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This Question Paper consists of 36 questions including 3 figures and 12 printed pages + Graph Sheet.

§â ÂýàÙ-˜æ ×ð´

³⁶

ÂýàÙ ÌÍæ

³

ç¿˜æ °ß´

¹²

×éçÎýÌ ÂëcÆU + »ýæȤ àæèÅU ãñ´Ð

Roll No.

¥Ùé·ý¤×æ´·¤

^{Code No.}

·¤æðÇU Ù´. 49/HIS/1

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.

49/HIS/1-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 49/HIS/1-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 : 3 Hours ] [ Maximum Marks : 100

â×Ø Ñ

3

ƒæ‡ÅðU ] [ Âê‡ææZ·¤ Ñ

100

Note : (1) Question Numbers (1-14) 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.

(2) Question Numbers (15-24) carry 2 marks each.

(3) Question Numbers (25-33) carry 5 marks each.

(4) Question Numbers (34-36) carry 7 marks each.

(5) All questions are compulsory.

çÙÎðüàæ Ñ

⁽¹⁾

Âýà٠ⴁØæ

^(1-14)

Ì·¤ Õãéçß·¤ËÂè ÂýàÙ

(Multiple Choice Question)

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

(2)

Âýà٠ⴁØæ

(15-24)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

2

¥´·¤ ãñ´Ð

(3)

Âýà٠ⴁØæ

^(25-33)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

⁵

¥´·¤ ãñ´Ð

(4)

Âýà٠ⴁØæ

^(34-36)

Ì·¤ ÂýˆØð·¤ ÂýàÙ ·ð¤

⁷

¥´·¤ ãñ´Ð

(5)

âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð

1. A rational number equivalent to the rational number 5 9

2 is : 1

ÂçÚU×ðØ â´Øæ

⁵

9

2

·ð¤ â×ÌéËØ ÂçÚU×ðØ â´Øæ ãñ Ñ

(A) 5

9 (B) 10

9 2

(C) 10

18

2 (D) 10

18

2. 2.07 as a percent can be written as : 1

2.07

·¤æð ÂýçÌàæÌ ·ð¤ M¤Â ×ð´ çܹÙð ÂÚU ÂýæŒÌ ãæðÌæ ãñ Ñ

(A) 207% (B) 20.7%

(C) 2.07% (D) 0.207%

3. ` 2000 at the rate of 8.5% per annum simple interest will yield ` 510 in : 1

(A) 1 year (B) 2 years

(C) 3 years (D) 4 years

` 2000

ÂÚU

^8.5%

ßæçáü·¤ âæÏæÚU‡æ ŽØæÁ ·¤è ÎÚU âð

^{` 510}

çÁÌÙð ßáæðZ ×ð´ ÂýæŒÌ ãæð´»ð ßã ãñ Ñ

(A) 1

ßáü

^{(B) 2}

ßáü

(C) 3

ßáü

^{(D) 4}

ßáü

4. A shopkeeper marks his goods 10% more than their cost price and allows a discount of 10%. His gain or loss percent is :

(A) 1% gain (B) 1% loss

(C) 0% gain or loss (D) 10% gain

°·¤ Îé·¤æÙÎæÚU ¥ÂÙð âæ×æÙ ÂÚU ·ý¤Ø ×êËØ âð

10%

¥çÏ·¤ ×êËØ ¥´ç·¤Ì ·¤ÚUÌæ ãñ, ÌÍæ

10%

Õ^æ ÎðÌæ ãñÐ

©â·¤æ ÂýçÌàæÌ ÜæÖ Øæ ãæçÙ ãñ Ñ

(A) 1%

ÜæÖ

(B) 1%

ãæçÙ

(C) 0%

ÜæÖ Øæ ãæçÙ

(D) 10%

ÜæÖ

1

5. If x 1 5

2 5 x , then ³ 1₃

x 2 x equals : 1

ØçÎ

^{x2 5 1}_x ⁵

ãñ, Ìæð

³ 3

x 1

2 x

·¤æ ×æÙ ãñ Ñ

(A) 140 (B) 145

(C) 135 (D) 130

6. If cos A5 1

3, then the value of tan A is : 1

ØçÎ

^{cos A5 1}₃

ãñ, Ìæð

^{tan A}

·¤æ ×æÙ ãñ Ñ

(A) 2 (B) 1

2 (C) 1

2 (D) 2

7. If a ladder 10 m long is touching the top of a wall, making an angle of 608 with the wall, the height of wall (in meters) is :

