Students and Teachers Forum

1. In the  adjoining figure,POQ and ROT are two diameters of a circle  with centre at O. If Q is the midpoint of the arc  TQS  and ∡ QOR is obtuse , prove that : PQ// RS.

1. ⋖TOQ = ⋖QOS [ Equal arcs subtent equal angles at the centre since Q is mid-point of the arc TS] 2. ⋖SOT = 2⋖SOQ 3. ⋖ORS = ⋖OSR [ OR = OS = radius ] 4. ⋖ORS + ⋖OSR = ⋖SOT [ Sum of angles of interior angles of .....

2. In the given figure, two circles intersect at the points A and D. If ABCD and AXYD are cyclic quadrilaterals, prove that BC // X Y. 

 

Given, ABCD and AXYD are cyclic quadrilaterals. Here, ⋖DAB + ⋖DCB = 180 ----(I)[ Opposite angle of a cyclic quadrilateral is supplementary ] Similarly, ⋖DAX + ⋖DYX = 180 ----(II)[ Opposite angle of a cyclic quadrilateral is .....

3. In the figure , ∡AEC = ∡ BFD , prove that : 
 AB// CD

 

1. ⋖AEC = ⋖BFD [ Given ] 2. ⋖AEC = ⋖ABC [ Angles in the circumference standing on the same arc ] 3. ⋖BFD = ⋖BCD [ Angles in the circumference standing on the same arc ] 4. ⋖ABC = ⋖BCD [ From .....

4. In the given figure, PA and PB are tangents from P to a circle with centre O. At M, a tangent is drawn intersecting  PA at K and PB at N. Prove that PA + PB = PK + KN + PN.

Here, KA = KM           [ Tangents from a external common points are equal.] Similarly, NB = NM Now, PA + PB = (PK + KA) + (PN + NB)                      .....

5. In the adjoining figure, PQR is the secant and PT is the tangent to the circle with centre O.

Prove that  PT2 = PQ.QR

Here, Join T & Q and T & R. Now, show triangles PTQ & PTR similar. Since, ∡P = ∡P   [ common angle.] ∡PTQ = ∡PRT     [ Angle at alternate segment.] Now take ratios of corresponding .....

6. In the given figure , M is any point on the chord AB and MN // PQ . Prove that MNCB  is a cyclic quadrilateral.

 

Here, ⋖QAN = ⋖MNA [ Being alternate angle ] ⋖PAM = ⋖AMN [ Being alternate angle ] Similarly, ⋖QAN = ⋖CBA [ Angle made by CA with the tangent PAQ at the point of contact is equal to angle in alternate segment ] ⋖PAM .....

7. In the given figure prove that:
(i) ∆PXR ∼ ∆QXS
(ii) PX/RX = SX/QX

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8. In the given figure, O is the circumcentre of Δ ABC and OD⊥ BC. Prove that ∠BOD = ∠ BAC.

OD is perpendicular to BS that mean D is midpoint of BC. So we can show that ∢ BOD is half of ∢ BOC ( it is bisector because it bisect base of isosceles triangle ) also so we can show that ∢BAC is half of ∡ BOC.  ( .....

9. Not only adarsh but also pankaj got a prize

Not only adarsh but also pankaj got a prize - Not only Adarsha but also Pankaj got a .....

10. In the given figure AB and CD are diameter and AB is parallel to CE. Prove that B is midpoint of DBE.

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11. Find the unknown angles.

From the figure 300 + 350 + b = 180o  ( sum of angle of triangle.) a = b ( opposite angle of parallelogram) x = 30o ( alternate angle ) y = 35o ( alternate .....

12. Why do animals excrete?

Do you know every moment, animal are using various substances for their survival. After consuming these substances, some waste products are also formed. These substances are toxic in nature and can be harmful if remains in body for long periods of .....

13. What is internal transport?

Internal transportation is a process by which various materials are transported to the different part of organisms. In humans, blood is a medium which transports different materials such as nutrients to all the cells. This process can be called as .....

14. What is the importance of reproduction?

Reproduction is the process by which living organisms produces similar organisms. It is the way by which life can continue in earth. It is the process by which all living organisms are preserved in one or another .....

