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INSTRUCTIONS:

1. Answer ALL the questions in a separate answer booklet.

2. The question paper consists of FOUR sections and 33questions.

3. There is an Internal Choice in Section – IV.

4. Write answers neatly and legibly.

SECTION – I

Note: i) Answer ALL the questions.

ii) Each question carries 12 mark. (12 12 = 6)1. Find the midpoint of line segment joining the points (3, 0)

and (1, – 4).

2. The end points of line are (2, 3) and (4, 5). Find the slope of

the line.

3. State SSS similarity criterion.

4. Match the following.

Group A Group B

3 a

i) The diagonal of a square is a) 4

........ times to its side

ii) Area of an equilateral triangle b) 2

is ........ sq.u.

3 a2

iii) Height of an equilateral triangle c) 4

is ........ u.

A) i-a, ii-b, iii-c B) i-b, ii-a, iii-c

C) i-a, ii-c, iii-b D) i-b, ii-c, iii-a

5. What is the name of the mathematician who introduced the

word 'tangent'?

6. If sec x + tan x = p then find sec x – tan x.

7. Express sin 81 + tan 81 in terms of trigonometric ratios of

angles between 0 and 45.8. Define Angle of depression.

9. If P(E) = 0.05, what is the probability of 'not E'?

10. A die is thrown once. What is the probability of getting a

number greater than 4?

11. Define the mean for ungrouped data.

12. Find the mode of 5, 6, 9, 10, 6, 12, 3, 6, 11, 10, 4, 6, 7.

SECTION – II

Note: i) Answer ALL the questions. ii) Each question carries ONE mark. (8 1 = 8)

13. What is the distance between A(8, 3) and B(–4, 3).

AD 314. In ABC, DE // BC and = , AC = 5.6 . Then find AE?

DB 5

15. Draw a circle and two lines parallel to given line such thatone is a tangent and the other a secant to the circle?

16. Find the area of sector whose radius is 7 cm, with the givenangle 90?

sec 3517. Evaluate .

cosec 3518. The top of a clock tower is observed at an angle of eleva-

tion and the foot of the tower is at the distance of 'd'meters from the observer. Draw the diagram for this data.

19. Find the probability of getting a head when a coin is tossedonce. Also find the probability of getting a tail.

20. Find the median of 2, 3, 6, 0, 1, 4, 8, 2, 5.

SECTION – III

Note: i) Answer ALL questions. ii) Each question carries TWO marks. (8 2 = 16)

21. Find the coordinates of the point which divides the line seg-ment joining the points (4, –3) and (8, 5) in the ratio 3 : 1internally.

22. A person 1.65 m tall casts 1.8 m shadow. At the sameinstance, a lamp-post casts a shadow of 5.4 m. Find theheight of the lamp-post.

23. A tangent PQ at a point P of a circle of radius 5 cm meets aline through the centre O at a point Q so that OQ = 12 cm.Find the length of PQ.

24. A chord of circle of radius 6 cm is making an angle 60 atthe centre. Find the length of the chord.

25. A tower stands vertically on the ground. From a point which is15 m away from the foot. If the angle of elevation of the toweris 45. Then what is the height of the tower?

26. A bag contains lemon flavored candies only. Malini takesout one candy without looking into the bag. What is theprobability that she takes out

i) an orange flavored candy? ii) a lemon flavored candy?

27. One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will

i) be an ace, ii) not be an ace.

28. Find ‘x’ if the median of the observations in ascending order24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5.

SECTION – IV

Note: i) Answer ALL the questions.ii) Each question carries FOUR marks.

iii) There is an Internal Choice for each question.(5 4 = 20)

29. a) Show that the points A(a, 0), B(–a, 0), C(0, a3) are form

an equilateral triangle.

(OR)

b) Prove that three times the square of any side of anequilateral triangle is equal to four times the square of thealtitude.

30. a) Find the area of the shaded region in figure, if ABCD is asquare of side 7 cm. and APD and BPC are semicircles.

(OR)

b) Two men on either side of a temple of 30 m. heightobserve its top at the angles of elevation 30 and 60respectively. Find the distance between the two men.

31. a) Prove that (sin A + cosec A)2 + (cos A + sec A)2

= 7 + tan2 A + cot2 A.

(OR)

b) A box contain 5 red marbles, 8 white marbles and 4 greenmarbles. One marble is taken out of the box at random.What is the probability that the marble taken out will be i) red ii) white iii) green iv) not green.

32. a) Find the mean of the following frequency table?

(OR)

b) If the median of 60 observations is 28.5, find the valuesof x and y?