ØçÎ °·¤

¹⁰

×è Ü´Õè âèÉ¸è °·¤ ÎèßæÚU ·ð¤ çàæ¹ÚU ·¤æð ÀêUÌè ãé§ü, ÎèßæÚU ·ð¤ âæÍ

⁶⁰⁸

·¤æ ·¤æð‡æ ÕÙæ ÚUãè ãñ, Ìæð ÎèßæÚU ·¤è ª¡¤¿æ§ü (×èÅUÚUæð´ ×ð´) ãñ Ñ

(A) 5 3 (B) 5

(C) 5 2 (D) 5

2

8. If tan A5cot B, then the value of (A1B) is : 1

ØçÎ

tan A5cot B

ãñ, Ìæð

^(A1B)

·¤æ ×æÙ ãñ Ñ

(A) 458 (B) 608

(C) 908 (D) 1808

1

9. Two different coins are tossed at the same time. The probability of getting head on one and tail on the other coin is :

Îæð ç֋Ù-ç֋٠ç‷¤æð´ ·¤æð °·¤ âæÍ ©ÀUæÜæ »ØæÐ °·¤ ç‷ð¤ ÂÚU 翞æ ÌÍæ ÎêâÚðU ÂÚU ÂÅ÷ ¥æÙð ·¤è ÂýæçØ·¤Ìæ ãñ Ñ

(A) 1

4 (B) 3

4

(C) 1 (D) 1

2

10. The median of the data 16, 1, 6, 14, 4, 13, 8, 9, 23, 9, 7, 8, 17 is : 1

¥æ´·¤Ç¸æð´

16, 1, 6, 14, 4, 13, 8, 9, 23, 9, 7, 8, 17

·¤æ ×æŠØ·¤ ãñ Ñ

(A) 8 (B) 9

(C) 8.5 (D) 11

11. In the given figure, DE??BC. If AD53 cm, DB55 cm and AE56 cm, then length of AC is :

(A) 10 cm (B) 16 cm

(C) 6 cm (D) 8 cm

Îè »§ü ¥æ·ë¤çÌ ×ð´,

DE??BC

ãñÐ ØçÎ

AD53

âð.×è.,

DB55

âð.×è. ÌÍæ

AE56

âð.×è. ãñ, Ìæð

AC

·¤è Ü´Õæ§ü ãñ Ñ

(A) 10

âð.×è.

(B) 16

âð.×è.

(C) 6

âð.×è

^{. (D) 8}

âð.×è.

1

1

12. In the given figure, AB is a chord of a circle with centre O. If ÐOAB5508, then ÐACB is :

Îè »§ü ¥æ·ë¤çÌ ×ð´, ·ð¤‹Îý

^O

ßæÜð ßëžæ ·¤è °·¤ Áèßæ

^AB

ãñÐ ØçÎ

^ÐOAB5508

ãñ, Ìæð

^ÐACB

ÕÚUæÕÚU ãñ Ñ

(A) 408 (B) 508

(C) 1008 (D) 258

13. The co-ordinates of the point which divides the line segment joining the points (1,22) and (4, 7) internally in the ratio 1 : 2 is :

çÕ´Îé¥æð´

^(1,22)

ÌÍæ

^{(4, 7)}

·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ¹‡ÇU ·¤æð

^{1 : 2}

×ð´ ¥‹ÌÑ çßÖæÁÙ ·¤ÚUÙð ßæÜð çÕ´Îé ·ð¤

çÙÎðüàææ´·¤ ãñ´ Ñ

(A) (1, 3) (B) (3, 2)

(C) (2, 1) (D) (3, 1)

14. If tan⁴u1tan²u51, then sec²u is equal to : 1

ØçÎ

tan⁴u1tan²u51

ãñ, Ìæð

sec²u

·¤æ ×æÙ ãñ Ñ

(A) cot²u (B) tan²u

(C) tanu (D) cotu

15. Perimeter of a rhombus is 104 cm and the length of one of its diagonal is 48 cm. Find the length of its other diagonal.

