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PL7AWJX

‚¥∑§Á‹Ã ¬⁄UˡÊÊ - II, (2014-2015) SUMMATIVE ASSESSMENT – II

MATHEMATICS / ªÁáÊà Class – IX / ∑§ˇÊÊ - IX

ÁŸœÊ¸Á⁄Uà ‚◊ÿ — 3 ÉÊá≈U •Áœ∑§Ã◊ •¥∑§ — 90

Time allowed : 3 hours Maximum Marks : 90

‚Ê◊Êãÿ ÁŸŒ̧‡Ê —

(i) ‚÷Ë ¬˝‡Ÿ •ÁŸflÊÿ¸ „Ò¥–

(ii) ß‚ ¬˝‡Ÿ ¬òÊ ◊¥ 31 ¬˝‡Ÿ „Ò¥, Á¡ã„¥ ¬Ê¥ø πá«UÊ¥ •, ’, ‚, Œ ÃÕÊ ÿ ◊¥ ’Ê¥≈UÊ ªÿÊ „Ò– πá«U-• ◊¥ 4 ¬˝‡Ÿ „Ò¥ Á¡Ÿ◊¥ ¬˝àÿ∑§ 1 •¥∑§ ∑§Ê „Ò, πá«U-’ ◊¥ 6 ¬˝‡Ÿ „Ò¥ Á¡Ÿ◊¥ ¬˝àÿ∑§ ∑§ 2 •¥∑§ „Ò¥, πá«U-‚ ◊¥ 8 ¬˝‡Ÿ „Ò¥ Á¡Ÿ◊¥ ¬˝àÿ∑§ ∑§ 3 •¥∑§ „Ò¥, πá«U-Œ ◊¥ 10 ¬˝‡Ÿ „Ò¥ Á¡Ÿ◊¥ ¬à̋ÿ∑§ ∑§ 4 •¥∑§ „Ò¥ ÃÕÊ πá«U-ÿ ◊¥ ◊ÈQ ¬Ê∆ ¬⁄U •ÊœÊÁ⁄Uà 3-3 •¥∑§Ù¥ ∑§ 2 ¬˝‡Ÿ ÃÕÊ 4 •¥∑§Ê¥ ∑§Ê 1 ¬˝‡Ÿ „Ò–

(iii) ß‚ ¬˝‡Ÿ ¬òÊ ◊¥ ∑§Êß ̧÷Ë ‚flʬ̧Á⁄U Áfl∑§À¬ Ÿ„Ë¥ „Ò– (iv) ∑Ò§‹∑ȧ‹≈U⁄U ∑§Ê ¬˝ÿʪ flÁ¡¸Ã „Ò– General Instructions :

(i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into five sections A, B, C ,D and E.

Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions of 2 marks each, Section-C comprises of 8 questions of 3 marks each and Section-D comprises of 10 questions of 4 marks each. Section E comprises of two questions of 3 marks each and 1 question of 4 marks from Open Text theme.

(iii) There is no overall choice. (iv) Use of calculator is not permitted.

πá«U-• / SECTION-A

¬˝‡Ÿ ‚¥ïÿÊ 1 ‚ 4 ◊¥ ¬˝àÿ∑§ ∑§Ê 1 •¥∑§ „Ò– Question numbers 1 to 4 carry one mark each.

1 ;fn 3 9,x ky+ = ∑§Ê •Ê‹π fcUnq (1, –2) ls xqtjrÊ gS] rks k dk eku Kkr dhft,A 1

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If the graph of 3x + ky = 9, passes through the point (1, – 2), find k.

2 fcUnq (0] 0) ls nks pj okys fdrus jSf[kd lehdj.kksa ds vkys[k xqtj ldrs gSa \

How many graphs of linear equations in two variables can pass through point (0, 0) ?

