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This Question Paper consists of 36 questions including 5 figures and 12 printed pages + Graph sheet.

§â ÂýàÙ-˜æ ×ð´

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ÂýàÙ ÌÍæ

⁵

ç¿˜æ °ß´

¹²

×éçÎýÌ ÂëcÆU + »ýæȤ àæèÅU ãñ´Ð

Roll No.

¥Ùé·ý¤×æ´·¤

^{Code No.}

·¤æðÇU Ù´. 51/AS/3

MATHEMATICS

(»ç‡æÌ)

(211)

Day and Date of Examination

ÂÚUèÿææ ·¤æ çÎÙ ß çÎÙæ´·¤

Signature of Invigilators 1.

çÙÚUèÿæ·¤æð´ ·ð¤ ãSÌæÿæÚU

2.

General Instructions :

1. Candidate must write his/her Roll Number on the first page of the Question Paper.

2. Please check the Question Paper to verify that the total pages and total number of questions contained in the Question Paper are the same as those printed on the top of the first page.

Also check to see that the questions are in sequential order.

3. For the objective type of questions, you have to choose any one of the four alternatives given in the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the Answer-Book given to you.

4. All the questions including objective type questions are to be answered within the allotted time and no separate time limit is fixed for answering objective type questions.

5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than the specified places will lead to disqualification of the candidate.

6. Write your Question Paper code No.

51/AS/3-A

on the Answer-Book.

7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer in any one of the languages listed below :

English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.

You are required to indicate the language you have chosen to answer in the box provided in the Answer-Book.

(b) If you choose to write the answer in the language other than Hindi and English, the responsibility for any errors/mistakes in understanding the question will be yours only.

Set A

âæ×æ‹Ø ¥ÙéÎðàæ Ñ

1.

ÂÚUèÿææÍèü ÂýàÙÂ˜æ ·ð¤ ¤ÂãÜð ÂëcÆU ÂÚU ¥ÂÙæ ¥Ùé·ý¤×æ´·¤ ¥ßàØU çܹð´Ð

2

. ·ë¤ÂØæ ÂýàÙÂ˜æ ·¤æð Áæò¡¿ Üð´ ç·¤ ÂýàÙÂ˜æ ·ð¤ ·é¤Ü ÂëcÆUæð´ ÌÍæ ÂýàÙæð´ ·¤è ©ÌÙè ãè ⴁUØæ ãñ çÁÌÙè ÂýÍ× ÂëcÆ ·ð ¤âÕâ𠪤ÂÚU ÀUÂè ãñÐ §â ÕæÌ ·¤è Áæò¡¿ Öè ·¤ÚU Üð´ ç·¤ ÂýàÙ ·ý ç×·¤ UM¤Â ×ð´ ãñ´Ð

3.

ßSÌéçÙcÆU ÂýàÙæð´ ×𴠥淤æð ¿æÚU çß·¤ËÂæð´

(A), (B), (C)

ÌÍæ

(D)

×ð´ âð ·¤æð§ü °·¤ ©žæÚ ¿éÙÙæ ãñ ÌÍæ Îè »§ü

©žæÚU-ÂéçSUÌ·¤æ ×ð´ ¥æ âãè ©žæÚ çÜç¹°ÐU

4.

ßSÌéçÙcÆU ÂýàÙæð´ ·ð¤ âæÍ-âæÍ âÖè ÂýàÙæ𴠷𤠩žæÚ çÙÏæüçÚUÌ ¥ßçÏ ·ð ÖèÌÚU ãè ÎðÙð ãñ´Ð ßSÌéçÙcÆU ÂýàÙæð´ ·ð¤ çÜ°¤¥Ü»

âð â×Ø Ùãè´ çÎØæ Áæ°»æÐ

5.

¤ ©žæÚU-ÂéçSUÌ·¤æ ×ð´ Âã¿æÙ-ç¿q ÕÙæÙð ¥Íßæ çÙçÎücÅU SÍæÙæ𴠷𤤠¥çÌçÚU€Ì ·¤ãè´ Öè ¥Ùé·ý¤×æ´·¤ çܹÙð ÂÚU ÂÚUèÿææÍèü

·¤æð ¥Øæð‚Ø ÆUãÚUæØæ ÁæØð»æÐ

6.

¥ÂÙè ©žæÚU-ÂéçSUÌ·¤æ ÂÚU ÂýàÙÂ˜æ ·¤è ·¤æðÇU ⴁØæ 51/AS/3-A çܹð´Ð

7.