°·¤ â׿ÌéÖéüÁ ·¤æ ÂçÚU×æÂ

¹⁰⁴

âð×è ãñ ÌÍæ §â·ð¤ °·¤ çß·¤‡æü ·¤è Ü´Õæ§ü

⁴⁸

âð×è ãñ Ìæð §â·ð¤ ÎêâÚðU çß·¤‡æü

·¤è Ü´Õæ§ü ™ææÌ ·¤èçÁ°Ð

1

1

2

16. Prove the identity : 2

âßüâç×·¤æ ·¤æð çâh ·¤èçÁ° Ñ

tan A cot B

tan A. cot B.

cot A tan B 1 5 1

17. Three cubes of edge 6 cm each are joined end to end to form a cuboid. Find the surface area of the cuboid so formed.

6

âð.×è. ç·¤ÙæÚðU ßæÜð ÌèÙ ƒæÙæð´ ·¤æð çâÚðU âð çâÚUæ ç×Üæ ·¤ÚU °·¤ ƒæÙæÖ ÕÙæØæ ÁæÌæ ãñÐ §â ƒæÙæÖ ·¤æ ÂëcÆUèØ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð

18. L and M are the mid-points of the sides AB and AC of DABC, right angled at B. Show that 4 LC²5AB²14 BC².

ç·¤âè â×·¤æð‡æ ç˜æÖéÁ

^ABC,

çÁâ×ð´

^ÐB

â×·¤æð‡æ ãñ, ·¤è ÖéÁæ¥æð´

^AB

ÌÍæ

^AC

·ð¤ ׊ØçÕ´Îé ·ý¤×àæÑ

^L

ÌÍæ

M

ãñ´Ð Îàææü§° ç·¤

^{4 LC25AB214 BC2.}

19. Show that a cyclic parallelogram is a rectangle. 2

Îàææü§° ç·¤ °·¤ ¿·ý¤èØ â×æ´ÌÚU ¿ÌéÖéüÁ °·¤ ¥æØÌ ãæðÌæ ãñÐ

20. Factorise : 2

»é‡æÙ¹‡ÇU ·¤èçÁ° Ñ

a²2b²18b216.

21. If 110 is reduced to 88, find the reduction percent. 2

ØçÎ

110

·¤æð ƒæÅUæ ·¤ÚU

88

·¤ÚU çÎØæ Áæ°, Ìæð ÂýçÌàæÌ ·¤×è ™ææÌ ·¤èçÁ°Ð

2

2

22. The sides of a triangle are 28 cm, 36 cm and 48 cm. Find the lengths of line-segments into which the smallest side is divided by the bisector of the angle opposite to it.

°·¤ ç˜æÖéÁ ·¤è ÖéÁæ°¡

²⁸

âð.×è,

³⁶

âð.×è. ÌÍæ

⁴⁸

âð.×è. ãñ´Ð âÕâð ÀUæðÅUè ÖéÁæ ·ð¤ âæ×Ùð ·ð¤ ·¤æð‡æ ·¤æ â×çmÖæÁ·¤ ©â ÖéÁæ ·¤æð çÁÙ Îæð ÚðU¹æ¹‡ÇUæð´ ×ð´ çßÖæçÁÌ ·¤ÚðU»æ, ©Ù·¤è Ü´Õæ§Øæ¡ ™ææÌ ·¤èçÁ°Ð

23. In two similar triangles ABC and PQR, if the corresponding altitudes AD and PS are in the ratio 9 : 25, find the ratio of the areas of DABC and DPQR.

ØçÎ Îæð â×M¤Â ç˜æÖéÁæð´

^ABC

ÌÍæ

^PQR

·ð¤ ÌÎÙM¤Âè àæèáü Ü´Õæð´

^AD

ÌÍæ

^PS

×ð´

^{9 : 25}

·¤æ ¥ÙéÂæÌ ãñ Ìæð

DABC

ÌÍæ

^DPQR

·ð¤ ÿæð˜æȤÜæð´ ·¤æ ¥ÙéÂæÌ ™ææÌ ·¤èçÁ°Ð

24. Solve the following system of equations :

çِ٠â×è·¤ÚU‡æ çÙ·¤æØ ·¤æ ãÜ ™ææÌ ·¤èçÁ° Ñ

3x2y57, 4x25y52.