15. ग्रन्थचित्र भनेको के हो ?

शास्त्रको कथा वा विषय वस्तुमा आधारित चित्रलाई ग्रन्थचित्र भनिन्छ । .....

16. The reflection of the points A(2b, 3a - 5) about the line y = -x is A'(7 - a , b + 6). Find the value of a and b.

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17. Find the image of the point (4, 3) under the reflection
i. about the line x = 2.
ii. about the line y + 3 = 0.

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18. Find the image of the point
a. (6, 4) under the reflection in X-axis.
b. (-4 -8) under the reflection in (x = 0).
c. (1, -3) under the reflection about the line y = x.
d. (-2, 6) under the reflection about the line y = -x.

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19. Translation:

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20. Rotation:

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21. If ABCD is a regular pentagon, show that AB⃗ + BC⃗ + CD⃗ + DE⃗ + EA⃗ = 0.

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22. In the figure given below , ABCD is a quadrilateral in which AB⃗ = a⃗, BC⃗ = b⃗, CD⃗ = CD⃗ and DA⃗ = d⃗.
i. Express AC⃗ in term of a⃗ and b⃗.
ii. Express BD⃗ in terms of a⃗ and d⃗.
iii. Show that AB⃗ + BC⃗ + CD⃗ + DA⃗ = 0.

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23. In the adjoining figure, M is the middle points of BC. Show that AB⃗ + AC⃗ = 2AM⃗.

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24. In the adjoining figure, O is the middle points of AC. If AB⃗ = a⃗ and BC⃗ = b⃗, find AC⃗, AB⃗,CO⃗ and BO⃗.

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25. In a regular hexagon ABCDEF, if AB⃗ = a⃗ and BC⃗ = b⃗, find the vectors determined by the remaining sides taken in order.

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26. A(3,7) and B(5, -1) are two points. Express AB⃗ in terms of column vector and find the magnitude and direction of AB⃗. If M is mid-point of AB, find the position vector of M.

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27. If the, figure given below, the diagonals Ac and BD meet at O. If OA⃗ = a⃗,OB⃗ = b⃗, OC⃗ = c⃗ and OD⃗ = d⃗, show that AB⃗ + BC⃗ + CD⃗ + DA⃗ = 0.

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28. If the position vectors of M and N are 2-1 and 43 respectively, find MN⃗, is magnitude and the unit vector along the direction off MN⃗.

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29. If a⃗ = -24 and b⃗ 4-8, show that a⃗ and b⃗ are parallel to each other.

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30. सहस्राब्दी विकासका लक्ष्य भनेको के हो?

सन् २००० को सेप्टेम्बरमा १९१ राष्ट्रहरु एवं १४७ राष्ट्र तथा सरकार प्रमुखहरुले सहस्राब्दी .....

31. If an observer places his ear at the end of a long steel pipe or rod, he can hear two distinct sounds when a man hammers on the other end of the pipe. Explain.

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32. Describe an experiment to show that sound propagated through solid on the basis of the following points. (Requirement, method and conclusion).

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33. Draw a neat and labelled diagram to show that medium is necessary for the transmission of sound.

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34. Describe an experiment to show that a material medium is necessary for the propagation of sound.

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35. When a ringing bell is caught by hand, sound ceases. Why? Give reason.

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36. Sound waves are mechanical waves. Why? Give reason.

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37. Why is echo heard from mountains, hills and big halls?

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38. In which of the tree states of matter - solid, liquid and gas, do sound waves have their highest speed?

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39. A bell ringing inside a vacuum chamber cannot be heard outside. Why?

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40. Astronauts cannot talk on the moon as we do on the earth, Why?

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41. How is sound produced?

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42. In a of a community, 50% people speak English only and 160 don't speak English at all. Also, one third of the people speak Newri but 100 people don't speak both the language. 
i) Represent the above information in a Venn--diagram.
ii) Find the number of people who speak both the language. 

Here, Let total no.of people = x  People speak English only = no(E) = 50% =x/2.    People do not like English = n(E') = 160 People speak Newari = n(N) = x/3 People do not speak both = n(EUN)' = 100 We know,   .....