(·¤) ÂýàÙÂ˜æ ·ð¤ßÜ çã´Îè

^/

¥´»ýðÁè ×ð´ ãñÐ çȤÚU Öè, ØçÎ ¥æ ¿æãð´ Ìæð Ùè¿ð Îè »§ü ç·¤âè °·¤ Öæáæ ×ð´ ©žæÚ Îð â·¤Ìð ãñ´ Ñ

¥´»ýðÁè, çã´Îè, ©Îêü, ´ÁæÕè, Õ¡»Üæ, Ìç×Ü, ×ÜØæÜ×, ·¤‹ÙǸ, ÌðÜé»é, ×ÚUæÆUè, ©çǸØæ, »éÁÚUæÌè, ·¤æð´·¤‡æè,

×ç‡æÂéÚUè, ¥âç×Øæ, ÙðÂæÜè, ·¤à×èÚUè, â´S·ë¤Ì¤¥æñÚU çâ´ÏèÐ

·ë¤ÂØæ ©žæÚU-ÂéçSÌ·¤æ ×ð´ çΰ »° Õæò€â ×ð´ çܹð´ ç·¤ ¥æ 緤â Öæáæ ×ð´ ©žæÚU çܹ ÚUãð ãñ´Ð ¤

(¹) ØçÎ ¥æ çã´Îè °ß´ ¥´»ýðÁè ·ð¤ ¥çÌçÚU€Ì ç·¤âè ¥‹Ø Öæáæ ×ð´ ©žæÚU çܹÌð ãñ´ Ìæð ÂýàÙ ·¤æð â×ÛæÙð ×ð´ ãæðÙð ßæÜè

˜æéçÅUØæð´

/

»ÜçÌØæð´ ·¤è çÁ×ðUÎæÚè ·ð ßÜ ¥æ·¤è ãæð»èÐ

MATHEMATICS

(»ç‡æÌ)

(211)

Time : 2½ Hours ] [ Maximum Marks : 85

â×Ø Ñ

2½

ƒæ‡ÅðU ] [ Âê‡ææZ·¤ Ñ

85

Note : (1) Question Numbers (1-10) are Multiple Choice Questions. Each question carries one mark. For each question, four alternative choices A, B, C and D are provided, of which only one is correct. You have to select the correct alternative and indicate it in the answer-book provided to you by writing (A), (B), (C) or (D) as the case may be. Q. No. 11 to 15 also carry one mark each.

(2) Question Numbers (16-25) carry 2 marks each.

(3) Question Numbers (26-33) carry 4 marks each.

(4) Question Numbers (34-36) carry 6 marks each.

(5) All questions are compulsory.

çÙÎðüàæ Ñ

⁽¹⁾

Âýà٠ⴁØæ

^(1-10)

Ì·¤ Õãéçß·¤ËÂè ÂýàÙ

(Multiple Choice Questions)

ãñ´Ð ÂýˆØð·¤ ÂýàÙ °·¤

¥´·¤ ·¤æ ãñÐ ÂýˆØð·¤ ÂýàÙ ×ð´ ¿æÚU çß·¤ËÂ

A, B, C

ÌÍæ

D

çÎØð »Øð ãñ´, çÁÙ×ð´ âð ·ð¤ßÜ °·¤ âãè ãñÐ

¥æ·¤æð âãè çß·¤Ë ¿éÙÙæ ãñ ÌÍæ ÂýˆØð·¤ ÂýàÙ ·ð¤ ©žæÚU ¥ÂÙè ©žæÚU ÂéçSÌ·¤æ ×ð´

(A), (B), (C)

¥Íßæ

(D)

Áñâè Öè çSÍçÌ ãæð, çܹ·¤ÚU ÎàææüÙæ ãñÐ Âýà٠ⴁØæ

¹¹

âð

¹⁵

Öè °·¤ ¥´·¤ ·¤æ ãñÐ

(2)

Âýà٠ⴁØæ

(16-25)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

2

¥´·¤ ãñ´Ð

(3)

Âýà٠ⴁØæ

^(26-33)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

⁴

¥´·¤ ãñ´Ð

(4)

Âýà٠ⴁØæ

^(34-36)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

⁶

¥´·¤ ãñ´Ð

(5)

âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð

1. 60% of the students in a school are girls. If the number of boys in the school is 320, the total number of students in the school is :

