठो खान ____  । (बनाउ:पूर्ण वर्तमान)
(ख) उनीहरु चकचक ____  । (गर्:अभ्यस्त भूत)
(ग) गरिबलाई दया ____।(गर्: इच्छार्थक)
(घ) तिमीहरु गीत ____।(गाउ: आज्ञार्थक)

(क) सानीले मिठो खान बनेकी छे । (ख) उनीहरु चकचक गर्थे । (ग) गरिबलाई दया गरेस् । (घ) तिमीहरु गीत गाओ .....

33. ४१. 
(क) केशबराजलाई चस्माले धोका दिन्थ्यो ।
(ख) विदुर सँधै न्यायको पक्षमा बोल्नेछन् ।
(ग) तपाईं लुम्बिनी घुम्न जानुहोस् ।
(घ)  ऊ भाइलाई कथा लेखाउला ।

२. 
(क) सोनावा बजार घुमेछ ।
(ख) धेरै पर्यटकहरुले हिमाल आरोहण गरेका थिए  ।
(ग) उनीहरु किताव राम्ररि पढ्लान् ।
(घ) हामीले उर्जा संकटबाट मुक्ति पाउँछौ । 

३.
(क)  विद्यार्थीहरु मिहिनेत साथ पढ्दैछन् ।
(ख) भावना गीत गाउँथी ।
(ग) ईश्वरले सबैको रक्षा गरुन् ।
(घ) आज पानी पर्ला। 

४.
(क) आकाशमा बादल लागेछ ।
(ख) उसले क्रिकेटमा चौका हानेको हुनेछ। 
(ग) श्याम तिमी कार्यक्रममा भाग लिन आउनु ।
(घ) तँ चौरमा गएर मज्जाले भकुण्डो खेल्लास् । 

१.  (क) केशबराजलाई चस्माले धोका दिन्थ्यो । (ख) विदुर सँधै न्यायको पक्षमा बोल्नेछन् । (ग) तपाईं .....

34. कोष्ठकमा दिइएका धातु र सङ्केतका सहायताले वाक्य पूरा गर्नुहोस्:
(क)  विद्यार्थीहरु मिहिनेत साथ ................ । (पढ्: अपूर्ण वर्तमान)
(ख) भावना गीत ................ । (अभ्यस्त भूत)
(ग) ईश्वरले सबैको रक्षा ................। (गर्: इच्छर्थक)
(घ) आज पानी ................ । (पर्: सम्भावनार्थ)

(क)  विद्यार्थीहरु मिहिनेत साथ पढ्दैछन् । (ख) भावना गीत गाउँथी । (ग) ईश्वरले सबैको रक्षा गरुन् .....

35. कोष्ठकमा दिइएका धातु र सङ्केतका सहायताले वाक्य पूरा गर्नुहोस्:
(क) सोनावा बजार ................ । (घुम्: अज्ञात भूत)
(ख) धेरै पर्यटकहरुले हिमाल आरोहण ................ । (गर्: पूर्ण भूत)
(ग) उनीहरु किताव राम्ररि ................ । (पढ्: सम्भावनार्थ)
(घ) हामीले उर्जा संकटबाट मुक्ति ................ । (पाउ: सामान्यार्थ)

(क) सोनावा बजार घुमेछ । (ख) धेरै पर्यटकहरुले हिमाल आरोहण गरेका थिए  । (ग) उनीहरु किताव राम्ररि .....

36. (क) केशबराजलाई चस्माले धोका दिन्थ्यो ।
(ख) विदुर सँधै न्यायको पक्षमा बोल्नेछन् ।
(ग) तपाईं लुम्बिनी घुम्न जानुहोस् ।
(घ)  ऊ भाइलाई कथा लेखाउला ।

उत्तर :  (क) केशबराजलाई चस्माले धोका दिन्थ्यो । (ख) विदुर सँधै न्यायको पक्षमा बोल्नेछन् । (ग) .....

37. In a survey, one third youth like only iphone and 80 dont like i-phone at all. Also 40% youth like android phone but 40 like none of them.
(i) Show that above data in a Venn-diagram.
ii) How many youth like both types of phones?

Again, n(A)' = n(U) - n(A) n(A)' = n(U) - [n0(A) + n(A ∩ B) ]  From above equation,  You will get, n(A ∩ B) which is required .....

38. In a group of 58 people, 17 play football only and 28 play volleyball only. If 6 play neither of the two games, then.

i) Represent above information ina Venn - diagram
ii) Find the ratio of the people who plays  football to the people who play volleyball.
 

Here, Let, n(U) = 58 no(F) =  17  no(V) = 28 n(FUV) ' = 6 From the Venn-diagram, 17 + x + 26 + 6 = 58 Find x. Then,  n(F) = 17 + x = .......... n(V) = 26 + x =............ Finally, find .....

39. In  group of 85 students, 25 students like to read Neplai Novel only and 15 students like to read Englis Novel only. If 35 students do not like to read any of the novels, then 
i) Represent above information in a Venn-diagram.
ii) Find the ratio of the students who read Nepali Novel to the students who read English Novel. 

n(U) = 85 nₒ(N) = 25 nₒ(E) = 15  n(N∪E)' = 35 now,  n(U) = nₒ(N) + nₒ(E) + n(N∩E) + n(N∪E)' 85 = 25 + 15 + n(N∩E) +35 n(N∩E) = 85 - 25 - 15 -35 Now, calculate the value .....