25. Prove that the tangents drawn from an external point to a circle are of equal length.

çâh ·¤èçÁ° ç·¤ ç·¤âè Õæs çÕ´Îé âð ßëžæ ÂÚU ¹è´¿è »§ü SÂàæü ÚðU¹æ¥æð´ ·¤è Ü´Õæ§Øæ¡ â×æÙ ãæðÌè ãñ´Ð

26. From the top of a building 60 m high, the angles of depression of the top and bottom of a tower are observed to be 458 and 608 respectively. Find the height of the tower and its distance from the building. [ Use 351.73 ]

60

×è. ª¡¤¿ð °·¤ ÖßÙ ·ð¤ çàæ¹ÚU âð, °·¤ ×èÙæÚU ·ð¤ çàæ¹ÚU °ß´ ÂæÎ ·ð¤ ¥ßÙ×Ù ·¤æð‡æ ·ý¤×àæÑ

⁴⁵⁸

ÌÍæ

⁶⁰⁸

ãñ´Ð

×èÙæÚU ·¤è ª¡¤¿æ§ü ÌÍæ ÖßÙ âð §â·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð

[ 351.73

ÜèçÁ°

]

2

2

2

5

5

27. Draw a histogram for the following data :

Height (in cm) : 125 - 130 130 - 135 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 Number of

students : 1 2 3 5 4 3 2

çِ٠¥æ¡·¤Ç¸æð´ ·ð¤ çÜ° °·¤ ¥æØÌç¿˜æ ¹è´ç¿°Ð

†‰¤ËŒá (ÇÕ.¼Í. ¼Õ™) ¶

125 - 130 130 - 135 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160

ÌÄlË̲á½Ëՙ œ‰Í

Ǚ€½Ë ¶

^{1 2 3 5 4 3 2}

OR/

¥Íßæ

( For visually impaired candidates only )

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

The class marks of a distribution and the corresponding frequencies are given below :

Class marks 5 15 25 35 45 55 65 75

Frequencies 2 6 10 15 12 8 5 2

Determine the frequency table and hence construct the cumulative frequency table.

ç·¤âè Õ´ÅUÙ ·ð¤ ß»ü 翋㠥æñÚU â´»Ì ÕæÚU´ÕæÚUÌæ°¡ Ùè¿ð âæÚU‡æè ×ð´ Îè ãñ´ Ñ

Ä á ̤üÈ

^{5 15 25 35 45 55 65 75}

ºË¿™UºË¿U±Ë

^{2 6 10 15 12 8 5 2}

©ÂÚUæð€Ì ¥æ¡·¤Ç¸æð´ âð ÕæÚ´UÕæÚUÌæ âæÚU‡æè ÕÙ槰 ¥ÌÑ â´¿Øè ÕæÚ´UÕæÚUÌæ âæÚU‡æè ÕÙ槰Ð

28. The denominator of a rational number is greater than its numerator by 8. If the denominator is decreased by 1 and numerator is increased by 17, the number obtained is 3

2. Find the rational number.

°·¤ ÂçÚU×ðØ â´Øæ ·¤æ ãÚU, ©â·ð¤ ¥´àæ âð

⁸

ÕǸæ ãñÐ ØçÎ ãÚU ×ð´ âð

¹

ƒæÅUæ çÎØæ Áæ° ÌÍæ ¥´àæ ×ð´

¹⁷

ÁæðǸ çÎØæ Áæ°, Ìæð ⴁØæ

³₂

ÂýæŒÌ ãæðÌè ãñÐ ÂçÚU×ðØ â´Øæ ™ææÌ ·¤èçÁ°Ð

5

5

29. The cost of a machinery is ` 3,60,000 today. In the first year, the value depreciates by 12% and subsequently, the value depreciates by 8% each year. Find the depreciated value of the machinery at the end of 3 years.

¥æÁ °·¤ ×àæèÙÚUè ·¤æ ×êËØ

` 3,60,000

ãñÐ ÂãÜð ßáü ×ð´ §â·ð¤ ×êËØ ×ð´

^12%

·¤æ ¥ß×êËØÙ ãæðÌæ ãñ ¥æñÚU

©â·ð¤ Âà¿æÌ÷ ãÚU ßáü §â·¤æ ×êËØ

^8%

ƒæÅU ÁæÌæ ãñÐ ™ææÌ ·¤èçÁ° ç·¤

³

ßáü ·ð¤ ¥‹Ì ×ð´ ×àæèÙÚUè ·¤æ ×êËØ ç·¤ÌÙæ ÚUã ÁæØð»æ?