1

3 ‚◊Ê¥Ã⁄U øÃÈ÷¸È¡ ∑§ ©‚ Áfl‡Ê· ¬˝∑§Ê⁄U ∑§Ê ŸÊ◊ ’ÃÊß∞, Á¡‚∑§ Áfl∑§áʸ ’⁄UÊ’⁄U „Êà „Ò¥ ÃÕÊ ¬⁄US¬⁄U ‚◊Ám÷ÊÁ¡Ã ∑§⁄UÃ

„Ò¥– ‚ÊÕ „Ë, •ÊSÊ㟠÷È¡Ê•Ê¥ ∑§Ê ∞∑§ ÿÈÇ◊ •‚◊ÊŸ „Ò– ©‚∑§ ∞∑§ •ÊÒ⁄U ªÈáÊ ∑§Ê ∑§ÕŸ ŒËÁ¡∞–

Name the special type of parallelogram whose diagonals are equal and bisect each other. Also,

a pair of adjacent sides is unequal. State its one more property.

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4 •ÊœÊ⁄U ÁòÊíÿÊ r •ÊÒ⁄U ™°§øÊ߸ h flÊ‹ ’‹Ÿ ∑§Ê ¡Ê◊ÈŸË ¬¥≈U ‚ ÷⁄UË „È߸ ’ÊÀ≈UË ◊¥ ™§äflÊœ̧⁄U •ÊœÊ «ÈU’ÊÿÊ ªÿÊ– ©‚

¬Îc∆UËÿ ˇÊòÊ»§‹ ∑§Ê ôÊÊà ∑§ËÁ¡∞ ¡Ê Á∑§ ¬¥≈U „Ê ªÿÊ–

A cylinder of base radius r and height h is dipped vertically to half the height in a bucket full

of purple paint. Find the area of the surface which gets painted.

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πá«U-’ / SECTION-B

¬˝‡Ÿ ‚¥ïÿÊ 5 ‚ 10 ◊¥ ¬˝àÿ∑§ ∑§ 2 •¥∑§ „¥Ò–

Question numbers 5 to 10 carry two marks each.

5 ŒË „È߸ •Ê∑ΧÁà ◊¥, ∆ ABC ∑§Ê ˇÊòÊ»§‹ 18 cm2 „Ò– ÿÁŒ D •ÊÒ⁄U E ∑§̋◊‡Ê— ÷È¡Ê BC •ÊÒ⁄U ◊ÊÁäÿ∑§Ê AD ∑§ ◊äÿ-

Á’¥ŒÈ „Ò¥, ÃÊ ∆BED ∑§Ê ˇÊòÊ»§‹ ôÊÊà ∑§ËÁ¡∞–

In the given figure, area of ∆ABC=18 cm2. If D and E are the mid - points of the side BC and

median AD respectively, find the area of the ∆BED.

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6 M§‹⁄U •ÊÒ⁄U ¬⁄U∑§Ê⁄U ∑§ ¬˝ÿʪ ‚ 4∠XYZ ∑§Ë ⁄UøŸÊ ∑§ËÁ¡∞, ¡’Á∑§ ∠XYZ=20� „Ò–

Using ruler and compass, construct 4∠XYZ if ∠XYZ=20�.

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7 PQR ∞∑§ ÁòÊ÷È¡ „Ò– ÿÁŒ P, Q •ÊÒ⁄U R ‚ „Ê∑§⁄U ∑˝§◊‡Ê— ÷È¡Ê•Ê¥ QR, PR •ÊÒ⁄U PQ ∑§ ‚◊Ê¥Ã⁄U ⁄UπÊ∞° πË¥øË ¡ÊÃË

„Ò¥, Á¡‚‚ ∆ABC ¬Ê̋åà „ÊÃÊ „Ò, ¡Ò‚Ê Á∑§ •Ê∑ΧÁà ◊¥ Œ‡ÊʸÿÊ ªÿÊ „Ò, ÃÊ Œ‡ÊÊß̧∞ Á∑§ 1

PQ AB2

= „Ò–

PQR is a triangle. If lines drawn through P, Q and R are parallel respectively to the sides QR,