33. a) Construct a triangle of sides 4 cm, 5 cm, 6 cm. Then construct a triangle similar to it whose sides are 5/4 ofcorresponding sides of first triangle.

(OR)

b) Construct a tangent to a circle 4 cm from a point on theconcentric circle of radius 6 cm and measure its length.Also verify the measurement by actual calculation.

SUMMATIVE ASSESSMENT - 2

MATHEMATICS PAPER - II

Time: 2 Hrs. 45 Min. (English Version) Max. Marks: 50

TENTH CLASS MODEL PAPER

C.I 15-25 25-35 35-45 45-55 55-65 65-75 75-85

No.students 6 11 7 4 4 2 1

C.I 0-10 10-20 20-30 30-40 40-50 50-60

Frequency 5 x 20 15 y 5

2020New

Pattern

12

Mark Questions1. State the condition if the points (a, 0), (0,

b) and (1, 1) are collinear2. Find the length of the side of a square

whose opposite vertices are (1, 3) and (6, 0)3. Let A (x1, y1) and B (x2, y2) be two points

joining a line segement then match the following.

Group A Group B

i) Slope of the line a) (x2x1)2 + (y2 y1)2

segment AB =

ii) Mid point of the y2 y1b)

line segment x2 x1

AB is

iii) Distance between x1 + x2 y1 + y2c) (, )A and B is 2 2

A) i a, ii b, iii c B. i b, ii c, iii a

C) i c, ii a, iii b D. i c, ii b, iii a

4. State Baudhayana's theorem.5. A man goes 3 m. due East and 4 m. due

North. How far is he from the starting point?6. ABCDEF and their areas are

respectively 64 sq.cm and 121 sq.cm. IfEF = 15.4 cm then find BC.

7. How can you find the area of major segmentusing area of minor segment?

8. What is the distance between two paralleltangents of a circle of the radius 4 cm?

9. If two tangents inclined at an angle of 60are drawn to circle of radius 3 cm. Thenfind the length of each tangent?

10. If sec + tan = k, then find the value ofsec tan

11. Write sin in terms of sec 12. Evaluate (sec2 1) (cosec2 1)13. What is angle of elevation?

14. The length of the shadow of a verticle

tower is 3 times its height. Find the angle

of elevation of the sun.

15. Can 75 be the probability of an event.

Explain.16. If F is the complement of an event E, what

is the value of P(E) + P(F)?17. Define mutually exclusive events with an

example.18. Write the formula to find the median of a

grouped data.19. The wickets taken by a bowler in 10 cricket

matches are as follows: 2, 6, 4, 5, 0, 2, 1,3, 2, 3. Find mode of the data.

20. What is the measure of cenral tendencyused to give rating to T.V. programmes?

One Mark Questions

1. Find the distance between (sin 90, cos 90) and (tan 45 , cot 45 )

2. The verticles of a triangle are (0, 0), (a, 0)

and (0, 6). Its centroid is (2, 2) then find thevalue of 'a'.

3. Find the area of the triangle whose ver-tices are (0, 0), (3, 0) and (0, 4)

4. The lengths of the diagonals of rhombusare 24 cm and 10 cm then find its side.

5. Define A.A. similarity criterion for two triangles.

6. The altitude of an equilateral triangle is6

3 cm find the length of its side.

7. If PA and PB are two tangents and anglebetween them is 80 then find POA,POB.

-T.S.V.S. Suryanarayana Murthy

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Model Questions

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Directions (Q.No.1-8): Read the followingpassage and answer the following questionsbased on the given passage. Some of thewords are highlighted which would help you toanswer some of the questions given.

All political parties must be mindful of thecore values that invigorate Indian democracy

As the countdown for elections to the 17thLok Sabha begins, the world’s largest democ-racy has a chance to re-imagine itself. Overthe last 16 general elections and numerouselections at lower levels, the resolute trust thatthe founding fathers of the Republic put in theparliamentary democratic system has beensubstantially proven wise. India did makesome dangerous turns and show signs offragility, especially during the Emergency inthe 1970s, but in the long term it expanded thescope of its democracy through widening rep-resentation, devolution of power and redistrib-ution of resources. This is not to overlook thevarious maladies that have afflicted the coun-try’s democracy, such as disinformation cam-paigns, corruption, disenfranchisement of theweaker sections of the society, the corrodinginfluence of money and muscle power in elec-tions, and divisive majoritarian tendencies.(i) The representative character of institutionshas in general improved, women and religiousminorities are alarmingly underrepresented.The exercise of elections itself is a matter ofgreat pride for all Indians. The ElectionCommission of India has over the decadesevolved itself into a fine institution and plays acritical role in the support of democracy. Itsefforts to increase voter participation througha series of small steps over the years, includ-ing the use of the Electronic Voting Machines,have been praiseworthy.

