ASSIGNMENT FOR CLASS 10TH Writing Skills &Grammar

Q.1. write the following letters 1. our Metropolitan cities witness a large number of accidents everyday full stop what do you think is the reason what can be done to bring down the rate of accidents. Write a letter in 100-200 words to the editor of a national daily expressing your concerns and offering solutions to this problem you are Arun/Aruna 112 Model Town, Delhi 2. Many complaints about unfair means being used in exams have come in write a letter to the editor of a national daily newspaper in 120 words giving reasons for this friend and suggest measures to come back this you are Vikas Vaishali 12 foot road Kochi. 3. You are concerned about the increased incidents involving school children the main reason is a reckless driving habits of children you decide to express your views in the form of a letter to the editor The Hindu discussing this problem also suggest measures to come back this problem write a letter to the editor in not more than 120 words. 4. The condition of the public Park in your locality is miserable and it is also misused by some mysterious people write a letter to the editor of a local newspaper with the help of points given below in 120 words you are Ritu/Ravi, A-15 Kailash Colony, New Delhi. : Poorly managed parks, heaps of garbage lying everywhere, boundary wall broken, grass is unmanaged, very dirty animals reeting there, drunkards sit in it,sometimes rob lonely passerby, people are scared to go there. Q2. write the following stories write a story in 150 to 200 words on the inputs given below 1) She finally had it- the key to the Treasure- the map she trembled- excitement –anticipation 2). learning to swim - enjoyed - not fully trained -pushed inside- started drowning. 3).Write a story that starts with the following words in 200 -250 words. ‘There was a money lender who had more money than brain and his words was to give loans and take the money with a good amount of interest. One day ---------------------------- 4). He opened the factory door - kept inside -some light last shift over -could be the thieves Q3. complete the paragraph given below by filling in blanks with the help of options that follow (1) The daughter of rich merchant a)_________ upset b)_________ a father for c)__________ her a second hand car as a birthday gift. she angrily d)___________out of the house. (a) 1) get 2) gets 3) got 4) will get (b) 1) on 2) with 3) upon 4) for (c) 1) giving 2) given 3) gave 4) gives 2) Reading a novel or short story a)__________second language b)___________dramatically c) _______________psychological responses to emotions such d)__________smiling. a) 1) of 2) in 3)from 4)at b) 1) would 2) should 3)could 4)May c) 1)reduce 2) reduces 3)reduced 4) reducing d) 1)like 2)similar to 3)As 4) alike 3) There is a general belief (a) ___________students that (b) ___________who writes long sentences get (c)____________ marks short answers get (d)_____________marks.

a) 1) in 2) of 3)among 4)between b) 1)they 2)those 3)all 4)them c) 1)more 2)many 3)most 4)much d) 1)least 2)less 3)few 4)small

Q4 .The following paragraph has not been edited there is an error in each line write the error and its correction INCORRECT CORRECT (1)A puppy can go on its new home a)____________ __________ when it is six and eight weeks old b) ___________ __________ make sure your puppy have been c)___________ __________ charged to a veterinarian d)___________ __________ (2)it is unfortunate as many people a) ____________ ___________ regard old people for Geriatrics b)____________ ____________ who has one foot into the grave c)____________ _____________ someone should remind them that they too d)____________ _____________ (3)our country can become a heaven a)____________ ______________ for tourist it has the rich cultural b)____________ _____________ heritage, ancient monuments for c)____________ ______________ wonderful architecture and such natural beauty of flora and fauna d)____________ _____________ Q 5.Rearrange the following words to form meaningful sentences

a) Algebra and/ a week/ me /geometry/ twice/ he taught b) very poor/ subjects/ I was /in these /earlier c) very /now /proficient/ have become/ in them /I d) and my /persistence /hard work /to his /Thanks e) on /are/ the /their/ feet/ Quick/ Siberians f) Without/ also born/ is /its teeth /it g) the senses /begin /it /its /does not /life /with all/ got/walk/a/ they/ smooth/ with h) They are/only /Hurry/ they /went/ hunting i) Also/ active/ are/ and /playful/ Siberians (Literature: textbook and long reading text) Q6. Read the extract given below and answer the questions that follow (1)dumbstruck sat the gaping frog and the whole admiring bog stared towards the sumac, rapt And when she had ended, clapped

a) How did the frog sit? B) What is the whole bog admiring? C) What did the admiring do ? (2) ducks and sum and herons waded to her as she serenaded and a solitary Loon wept,belneath the summer moon .

a) whom does ‘she’ in this stanza refer to? B) why did the solitary Loon weep? C) what had the ducks and Heron been doing prior to swimming and waiting?