ç·¤âè çßlæÜØ ×ð´

^60%

çßlæÍèü ÜǸ緤Øæ¡ ãñ´Ð ØçÎ çßlæÜØ ×ð´ ÜǸ·¤æð´ ·¤è ⴁØæ

³²⁰

ãæð, Ìæð çßlæÜØ ×ð´

·é¤Ü çßlæçÍüØæð´ ·¤è ⴁØæ ãæð»è Ñ

(A) 400 (B) 450 (C) 600 (D) 800

2. An article is sold for ` 2,000 cash or for ` 600 as cash down payment followed by

` 1680 after one year. The rate of interest charged under instalment plan is :

ç·¤âè ßSÌé ·¤æð

^{` 2,000}

·ð¤ Ù·¤Î Öé»ÌæÙ ÂÚU ¥Íßæ

^{` 600}

·ð¤ ÌéÚ´UÌ Öé»ÌæÙ ÌÍæ ©â·ð¤ °·¤ ßáü Âà¿æÌ÷

` 1680

·ð¤ Öé»ÌæÙ ÂÚU Õð¿æ ÁæÌæ ãñÐ ç·¤SÌ ØæðÁÙæ ·ð¤ ¥‹Ì»üÌ Ü»æ° ÁæÙð ßæÜð ŽØæÁ ·¤è ÎÚU ãñ Ñ

(A) 16% (B) 20% (C) 28% (D) 40%

3. In the figure, given here, ÐACD1ÐCBF1ÐBAE is equal to :

Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´

ÐACD1ÐCBF1ÐBAE

ÕÚUæÕÚU ãñ Ñ

(A) 1808 (B) 3608 (C) 4508 (D) 5408

4. The length of the arc of a sector of a circle of radius r and central angle u is equal to :

ç˜æ’Øæ

r

ÌÍæ ·ð¤‹ÎýèØ ·¤æð‡æ

u

ßæÜð ç·¤âè ßëžæ ·ð¤ °·¤ ç˜æ’Ø ¹´ÇU ·ð¤ ¿æ ·¤è ܐÕæ§ü ãæðÌè ãñ Ñ

(A) 2r 1 720

 

 

 

1 pu

8 (B) 2r 1

360

 

 

 

1 pu 8

(C) r

360 p u

8 (D) r

180 p u

8 5. sin² 6081cos² 458 is equal to :

sin² 6081cos² 458

ÕÚUæÕÚU ãñ Ñ

(A) 3 2

2

1 (B) 5

4 (C) 3

4 (D) 1

4

1

1 1

1

1

6. 9.09 in the form p

q is equal to :

9.09, p

q

·ð¤ L¤Â ×ð´ ÕÚUæÕÚU ãñ Ñ

(A) 1

1 (B) 101

11 (C) 100

11 (D) 10

1

7. If a 5 2 65 1 , then a 1

2 a is equal to :

ØçÎ

a 5 2 65 1

ãæð, Ìæð

^{a 2} _a¹

ÕÚUæÕÚU ãæð»æ Ñ

(A) 4 6 (B) 24 6 (C) 10 (D) 210

8. A triangle ABC is necessarily congruent to another triangle PQR if :

·¤æð§ü ç˜æÖéÁ

^ABC

°·¤ ¥‹Ø ç˜æÖéÁ

^PQR

·ð¤ ¥ßàØ×ðß âßæZ»â× ãæð»è ØçÎ Ñ

(A) ÐA5ÐP, ÐB5ÐQ, ÐC5ÐR (B) ÐA5ÐP, ÐB5ÐQ, AB5QR

(C) AB5PQ, BC5QR, ÐC5ÐQ (D) ÐB5ÐQ, ÐC5ÐR, BC5QR

9. In the plane of a triangle, the point equidistant from the vertices of the triangle is its : (A) centroid (B) incentre (C) circumcentre (D) orthocentre

ç·¤âè ç˜æÖéÁ ·ð¤ â×ÌÜ ×ð´ ç˜æÖéÁ ·ð¤ àæèáü çՋÎé¥æð´ âð â×æÙ ÎêÚUè ÂÚU çSÍÌ çՋÎé ©â ç˜æÖéÁ ·¤æ ãæðÌæ ãñ Ñ

(A)

·ð¤‹Îý·¤

(B)

¥‹ÌÑ·ð¤‹Îý

(C)

ÂçÚU·ð¤‹Îý

(D)

ËæÕ ·ð¤‹Îý

1 1

1

1

10. Which of the following is not true ?

(A) A trapezium is also a parallelogram.