40. In a group of 50 students, 15 like both Nepali and English subject and 5 do not like any of the two subjects. If the number of students who like Nepali only and the number of students who like English only are in the ratio of 2:1, find the number of students who do not like English subject by using Venn-diagram.

n(U) = 50 n(N∩E) = 15 n(N∪E)' = 5 nₒ(N) : nₒ(E) = 2:1 Let, the no. of students who like Nepali only and English only be 2x and x. Now , From Venn-diagram then, n(U) = nₒ(N) + nₒ(E) + n(N∩E) .....

41. In a group of 100 students, the ratio of students who like Geography and Sociology is 3:5. If 30 of them like both the subjects and 10 of them like none of the subjects then by drawing a Venn-diagram, find how many students of them (i) like Geography only (ii) like Sociology only.

Here, given n(U) = 100 n(G∩S) = 30 n(G∪S)' = 10 n(G) : n(S) = 3:5 Let, the no. of students who like Geography and Sociology be 3x and 5x. Now , From Venn-diagram then, n(U) = n(G) + n(S) - n(G∩S) .....

42. In a school, 32 teachers like either milk or curd or both. The ratio of number of teacher who like milk to the number of teachers who like curd is 3:2 and 8 teachers like both milk and curd. Find: (i) ? (How many teachers like milk?) (ii) ? (How many teachers like curd only? 

n(U) = 32 n(M∩C) = 8 n(M) : n(C) = 3:2 Let, the no. of teachers who like milk and curd be 3x and 2x respectively. Now , From Venn-diagram then, n(U) = n(M) + n(C) + n(M∩C) 32 = 3x - 8 + 8 + 2x - 8 32 + 8 = 5x 5x = 40 x = .....

43. Out of 120 students, 32 passed in Mathematics only, 8 passed in both Mathematics and Nepali. The number of students who passed in Nepali is twice the number of students who passed in Mathematics. Using a Vem. diagram, find the number of students who passed in Nepali only and who didn't pass in both subjects. 

Here given, n(U) = 120 nₒ(M) = 32 n(M∩N) = 8 n(M) = x(say) n(N) = 2x Here,  n(M) = nₒ(M) + n(M∩N) x = 32 + 8 x = 40 Again, n(N) = 2x = 80 Now, the no. of students who passed in Nepali only [nₒ(N)] = n(N) .....

44. In a certain examination, 50% students passed in Account, 30% passed in English, 30% failed in both and 25 students passed in both subjects. By drawing Venn-diagram, find the number of students who passed in Account only.

Here given, n(U) = 100% n(A) = 50% n(E) = 30% n(A∪E)' = 30% n(A∩E) = 25 Let, x% students like both the subjects. then the Venn-diagram be From venn diagram, 100% = (50 - x + x + 30 - x + 30)% 100% - 50% -30% - 30% = -x - x = - 10% x .....

45. In a group of student 50% like tea, 70% like coffee, 10% dont like both and 120 like both. By using Venn-diagram, find the total number of students

Here, let n(U) = x n(T) = 50% of x         = 0.5 x n(C) = 70% of x          = 0.7 x n(T ∪ C)' = 10%v of x                  = 0.1 .....

46. In a survey of the students, it was found that 70% of the students studied BBA courses, 65% of the students studied BBS courses, 430 students studied both the course and 8% did not study both courses then:
i) Show the above information in a Venn-diagram.
ii) FInd the total number of students in the survey.
 

Here, given students who study BBA [n(Ba)]=70% students who study BBS [n(Bs)] =65% students who study both courses n(Ba ∩Bs )= 430 students who study don't study both the courses n(Ba ∪ Bs)' = 8% now , n(U) = n(Ba) .....

47. In a survey of a group of students, it was found that 35% of the students liked maths, 30% liked account, 3000 students liked both of them and 50% liked none of them,
i) Draw a Venn-diagram to illustrate the above information.
ii) Find the total number of students in the survey.

Here, given n(U)=100% n(M) =35% n(A) = 30% n(A∩M)= 3000 n(A∪M)' = 50% now , n(U) = n(A) + n(M) - n(A∩M) + n(A∪M)' 100%  = 30%  + 35%  - n(A∩M) + 50% 100%  .....

48. Higher we go cooler we feel. Give one geographical reason why we feel cool in the higher altitude?

Altitude is one of the factors that affect the climate of a place. As the altitude increases, the density of the air becomes thinner and thinner as they contain fewer amounts of dust particles and water vapour. Therefore, they absorb less heat .....

49. What do you mean by human rights? Write down the functions of human rights commission and make a list of any five worldwide announcements regarding human rights. 

The National Human Rights Commission (NHRC) of Nepal is an independent and autonomous constitutional body. It is the apex constitutional body for the protection and promotion of human rights in Nepal. The functions of National Human Rights .....

50. Write any six functions of National Human Rights Commission Nepal.

The National Human Rights Commission (NHRC) of Nepal is an independent and autonomous constitutional body. The Interim Constitution of Nepal 2007 (2063 BS) has made the NHRC a constitutional body. It is the apex constitutional body for the .....