(3) In me if she has drowned a young girl Anne in me an old woman Rises towards her Day After day like a terrible fish

a) Why is a pronoun ‘me’ being used in the stanza? B) What do you mean by ‘terrible fish’ here? c) What has the mirror drowned and replaced it with ?

4) when was full watch cell statues overturn, and broils root out the work of masonry

a) In This stanza, what does the word ‘broils’ mean? B) What does the phrase ‘the work of masonry’ imply? c) What will the wasteful war do?

5) one night, we came upon them in the windy and deserted square, resting on the stone pavement Winnie the lights a) who is the speaker of these lines ? b) who are them ? c) why are they resting on the payment at night?

Q 8.Answer the following questions in 30 to 40 words each 1. what were the boys doing one midnight sitting on the windy and deserted square stone pavement beneath the lights? 2. what did the nurse tell the narrator about the boys? 3. what planes does Mrs packletide conceive before shooting Tiger 4. what happened after Mrs packletide had fired the short? 5. why did Ali give up hunting ? 6. how was the heart of the Postmaster brimming with sympathy for Ali? 7. how did the frog convince The Nightinage that she needed a trainee 8. why is the mirror important to a woman ?what makes her feel like a terrible fish? 9. Describe how poetry survive all wars and destruction Q 9.Answer the following question 80 -100 words. 1) how does the story ‘two gentlemen of Verona’ promise hope for society? how can you promise hope for society 2) “ Before targeting anyone, one must not forget that even a biter can be bitter” Explain with the reference to the story. Mrs. packletide's Tiger. what values do you learn from the story. 3) “No one can Guage the depth of human emotions till one identifies with one's fellow beings” the Postmaster realises the pain of Ali when his own daughter was sick. He was full of remorse, quite and repentance for his ill treatment to Ali. what values do you learn from the condition of Postmaster? Ques 10.Answer the following questions in 150 to 200 words

1) Describe the character sketch of Anne Frank . 2) How did the diary help Anne overcome her loneliness? 3) What is the main theme of “The Diary of a Young Girl”? 4) Under what circumstances did the friends have to go into hiding? 5) Write the character sketch of otto Frank. 6) Anne disliked Mrs van Daan. What was the reason? 7) Give an account of some of the problems faced by the persons in the secret Annexe.

MOUNT HILL ACADEMY SUBJECT:-HINDI CLASS:-XTIME:-3 Hrs. M.M:-80funsZ’k%&

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MOUNT HILL ACADEMY SUBJECT:-MATHS CLASS:- X[SIMILAR TRIANGLE]

Q.1 If a line if drawn parallel to one side of a triangle intersecting thetwo other sides, then other two sides are divided in the same ratio.

Q.2 In the given figure, DE is parallel to BC if3

2

DB

AD and AC = 18cm Find AE.

Q.3 What value of X will make DE║AB in the given figure.Q.4 In ∆ABC if DE║BC and AD = 3x―2, AE = 5x―4, BD = 7x―5 andCE = 5x―3. Find xQ.5 If D is a point on the side BC of a triangle ABC such that DF,DE aredrawn parallel to AC and AB meeting AC, AB at E, F respectively EFmeets BC produced in O. Prove that OD 2 = OB.OC.Q.6 In the given figure, AB║DE and BD║EF. Prove that DC 2 = CF ×AC.Q.7 Any point X inside ∆DEF is joined to its vertices. From a point P inDX PQ is drawn parallel to DE meeting XE at Q and QR is drawn parallel

to EF meeting XF at R. Prove that PR║DF.Q.8 Prove that the line segments joining, the mid points of the adjacentside of a quadrilateral form a parallelgram.

Q.9 In a ∆ABC, D and E are points in the sides AB and AC respectivelysuch that AD×EC = AE×AD. Prove that DE║BC.Q.10 In figure. If AB║CD find the value of X.Q.11 The perimeter of two similar triangle ABC and PQR respectively36cm and 24cm. If PQ=10cm find AB.

Q.12 Two poles of height a metres and b m are p m apart. Prove that the height of the point ofintersection of the lines joining the top of each pole to the foot of the opposite pole is given by

ba

ab

metres.

Q.13 The diagonal BD of a parallelogram ABCD intersects AE at a point F where E is any pointon the side BC. Prove that DF×EF=FB×FA.Q.14 In figure, ABD=CDB=PQB =90º. If AB= x units

CD= y units and PQ= z units. Prove thatzyx

111 .