(B) A rhombus is also a parallelogram.

(C) A rectangle is also a parallelogram.

(D) A square is also a parallelogram.

ç‹æÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ âˆØ Ùãè´ ãñ?

(A)

°·¤ â×Ü´Õ °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ

(B)

°·¤ â׿ÌéÖéüÁ °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ

(C)

°·¤ ¥æØÌ °·¤ â×æ‹ÌÚU ¿ÌéÖüéÁ Öè ãæðÌæ ãñÐ

(D)

°·¤ ß»ü °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ

11. In the figure, given here, O is the centre of the circle and OP^AB. If AB58 cm and OP53 cm, find the diameter of the circle.

Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´

^O

ßëžæ ·¤æ ·ð¤‹Îý ãñ ÌÍæ

^{OP^AB}

ãñÐ ØçÎ

^AB58

âð.×è. ÌÍæ

^OP53

âð.×è. ãæð, Ìæð ßëžæ ·¤æ ÃØæ⠙ææÌ ·¤èçÁ°Ð

12. Find the volume of a right circular cone whose area of the base is 36p cm² and slant height is 10 cm.

©â ÜÕ ßëžæèØ àæ´·é¤ ·¤æ ¥æØÌÙ ™ææÌ ·¤èçÁ° çÁâ·ð¤ ¥æÏæÚU ·¤æ ÿæð˜æȤÜ

^36p

âð.×è

²

. ãñ ÌÍæ çÁâ·¤è çÌUØü·÷¤

ª¡¤¿æ§ü

¹⁰

âð.×è. ãñÐ

13. In a DABC, ÐB5908, AB55 cm and BC57 cm. Find the value of tan A2cot C.

ç·¤âè ç˜æÖéÁ

^ABC

×ð´,

ÐB5908, AB55

âð.×è. ÌÍæ

^BC57

âð.×è. ãñÐ

tan A2cot C

·¤æ ×æÙ ™ææÌ

·¤èçÁ°Ð

1 1

1

1

14. A bag contains 15 red balls and some white balls. If the probability of drawing a white ball from the bag is 1

6, find the number of white balls in the bag.

ç·¤âè ÍñÜð ×ð´

¹⁵

ÜæÜ ÌÍæ ·é¤ÀU âÈð¤Î »ð´Î ãñÐ ØçÎ ÍñÜð ×ð´ âð °·¤ âÈð¤Î »ð´Î çÙ·¤æÜð ÁæÙð ·¤è ÂýýæçØ·¤Ìæ

¹₆

ãæð, Ìæð ÍñÜð ×ð´ âÈð¤Î »ð´Îæð´ ·¤è ⴁØæ ™ææÌ ·¤èçÁ°Ð

15. The mean of 8 observations was found to be 30. Later it was detected that one observation 64 was mistakenly read as 24. Find the correct mean.

8

Âýðÿæ‡ææð´ ·¤æ ×æŠØ

30

çÙ·¤æÜæ »ØæÐ ÕæÎ ×ð´ ÂÌæ ¿Üæ ç·¤ °·¤ Âýðÿæ‡æ

64

·¤æð »ÜÌè âð

24

Âɸ çÜØæ »Øæ ÍæÐ âãè ×æŠØ ™ææÌ ·¤èçÁ°Ð

16. Evaluate the polynomial 2x³23x²28x112 for x522 and state whether this value of x is a zero of the given polynomial or not.

x522

·ð¤ çÜ° ÕãéÂÎ

^{2x323x228x112}

·¤æ ×æÙ ™ææÌ ·¤èçÁ° ÌÍæ ÕÌ槰 ç·¤

^x

·¤æ Øã ×æÙ çÎØð »°

ÕãéÂÎ ·¤æ °·¤ àæê‹Ø·¤ ãñ ¥Íßæ Ùãè´Ð

17. Find the distance between the points (26, 21) and (26, 11).

çՋÎé¥æð´

^{(26, 21)}

ÌÍæ

^{(26, 11)}

·ð¤ Õè¿ ·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð

18. Find the coordinates of the point which divides the line-segment joining the points (21, 4) and (0, 23) in the ratio 1 : 4 internally.