The vulnerabilities of Indian democracyhave been pronounced in the last five years,and some of its long-term gains have beenundermined. Therefore, this election is morethan an exercise to elect a new government.This should also be an occasion to reiterateand reinforce Indian democracy’s core values,its representative character and its promise ofa constant rejuvenation of the collective spirit.The ECI has announced a series of freshmeasures to strengthen the integrity of theelectoral process and curb some rapidly grow-ing hazards such as the spread of falsehoodsaimed at creating social polarisation for con-solidation of votes. Measures such as bettermonitoring of social media campaigns, whilesteps in the right direction, are not in them-selves adequate to deal with the challengesof these times. The stakes are high for all con-tenders this year, and Indian politics hasreached a level of competitiveness whereground rules of engagement are routinely dis-regarded. Prime Minister Narendra Modi, whorode to power in 2014 on the agenda of mate-rial progress through Hindutva, has to defendhis reign to seek a second term. His oppo-nents sense an existential danger from himand are trying to mobilise those left behind orwho feel disempowered by his governance.While furthering individual interests, all partiesmust realise that democracy itself is at stake ifthe campaign is aimed at communal polarisa-tion. Though the promise of Indian democracyhas not been fully realised, voters have

remained committed to it. They turn up inlarge numbers to vote, and consider the veryact of voting as empowerment. That trustshould be upheld.1. As per the passage given above, how has

India managed to amplify its democraticbase?i) allocation of resources in a way to

achieve higher equalityii) dilated representationiii) decentralized structure of power sharing1) Both i & ii 2) Both ii & iii3) Both i & iii 4) All 5) None

2. According to the passage given above,what has been the primary reasonability ofthe Election Commissions?1) to designate political party insignia and

prohibit from allowing the same insigniaby two different parties

2) maintenance of the electoral rolls andestablishing the schedules of elections

3) empowered with prohibiting dissemina-tion or publication of voting trends

4) sustenance of democracy throughwidening the voter engagement base

5) None of these3. What is the tone used by author in the ital-

icized statement (i) in the passage givenabove?1) introspective 2) indignant 3) irony4) bellicose 5) grandiose

4. How can the upcoming general electionsbe “more than an exercise to elect newgovernment”?1) They can provide the best expression

of the electorate's political preferences.2) They can bolster India’s core democra-

tic values and representative character3) They can lead to persistent rejuvenation

of India’s essence of diversity and unity4) Both 2 & 3 5) Both 1 & 3

5. Which of the following statements is true incontext of the information available in theabove passage?1) the Indian politics is facing a crisis

where ground rules are paid heed2) for making the elections process fair,

Election Commission has adoptedmeasures to strengthen integrity of theelectoral candidates.

3) disenfranchisement of the wealthiersections of the society has created ademocratic disorder

4) emergency imposed in 1970s posed athreat to Indian democracy.

5) All are incorrect6. Which of the following can be the most

appropriate title for the passage givenabove?1) Why India’s election is among world’s

most expensive elections?2) Decoding the BJP’s victory3) Rhetoric over real issues4) A promise to live by: on Indian democ-

racy5) All are correct

7. How are the opponents of Modi govern-ment trying to create possibilities of theirfurther survival in politics?1) making mandatory for every candidate

to give details of his property and crim-inal cases pending against him

2) members of the parties must be pre-vented from deflecting

3) trying to win over and mobilize thosewho felt neglected and subjugatedunder the first term of Modi government

4) making a diverse representation,involving all the sections of the society

5) None of these8. Which of the following word is most similar

to Adequate, as highlighted in the abovepassage?1) piddling 2) paltry 3) apposite4) scant 5) meagre

Directions (Q.No.9-14): In the following pas-sage, some of the words have been left out,each of which is indicated by a number. Findthe suitable word from the options givenagainst each number and fill up the blankswith appropriate words to make the paragraphmeaningfully complete.