43. Find the upper or third quartile class of the follwing data:

Here,    Marks obtained No.of students (f) cf 0-10 5 5 10-20 5 10 20-30 5 15 30-40 2 17 40-50 3 20 Third quartile lies in (3N)/4 = .....

44. If the median class = 50-70 and if (N2 - c.f) = 5 then find the median.

Here, Median class = 50 - 70 So, L = 50. i/f(N/2 - cf ) = 5. Median = ? We know, Median = L + i/f( N/2 - c.f.)              = 50 + 5              = .....

45. Read the text and do the activities that follow.
Once Tom nearly went to prison. George was terribly upset. He went into the whole discreditable affair. Really Tom had gone too far. He had been wild, thoughtless, and selfish, but he had never before done anything dishonest, by which George meant illegal; and if he were prosecuted he would assuredly be convicted. But you cannot allow your only brother to go to gaol. The man Tom had cheated, a man called Cronshaw, was vindictive. He was determined to take the matter into court; he said Tom was a scoundrel and should be punished. It cost George an infinite deal of trouble and five hundred pounds to settle the affair. I have never seen him in such a rage as when he heard that Tom and Cronshaw had gone off together to Monte Carlo the moment they cashed the cheque. They spent a happy month there. 

A. Find out the best alternative words (synonym) and write next to them for the following words. 
a. prison : person, custody, goal 
b. illegal : unlawful, illicit, lawful 
c. prosecuted : put on trial, taken legal action, freed to court 

B. Answer these questions based on the text. 
a. How much did George pay to settle down the affair? 
b. Why was George terribly upset? 

B) a. The George paid five hundred pounds to settle the affair. b) The George was terribly upset because he heard that Tom and Cronshaw had gone off together to Monte .....

46. Read the poem given below and do the tasks.

                                     The Road not Taken

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Through as for that the passing there
Had worn them really about the same,

And both that morning equally lay
It leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,

I doubted if I should ever come back.
I shall be telling this with a sigh
Some where ages and ages hence:
Two roads diverged in a wood, and I
I took the one less traveled by,
And that has made all the difference.
                                                   Robert Frost

A. On the basis of your understanding of the poem, answer the following questions by ticking the correct choice.
(a) The traveler could not see where the road was going because
(i) it .wasn't straight                    (ii) the woods were too dark
(iii) it was covered by leaves      (iv) it was very grassy 

(b) 'Yet knowing how way leads on to way, I doubted if I should ever come back." What does the speaker mean by these lines, He means that .
(i) one road was less traveled than the other            (ii) he could never take the other road
(iii) both roads looked the same                              (iv) one road was more difficult than the Other 

Answer these questions based on the poem above.
a. Does the poet regret his decision?
b. What is the significance of the fact that the road "bent in the undergrowth"?
c. What is the speaker's dilemma?

A. a) it was covered by leaves b) he could never take the other road B. a) No, the poet is happy in his decision because he experiences the difference at the end. b) The significance of the fact that the road 'bent in the .....

47. Write some point about dog.

The dog is a domestic pet animal. Everybody likes to keep it in their home. It helps people so much in various fields. The dog is a very faithful animal in the world. It has two eyes, two ears, four thin legs and sharp teeth.  It .....

48. Find the LCM of :
(x + 3) (x -2) and (x - 2) (x + 5)

Here, First expression = (x + 3) (x -2) Second expression =  (x - 2) (x + 5) Common factors = (x - 2) LCM = common factors ⨯ remaining factors           = (x - 2) ( x + 3) (x + .....

49. In the given figure,the area of the triangle AEC is 65cm2, find the area ∆AED.

Here, Area of triangle ADE = 65cm2 Area of triangle AEC = ? Here, D is mid-point of AC. So, ED is median. Median bisects the triangle in equal area. So,  Area of AED= 1/ 2 ⨯ area of triangle AEC           .....

50. In the  given figure,the area of the triangle AED is 77cm2 ,find the area of ∆AEC.

Here, Area of triangle ADE = 77cm2 Area of triangle AEC = ? Here, D is mid-point of AC. So, ED is median. Median bisects the triangle in equal area. So,  Area of AEC= 2 ⨯ area of triangle AED           .....

Marks obtained 0-10 0-20 0-30 0-40 0-50
No. of students 5 10 15 17 20