©â çՋÎé ·ð¤ çÙÎðüàææ´·¤ ™ææÌ ·¤èçÁ° Áæð çՋÎé¥æð´

^{(21, 4)}

ÌÍæ

^{(0, 23)}

·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ-¹´ÇU ·¤æð

^{1 : 4}

·ð¤ ¥æ‹ÌçÚU·¤ ¥ÙéÂæÌ ×ð´ çßÖ€Ì ·¤ÚUÌæ ãñÐ

19. An integer is chosen between 0 and 20. Find the probability that the chosen integer is a prime number.

0

ÌÍæ

²⁰

·ð¤ Õè¿ °·¤ Âê‡ææZ·¤ ·¤æ ¿ØÙ ç·¤Øæ ÁæÌæ ãñÐ ¿éÙð »° Âê‡ææZ·¤ ·¤æ °·¤ ¥Öæ’Ø ⴁØæ ãæðÙð ·¤è ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ°Ð

1

1

2

2

2

2

20. The perimeter of a rectangular plot of land is 32 m. If the length is increased by 2 m and the breadth decreased by 1 m, the area of the plot remains the same. Find the length and breadth of the plot.

ç·¤âè ¥æØÌæ·¤æÚU Öê¹´ÇU ·¤æ ÂçÚU×æÂ

³²

×è ãñÐ ØçΠܐÕæ§ü ×ð´

²

×è ·¤è ßëçh ÌÍæ ¿æñǸæ§ü ×ð´

¹

×è ·¤è ·¤×è

·¤è Áæ°, Ìæð Öè Öê¹´ÇU ·¤æ ÿæð˜æÈ¤Ü ÂãÜð ·ð¤ â×æÙ ãè ÚUãÌæ ãñÐ Öê¹´ÇU ·¤è ܐÕæ§ü ÌÍæ ¿æñǸæ§ü ™ææÌ ·¤èçÁ°Ð

21. At what rate of interest per annum will simple interest be half of the principal in 5 years ?

ŽØæÁ ·¤è ç·¤â ßæçáü·¤ ÎÚU âð

⁵

ßáü ×ð´ âæÏæÚU‡æ ŽØæÁ ×êÜÏÙ ·ð¤ ¥æÏð ·ð¤ ÕÚUæÕÚU ãæð»æ?

22. Show that a cyclic parallelogram is a rectangle.

çι槰 ç·¤ °·¤ ¿·ý¤èØ â×æ‹ÌÚU ¿ÌéÖüéÁ °·¤ ¥æØÌ ãæðÌæ ãñÐ

23. In the figure, given here, O is the centre of the circle and PQ and PR are the tangent - segments of the circle. Find ÐRPO.

Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´

O

ßëžæ ·¤æ ·ð¤‹Îý ãñ ÌÍæ

PQ

ÌÍæ

PR

ßëžæ ·ð¤ SÂàæü-ÚðU¹æ¹´ÇU ãñ´Ð

ÐRPO

·¤è ×栙ææÌ

·¤èçÁ°Ð

24. The volume of a solid hemisphere is 2

7183 cm³. Find its total surface area. [use 22 p 5 7 ]

ç·¤âè ÆUæðâ ¥hü-»æðÜð ·¤æ ¥æØÌÙ

⁷¹⁸²₃

âð.×è.

³

ãñÐ §â·¤æ âÂê‡ææü ÂëcÆèØ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð

[ 22

p 5 7

ÜèçÁ°Ð

]

2

2

2

2

2

25. Standing on the top of a tower, 100 m high, Swati observes two cars parked on the opposite sides of the tower. If their angles of depression are 458 and 308, find the distance between the cars.

°·¤

¹⁰⁰

×è ª¡¤¿è ×èÙæÚU ·ð¤ çàæ¹ÚU ÂÚU ¹Ç¸è ãæð·¤ÚU SßæçÌ ×èÙæÚU ·¤è çßÂÚUèÌ çÎàææ¥æð´ ×ð´ ¹Ç¸è ·¤è »Øè Îæð ·¤æÚUæð´

·¤æ ¥ßÜæð·¤Ù ·¤ÚUÌè ãñÐ ØçÎ ©Ù·ð¤ ¥ßÙØÙ ·¤æð‡æ

⁴⁵⁸

ÌÍæ

³⁰⁸

ãñ´, Ìæð ·¤æÚUæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð

26. At what rate percent per annum will a sum of ` 15,625 become ` 17,576 in 3 years on compound interest when the interest is compounded annually ?