People who have been ....... (9) ....... formajor economic reforms from the NarendraModi government, it seems, will have to waitto have their dreams come true. FinanceMinister Nirmala Sitharaman on Saturday pre-sented the third round of stimulus measures toresuscitate the ....... (10) ....... economy, butonce again these have largely failed to live upto the initial hype around them. The previoustwo rounds of the stimulus plan, presented atpress conferences held by the Minister overthe last few weeks, focused primarily on .......(11) ....... the automobile sector, boosting theconfidence of foreign investors who werespooked by the Budget announcements inJuly, and improving the health of dangerously....... (12) ....... state-owned banks by doingeverything short of privatising them. This timearound the focus has been on helping out theunderperforming export and real estate sec-tors through piecemeal fiscal reforms. Amongother things, Ms. Sitharaman ....... (13) ....... anew tax refund scheme and greater prioritysector lending for the export sector to incen-tivise exports. It is expected that the new taxbreaks to the exports sector will cause a .......(14) ....... of up to Rs.50,000 crore to the gov-ernment’s revenue. Further, external commer-cial borrowing norms have been eased tomake it easier for Indian real estate compa-nies to tap funds from abroad, and fundsworth Rs.10,000 crore have also been allocat-ed to aid the completion of affordable housingprojects.9. 1) securing 2) yearning 3) hoarding

4) achieving 5) ascertaining10. 1) parallel 2) technological

3) struggling 4) reasonable5) professional

11. 1) preparing 2) ascertaining3) challenging 4) merging5) reviving

12. 1) communicable 2) valuable3) stable 4) fragile5) affordable

13. 1) concluded 2) unlimited3) concerned 4) announced5) sponsored

14. 1) writ 2) federal 3) overstaff4) dent 5) magnitude

Directions (Q.No.15-21): Read each sen-tence to find out if there is any error in it. Theerror, if any will be in one part of the sentence.

The number of that part is the answer if thereis no error, the answer is 5.15. The Indian economy has been (A)/ in dol-

drums, exhibiting (B)/ slackened growthacross sectors (C)/ for the fifth consecu-tive quarter. (D)/ No Error (E)

1) A 2) C 3) D 4) B 5) No Error16. In the world of climate science, (A)/models

come under particularly (B)/ intense scruti-ny, with some skeptics (C)/ dismissingthem entirely. (D)/ No Error (E)

1) B 2) D 3) A 4) C 5) No Error17. District Collector Divya (A)/ Devarajan

urged Adivasis(B)/ to excel with acade-mics and (C)/ to secure government jobs.(D)/ No Error (E)

1) C 2) A 3) B 4) D 5) No Error18. White might show scuffs very easily (A)/

than a darker color, so white says (B)/thatyou're committed to keeping (C)/ yourphone looking brand new. (D)/ No Error (E)

1) D 2) A 3) B 4) C 5) No Error19. One of the world’s most (A)/legendary

band U2 is (B)/bringing its Joshua (C)/Tree tour to India (D)/ No Error (E)

1) A 2) B 3) C 4) D 5) No Error20. In her compositions, Siobhan(A)/ also

attempts to free herself with the(B)/ con-straints of traditional (C)/perspective andhorizon lines. (D)/ No Error (E)

1) C 2) D 3) A 4) B 5) No Error21. Workers in the services sector (A)/ com-

prised of 57.8 percent of the (B)/ totalemployed in July 2019, the (C)/largestproportion of the employed population.(D)/ No Error (E)

1) D 2) B 3) A 4) C 5) No Error

Directions (Q.No.22-25): In each of the ques-tions given below a part of the sentence isgiven in bold. It is then followed by threeoptions. Find the alternative that can replacethe given bold part to make the sentence gram-matically and contextually correct. If none of thealternatives is correct and the sentence is cor-rect as it is then select option 5) as your choice.22. It's difficult to ignore the feeling that the

Republican Party is indifferent aboutthe concerns of women.

i) is indifferent about the concerns regardingii) is indifferent to the concerns ofiii) is indifferent to the concerns to1) Only ii 2) Both i and iii3) Both ii and iii 4) Only iii5) No correction required

23. Severe floods remain in the four north-east provinces of Roi Et, Si Sa Ket, UbonRatchathani and Yasothon, and about24,000 residents have been evacuated.

i) remains in the four northeasternprovinces

ii) remained in the four northeast provincesiii) remain in the four northeastern

provinces1) Both i and iii 2) Only i3) Both ii and iii 4) Only iii5) No correction required

24. Virginia’s ethics enforcement is too weakthat it is one of seven states that cannotbe rated.i) is so weak that it is one of seven stateii) is so weak that it is one of seven statesiii) is too weak that it is one of seven state1) Only i 2) Only ii3) Both ii and iii 4) Both i and iii5) No correction is required

English Language

No. of Questions: 100 Max. Marks: 100 Time: 60 Minutes

IBPS Clerks Model PaperPreliminary Exam

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