30. From the following distribution of bulbs kept in boxes, find the mean number of bulbs kept in a box.

Number of bulbs : 50 - 52 52 - 54 54 - 56 56 - 58 58 - 60

Number of boxes : 15 100 126 105 30

Հâæð´ ×ð´ ÚU¹ð ÕËÕæð´ ·ð¤ çِ٠մÅÙ âð °·¤ Հâð ×ð´ ÚU¹ð ÕËÕæð´ ·¤æ ×æŠØ ⴁØæ ™ææÌ ·¤èçÁ° Ñ º°ºËՙ œ‰Í Ǚ€½Ë ¶

^{50 - 52 52 - 54 54 - 56 56 - 58 58 - 60}

ºþÇËՙ œ‰Í Ǚ€½Ë ¶

^{15 100 126 105 30}

31. In the given figure, BA and DC are two chords of a circle intersecting each other at a point P outside the circle. If PA54 cm, PB510 cm and CD53 cm, find PC.

Îè »§ü ¥æ·ë¤çÌ ×ð´, Áèßæ°¡

^BA

ÌÍæ

^DC

ßëÌ ·ð¤ ÕæãÚU °·¤ çÕ´Îé

^P

ÂÚU ÂÚUSÂÚU ·¤æÅUÌè ãñ´Ð ØçÎ

^PA54

âð.×è.,

PB510

âð.×è. ÌÍæ

^CD53

âð.×è. ãñ, Ìæð

^PC

™ææÌ ·¤èçÁ°Ð

32. Simplify and express the following as rational expression in lowest terms :

çِÙçÜç¹Ì ·¤æð âÚUÜ ·¤èçÁ° ÌÍæ ÂçÚU×ðØ ÃØ´Á·¤ ·ð¤ ‹ØêÙÌ× M¤Â ×ð´ ÃØ€Ì ·¤èçÁ° Ñ

2 2

2 2

2 24 6

12 9

x x x x

x x x .

1 2 4 2 2

2 2 2

5

5

5

5

33. Find the value of x 1

2 x if ⁴ 1₄

727

x 1 x 5 . 5

ØçÎ

^{x4 1}₄ ⁷²⁷

1 x 5

ãñ, Ìæð

^{x2 1}_x

·¤æ ×æÙ ™ææÌ ·¤èçÁ°Ð

34. Construct a DABC in which BC56.5 cm, ÐABC5608 and AB55 cm. Then construct another triangle whose sides are 3

5 times the corresponding sides of DABC.

°·¤ ç˜æÖéÁ

^ABC

·¤è ÚU¿Ùæ ·¤èçÁ° çÁâ×ð´

^BC56.5

âð.×è.,

^ÐABC5608

ÌÍæ

^AB55

âð.×è. ãñÐ çȤÚU

°·¤ ¥‹Ø ç˜æÖéÁ ·¤è ÚU¿Ùæ ·¤èçÁ° çÁâ·¤è ÖéÁæ°¡

^DABC

·¤è â´»Ì ÖéÁæ¥æð´ ·¤è

³₅

»éÙè ãñ´Ð

OR/

¥Íßæ

( For visually impaired candidates only )

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

Write the steps of construction for constructing a DABC in which AB54 cm, ÐA5458 and AC2BC51 cm.

°·¤

DABC,

çÁâ×ð´

AB54

âð.×è.,

ÐA5458

ÌÍæ

AC2BC51

âð.×è. ãñ, ·¤è ÚU¿Ùæ ·ð¤ çÜ°, ÚU¿Ùæ ·ð¤

ÂÎ çÜç¹°Ð

35. The product of digits of a two digit number is 12. When 9 is added to the number, the digits interchange their places. Determine the number.

Îæð ¥´·¤æð´ ·¤è °·¤ ⴁØæ ·ð¤ ¥´·¤æð´ ·¤æ »é‡æÙȤÜ

12

ãñРⴁØæ ×ð´

9

ÁæðǸÙð ÂÚU ¥´·¤ ¥ÂÙæ SÍæÙ ÕÎÜ ÜðÌð ãñ´Ð ⴁØæ ™ææÌ ·¤èçÁ°Ð

36. Find the area of a trapezium whose parallel sides are 11 cm and 25 cm and whose non-parallel sides are 15 cm and 13 cm.

°·¤ â×Ü´Õ ·¤æ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ° çÁâ·¤è â×æ´ÌÚU ÖéÁæ¥æð´ ·¤è Ü´Õæ§Øæ¡

11

âð.×è. ¥æñÚU

25

âð.×è. ãñ´ ÌÍæ

¥â×æ´ÌÚU ÖéÁæ¥æð´ ·¤è Ü´Õæ§Øæ¡

¹⁵

âð.×è. ¥æñÚU

¹³

âð.×è. ãñ´Ð

7

7

7