Q.15 P and Q are respectively the points in the sides AB andAC of a ∆ABC. If AP=2cm, PB=6cm AQ=3cm and QC=9cm. Prove that BC=4PQ.

Q.16 In ∆ABC, DE is parallel to base BC with D on AB and E on AC. If3

2

BD

AD findDE

BC .

Q.17 ∆ABC is a triangle in which AB=AC and D is a point on AC such that BC 2 =AC×AD. Provethat BD=BC.Q.18 If two triangles are equiangular. Prove that the ratio of the corresponding sides is same asthe ratio of the corresponding medians.Q.19 Prove that the ration of the areas of two similar triangles is equal to the ratio of thesquare of any two corresponding sides.Q.20 ABC and DEF are two similar triangles such that BC=4cm, EF=5cm and areas of∆ABC=64cm 2 . Find the areas of ∆DEF.

Q.21 The areas of two similar triangles are 100cm 2 and 49cm 2 respectively. If the altitude of thebigger triangles is 5cm.Find the corresponding altitude of the other.Q.22 The areas of two similar triangles are 121cm 2 and 64cm 2 respectively. If the median of thefirst triangle is 12.1cm. Find the corresponding median of the other.Q.23 Two isosceles triangles have equal vertical angles and their area are in the ratio 16:25.Find the ratio of their corresponding heights.Q.24 Prove that the areas of the equilateral triangle described on the side of asquare is half the areas of the equilateral triangles described on its diagonal.Q.25 In a ∆ABC if ADBC and AD 2 =BD×DC. Prove that BAC=90º.Q.26 In a ∆ABC, if A=90º and ADBC. Prove that AD 2 =BD×DC.Q.27 In a ∆ABC, BCA is a right angle. If Q is midpoint of side BC,AC=4cm and AQ=5cm. find (AB)2.Q.28 The diagonals of a rhombus are 15 cm and 36cm long. find its perimeters.Q.29 Ina right triangle ABC, right angled at C,P and Q are the points of the sides CA and CBrespectively which divide these sides in the ratio 2:1. Prove that

a) 9AQ 2 =9AC 2 +4BC 2 b. 9BC 2 =9BC 2 +4AC 2 c. 9(AQ 2 BP 2 )=13AB 2

Q.30 Prove that the sum of the squares of the sides of a rhombus is equal to the sum of squaresof its diagonals.Q.31 In an isosceles triangle ABC if AC=BC and AB 2 =2AC 2 . Prove that C is right angle.Q.32 ∆PQR is an isosceles right triangle right angled at R. Prove that PQ 2 =2PR 2 .Q.33 In a ∆ABC, ADBC. Prove that AB 2 CD 2 =AC 2 +DB 2 .Q.34 Prove that the areas of a semi ―circle on the hypotenuse of a right angles triangles is equalto the sum of the areas of semi circles on the other two sides.Q.35 Two right triangles ABC and DBC are drawn on the same hypotenuse BC. If BC and ACintersect at P, Prove that AP×PC=BP×PD.Q.36 Through the midpoint of a side CD of aparallelogram ABCD the line BC is drawn, intersecting

AC in L and AD produced in E. Prove that EL=2BL.Q.37 AD is an altitude of an equilateral triangle ABC.On AD as base, another equilateral triangle ADE is constructed. Prove thatar(ADE) : ar(ABC)=3:4.Q.38 In the given figure, if PQ║BC and PR║CD, Prove that:

a.AB

AQ

AD

AR b.

AR

DR

AQ

BQ

Q.39 In figure, S and T are points on the side PQ and PR respectively of a∆PQR such that PT=2cm, TR=4cm and ST║QR. Find the ratio of the areasof ∆PST and ∆PQR.

Q.40 ∆ABC is a right triangles in which C=90º and CDAB. If BC=a,CA=b, AB=c and CD=p, then prove that.

a. CP=ab b.222

111

bap

Q.41 In a given figure, D and E trisects BC. Prove that 8AE 2 =3AC 2 +5AD 2 .Q.42 In right angled triangle ∆ABC in which C=90º, if D is the mid pointof BC. Prove that AB 2 =4AB 2 ― 3AC 2 .Q.43 In given figure, ABC is a right angled triangle in which C=90ºand D is the mid point of BC. Show that AC2=AD2+3CD2.