ØçÎ ŽØæÁ ßæçáü·¤ L¤Â ×ð´ â´ØæðçÁÌ ãæð, Ìæð

^{` 15,625}

·¤è ÏÙÚUæçàæ ç·¤â ßæçáü·¤ ÎÚU ÂýçÌàæÌ âð ¿·ý¤ßëçh ŽØæÁ ÂÚU

3

ßáZ ×ð´

` 17,576

ãæð»è?

27. In the figure, given here, AD is the bisector of ÐBAC. If AB59 cm, AC512 cm and BC57 cm, find the measures of BD and DC.

Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´,

AD

·¤æð‡æ

ÐBAC

·¤æ â×çmÖæÁ·¤ ãñÐ ØçÎ

AB59

âð.×è.,

AC512

âð.×è. ÌÍæ

BC57

âð.×è. ãæð´, Ìæð

BD

ÌÍæ

DC

·¤è ×栙ææÌ ·¤èçÁ°Ð

28. Find the mean of the following data by step-deviation method :

Classes : 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequencies : 2 3 5 7 5 3

ÂÎ çß¿ÜÙ çßçÏ âð çِÙçÜç¹Ì ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ ™ææÌ ·¤èçÁ° Ñ

ᯁ

^{: 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70}

ÕæÚ´UÕæÚUÌæ°¡

^{: 2 3 5 7 5 3}

29. Find the values of m for which the equation 3x²16x1m50 has two distinct real roots.

m

·ð¤ ©Ù ×æÙæð´ ·¤æð ™ææÌ ·¤èçÁ° çÁÙ·ð¤ çÜ° â×è·¤ÚU‡æ

3x²16x1m50

·ð¤ Îæð ç֋٠ßæSÌçß·¤ ×êÜ ÂýæŒÌ ãæð´Ð

2

4

4

4

4

30. Find the circumradius of equilateral triangle of side 6 cm. 4 6

âð.×è. ÖéÁæ ßæÜðð â×Õæãé ç˜æÖéÁ ·¤è ÂçÚUç˜æ’Øæ ™ææÌ ·¤èçÁ°Ð

31. Simplify : 4

(5x13y)³13(5x13y)²(5x23y)13(5x13y)(5x23y)²1(5x23y)³

âÚUÜ ·¤èçÁ° Ñ

(5x13y)³13(5x13y)²(5x23y)13(5x13y)(5x23y)²1(5x23y)³

32. Construct a right triangle ABC, right - angled at B in which BC53 cm and AC56 cm.

°·¤ °ðâð â×·¤æð‡æ ç˜æÖéÁ

^ABC

·¤è ÚU¿Ùæ ·¤èçÁ° çÁâ·¤æ ·¤æð‡æ

^B

â×·¤æð‡æ, ÖéÁæ

^BC53

âð.×è. ÌÍæ

AC56

âð.×è. ãæðÐ

OR

(¥Íßæ)

For visually impaired learners only

(·ð¤ßÜ ÎëçcÅU çß·¤Üæ´» çßlæçÍüØæð´ ·ð¤ çÜ°)

Write the steps of construction of a tangent to a circle at a given point on it using the centre of the circle.

ßëžæ ·ð¤ ·ð¤‹Îý ·¤æ ©ÂØæð» ·¤ÚU·ð¤, ßëžæ ÂÚU çSÍÌ °·¤ çՋÎé ÂÚU ßëžæ ·¤è SÂàæü ÚðU¹æ ·¤è ÚU¿Ùæ ·ð¤ ¿ÚU‡æ çÜç¹°Ð

33. A survey of 200 students of a school was done to find which activity they prefer to do in their free time and the information, thus collected is recorded in the following table :

Preferred Activity Number of Students

Playing 60

Reading story books 45

Watching TV 40

Listening to music 25

Painting 30

Draw a bar graph for this data.