Q.44 A and B are points in sides of PQ and QR of a ∆PQR, right anglesare Q. Prove that AR 2 + PB 2 =AB 2 +PR 2 .Q.45 The perpendicular PS on the base QR of a ∆PQR intersect QR atS so that QS=3RS. Prove that 2PQ 2 =2PR 2 +QR 2 .

Q.46 Prove that three times the square of any side of an equilateraltriangle is equal to four times the square of the altitude.Q.47 The areas of two similar triangles are 49cm 2 and 64cm 2 respectively. If the difference ofthe corresponding altitude is 10cm then find the length of altitude (in cm).

MOUNT HILL ACADEMY SUBJECT:-MATHS CLASS:- X[Area related to circle]

Q.1 A path of width 3.5m runs around a semi-circular grassy whose perimeter is 72m. Find theareas of the path. (Ans. 173.25m2)Q.2 A circular pond is of diameter 17.5m. it is surrounded by a 2m wide path . Find the cost ofconstrucing the path at the rate of Rs.25 per sq mtr.(Ans.3061.50)Q.3 In a circle of radius 21cm, an arc subtend an angle of 60º at thecentre. Find (i) Length of the arc. (ii)Area of the sector formed by arc.Q.4 The length of the minute hand of a clock is 14cm. Find the area sweptby the minute hand in 6 min.

Q.5 ABCD is a square of side 10cm semicircles are drawn with each sideof square as diameter. Find the area of (i) The unshaded region

(ii) The shaded region

Q.6 Find the area of shaded region. (Ans. 5.48cm2).

Q.7 Find the area of shaded region.(Ans. 154.88cm2).Q.8 Find the area of the shaded region of AC=24cm,BC=10cm and O is the centre of the circle.

(Ans.145.33cm2)Q.9 A circle is inscribed in an equilateral ∆ABC isside 12cm touching its sides. Find the radius of

inscribed circle and the area of the shaded part. (Ans. 2 cm3 , 24.638cm2)Q.10 Find the area of shaded region where a circular arc of radius 7cm, has beendrawn with vertex A of an equilateral ∆ABC of side 14cm as centre.Q.11 A regular hexagon is inscribed in a circle if the area of hexagon is

2324 cm . Find the area of the circle. (Ans. 50.24cm2).Q.12 Two circular pieces of equal radii and maximum area touching eachother are cut out from a rectangular card board of dimensions

14cm×7cm. Find the area of the remaining cardboard.(Ans. 21cm2).Q.13 PSR, RTQ and PAQ are three semicircular of diameter 10cm, 3cmand 7cm respectively. Find the perimeter of the shaded region. (Ans.31.4cm)

Q.14 The boundary of the shaded region consists of four semi circular arc,the smallest two being equal. If the diameter of the largest is 14cm andof the smallest is 3.5cm find(i) The length of the boundary

(ii) The area of the shaded region(Ans. (i)44cm (ii) 86.625cm2)

Q.15 ABCD is a trapezium of area 24.5cm2. In it AD║BC, DAB =90º,AD=10cm and BC=4cm, If ABE is a quadrant of a circle. Find the areaof the shaded region. (Ans. 14.875cm2)Q.16 If the diameter of a protactor is 14cm. Find itsperimeter. (Ans.36cm)

Q.17 Find the area of the largest triangle that can be inscribed in a semi circle of radius r.(Ans.r2)Q.18 ABCD is a trapezium with AB║DC, AB=18cm, DC=32cm and the distance B/w AB and DCis 14cm circle of equal radii 7cm with centres A, B, C and D have been drawn. Then find thearea of shaded region. (Ans. 196cm2)Chapter:-[A.P]Q.1 The first and the last term of an A.P are 8 and 350 respectively if itscommon difference is 9. How many terms are there and what is their sum.

Q.2 In an A.P the sum of first ten term is ―150 and the sum of its next term is ―550. Find theA.P. (Ans. a=3, d= ―4)Q.3 Sum of first 14 terms of an A.P is 1505 and its first term is 10. Find its 25 th term. (370)Q.4 In an A.P the first term is 22 , nth term is ―11 and the sum of first n terms is 66. Find n andd. (n=12, d=―3)

Q.5 In an A.P the sum of first n terms is2

133 2 nn find its 25th term. (Ans. 80)

Q.6 The sum of first 25 terms of an A.P whose nth term is given by a n =7— 3n. (―800)Q.7 Find the sum of:

1. All 3 digit number which are divisible by 13. (37674)2. All 3 digit numbers which are divisible by 11. (44550)

Q.8 How many terms of the A.P 63,60,57 …………….. must be taken so that the sum is 693?(21,22)Q.9 If Sn, the sum of first n terms of an A.P is given by Sn=5n2+3n then find its nth term. (an=10n—2 )Q.10 Find the sum of all three digit natural numbers which are divisible by 7. (70336)Q.11 The sum of first six terms of an A.P is 42 the ratio of its 10th term to its 30th term is 1:3calculate the first and the thirteenth term of an A.P. (a=2, a13=26)Q.12 The 17th term of an A.P is 5 more than twice its 8th term. If the 11th term of an A.P is 43.Find the nth term. (4n―1)Q.13 Which term of the A.P 3,15,27,39 ……… will be 120 more than its 21st term. (31st )Q.14 The sum of 4th and 8th term of an A.P is 24 and the sum of 6th and 10th terms is 44. Findthe A.P. (―13, ―8, ―3, 2, 7 ………)Q.15 Find the 10th term from the end of the A.P. 8, 10, 12 ………….126.Q.16 Find the terms of an A.P 9,12, 15, 18 …….. which is 39 more than its 36th terms.(49th term)Q.17 If the Pth term of an A.P is q and the qth term is p then prove that its nth term is (p+q―n)Q.18 If m times the mth term of an A.P is equal to n times its nth term show that the (m+n)th

term of an A.P is zero.Q.19 The sum of 5th and 9th term of an A.P is 72 and the sum of 7th and 12th term is 97. Find theA.P. (6, 11, 16 .,……….)Q.20 If the 8th term of an A.P is 31 and the 15th term is 16 more than the 11th term. Find theA.P. (3, 7,11, 15 ………)Q.21 If the 10th term of an A.P is 52 and 17th term is 20 more than the 13th term. Find the A.P.

[A.P]

Q.1 The first and the last term of an A.P are 8 and 350 respectively if its common difference is 9.How many terms are there and what is their sum.Q.2 In an A.P the sum of first ten term is ―150 and the sum of its next term is ―550. Find theA.P. (Ans. a=3, d= ―4)Q.3 Sum of first 14 terms of an A.P is 1505 and its first term is 10. Find its 25 th term. (370)Q.4 In an A.P the first term is 22 , nth term is ―11 and the sum of first n terms is 66. Find n andd. (n=12, d=―3)

Q.5 In an A.P the sum of first n terms is2

133 2 nn find its 25th term. (Ans. 80)

Q.6 The sum of first 25 terms of an A.P whose nth term is given by a n =7— 3n. (―800)Q.7 Find the sum of:

1. All 3 digit number which are divisible by 13. (37674)2. All 3 digit numbers which are divisible by 11. (44550)

Q.8 How many terms of the A.P 63,60,57 …………….. must be taken so that the sum is 693?(21,22)Q.9 If Sn, the sum of first n terms of an A.P is given by Sn=5n2+3n then find its nth term.(an=10n—2 )Q.10 Find the sum of all three digit natural numbers which are divisible by 7. (70336)Q.11 The sum of first six terms of an A.P is 42 the ratio of its 10th term to its 30th term is 1:3calculate the first and the thirteenth term of an A.P. (a=2, a13=26)Q.12 The 17th term of an A.P is 5 more than twice its 8th term. If the 11th term of an A.P is 43.Find the nth term. (4n―1)Q.13 Which term of the A.P 3,15,27,39 ……… will be 120 more than its 21st term. (31st )Q.14 The sum of 4th and 8th term of an A.P is 24 and the sum of 6th and 10th terms is 44. Findthe A.P. (―13, ―8, ―3, 2, 7 ………)Q.15 Find the 10th term from the end of the A.P. 8, 10, 12 ………….126.Q.16 Find the terms of an A.P 9,12, 15, 18 …….. which is 39 more than its 36th terms.(49th term)Q.17 If the Pth term of an A.P is q and the qth term is p then prove that its nth term is (p+q―n)

Q.18 If m times the mth term of an A.P is equal to n times its nth term show that the (m+n)th

term of an A.P is zero.Q.19 The sum of 5th and 9th term of an A.P is 72 and the sum of 7th and 12th term is 97. Find theA.P. (6, 11, 16 .,……….)Q.20 If the 8th term of an A.P is 31 and the 15th term is 16 more than the 11th term. Find theA.P. (3, 7,11, 15 ………)Q.21 If the 10th term of an A.P is 52 and 17th term is 20 more than the 13th term. Find the A.P.