ç·¤âè çßlæÜØ ·ð¤

200

çßlæçÍüØæð´ ÂÚU °·¤ âßðüÿæ‡æ Øã ÁæÙÙð ·ð¤ çÜ° ç·¤Øæ »Øæ ç·¤ ßð ¥ÂÙð ¹æÜè â×Ø ×ð´

€Øæ ·¤ÚUÙæ Ââ´Î ·¤ÚUÌð ãñ´, ÌÍæ ÂýæŒÌ âê¿Ùæ ·¤æð Ùè¿ð Îè »Øè âæÚU‡æè ·ð¤ M¤Â ×ð´ çÚU·¤æÇüU ç·¤Øæ »Øæ Ñ

¼¾ §Ç™³ Ìœâ ½Ë œ‰Á˧ ÌÄlË̲á½Ëՙ œ‰Í Ǚ€½Ë

žÕÁ¾Ë

⁶⁰

œ‰ÈË¾Í œ‰Í §ÎS±œ™Õ‰ §®¾Ë

⁴⁵

ªÍ.ÄÍ. ³Õž¾Ë

⁴⁰

Ǚ Í± Çξ¾Ë

²⁵

§Õ™ÌªU™U 

³⁰

§Ù ¥æ¡·¤Ç¸æð´ ·ð¤ çÜ° °·¤ δÇUæÜð¹ ·¤è ÚU¿Ùæ ·¤èçÁ°Ð (¥Íßæ)

4

4

For visually impaired learners only

(·ð¤ßÜ ÎëçcÅU çß·¤Üæ´» çßlæçÍüØæð´ ·ð¤ çÜ°)

The following table gives the distribution of employees of different income groups residing in a locality.

Monthly income (in C) Number of employees

20,000 - 25,000 35

25,000 - 30,000 75

30,000 - 35,000 150

35,000 - 40,000 155

40,000 - 45,000 70

45,000 - 50,000 15

Form a cumulative frequency table for the data and answer the following questions : (a) How many employees earn less than or equal to ` 30,000 per month ?

(b) How many employees earn more than ` 30,000 per months ?

Ùè¿ð Îè »Øè âæÚU‡æè °·¤ ÕSÌè ×ð´ ÚUãÙð ßæÜð çßç֋٠¥æØ-â×êãæ𴠷𤠷¤×ü¿æçÚUØæð´ ·¤æ Õ´ÅUÙ ÂýÎçàæüÌ ·¤ÚUÌè ãñÐ

×æçâ·¤ ¥æØ (

^`

×ð´) ·¤×ü¿æçÚUØæð´ ·¤è ⴁØæ

20,000 - 25,000 35

25,000 - 30,000 75

30,000 - 35,000 150

35,000 - 40,000 155

40,000 - 45,000 70

45,000 - 50,000 15

§Ù ¥æ¡·¤Ç¸æð´ ·ð¤ çÜ° °·¤ â´¿Øè ÕæÚ´UÕæÚUÌæ âæÚU‡æè ÕÙ槰 ÌÍæ çِÙçÜç¹Ì ÂýàÙæ𴠷𤠩žæÚU ÎèçÁ° Ñ

(a)

ç·¤ÌÙð ·¤×ü¿æçÚUØæð´ ·¤è ×æçâ·¤ ¥æØ

^{` 30,000}

âð ·¤× ¥Íßæ ÕÚUæÕÚU ãñ?

(b)

ç·¤ÌÙð ·¤×ü¿æçÚUØæð´ ·¤è ×æçâ·¤ ¥æØ

^{` 30,000}

âð ¥çÏ·¤ ãñ?

34. If p^th, q^th and r^th terms of an A.P. are x, y, z respectively. Prove that x(q2r)1y(r2p)1z(p2q)50.

ØçÎ ç·¤âè â.Ÿæð.·ð¤

^pßð´

,

^qßð´

ÌÍæ

^rßð´

ÂÎ ·ý¤×àæÑ

^{x, y, z}

ãæð´ Ìæð çâh ·¤èçÁ° ç·¤ Ñ

x(q2r)1y(r2p)1z(p2q)50.

6

35. In the figure, given here, OAQB is a quadrant of a circle with centre O and radius 7 cm and APB is a semi circle. Find the area of the shaded region.

Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´

^{OAQB, O}

·ð¤‹Îý ÌÍæ

⁷

âð.×è. ç˜æ’Øæ ßæÜð ßëžæ ·¤æ ¿ÌéÍæZàæ ç˜æ’Ø ¹´ÇU ãñ ÌÍæ

^APB

°·¤ ¥hüßëžæ ãñÐ ÀUæØæ´ç·¤Ì Öæ» ·¤æ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð

36. If sec u1tan u5p, show that : 6

2 2

p 1 sin p 1

u 5 2 1

ØçÎ

sec u1tan u5p

ãæð, Ìæð çι槰 ç·¤ Ñ

2 2

p 1 sin p 1

u 5 2 1

- o O o -

6