PR and PQ and form ∆ABC as shown in the figure, show that 1

PQ AB.2

=

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8 ∞∑§ ∆UÊ‚ œÊÃÈ ∑§ ’‹Ÿ ∑§Ë ÁòÊíÿÊ 10.5 cm •ÊÒ⁄U ™°§øÊß ̧60 cm „Ò– ’‹Ÿ ∑§Ê Œ˝√ÿ◊ÊŸ ôÊÊà ∑§ËÁ¡∞, ¡’Á∑§ œÊÃÈ ∑§Ê

ÉÊŸàfl 5 ª̋Ê◊ ¬˝Áà cm3 „Ò–

The radius of a solid metal cylinder is 10.5 cm and height is 60 cm. Calculate the mass of

cylinder, if the density of metal of cylinder is 5 gm per cm3.

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9 ∞∑§ ¬Ê¥‚Ê 250 ’Ê⁄U »¥§∑§Ê ªÿÊ ÃÕÊ ¬Á⁄UáÊÊ◊ ß‚ ¬˝∑§Ê⁄U ¬˝Êåà „È•Ê —

¬˝Êåà ‚¥ïÿÊ 1 2 3 4 5 6

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’Ê⁄Uï’⁄UÃÊ 40 45 35 38 52 40

¬˝ÊÁÿ∑§ÃÊ ôÊÊà ∑§ËÁ¡∞–

(i) ‚◊ ‚¥ïÿÊ ∑§Ë

(ii) 3 ∑§ ªÈáÊ¡ ∑§Ë A dice is rolled 250 times and its outcomes are recorded as below :

Outcome 1 2 3 4 5 6

Frequency 40 45 35 38 52 40

Find the probability of getting :

(i) An even number

(ii) A multiple of 3

10 ∞∑§ Á‚Ä∑§ ∑§Ê ÁŸïŸ ’Ê⁄¥U’Ê⁄UÃÊ•Ê¥ ∑§ ‚ÊÕ 1000 ’Ê⁄U ©¿UÊ‹Ê ªÿÊ—

Áøà — 455, ¬≈U — 545

¬˝àÿ∑§ ÉÊ≈UŸÊ ∑§Ë ¬Ê̋Áÿ∑§ÃÊ •Á÷∑§Á‹Ã ∑§ËÁ¡∞–

A coin is tossed 1000 times with the following frequencies:

Head : 455, Tail : 545

Compute the probability for each event.

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πá«U-‚ / SECTION-C

¬˝‡Ÿ ‚¥ïÿÊ 11 ‚ 18 ◊¥ ¬˝àÿ∑§ ∑§ 3 •¥∑§ „Ò¥–

Question numbers 11 to 18 carry three marks each.

11 2x−y=0 ∑§ •Ê‹π ¬⁄U ÁSÕà ©Ÿ Á’¥ŒÈ•Ê¥ ∑§Ê ¬„øÊÁŸ∞ Á¡Ÿ∑§ ÁŸŒ¸‡ÊÊ¥∑§ ÁŸïŸ ÃÊÁ‹∑§Ê ◊¥ ÁŒ∞ ª∞ „Ò–

x −1 0 1 4 3

y −2 0 −2 2 6

‚◊Ë∑§⁄UáÊ ∑§Ê •Ê‹π πË¥Áø∞–

Identify the points whose co-ordinates are given in the following table which lie on the graph of 2x−y=0

x −1 0 1 4 3

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y −2 0 −2 2 6

Draw the graph of the equation.

12 ‚◊Ë∑§⁄UáÊ 4x=6 (1−y)+3x ∑§Ê ax+by=c ∑§ M§¬ ◊¥ Á‹Áπ∞ •ÊÒ⁄U ©Ÿ Á’¥ŒÈ•Ê¥ ∑§ ÁŸŒ¸‡ÊÊ¥∑§ ÷Ë ôÊÊà ∑§ËÁ¡∞ ¡„Ê°

©‚∑§Ê •Ê‹π ŒÊŸÊ¥ •ˇÊÊ¥ ∑§Ê ∑§Ê≈UÃÊ „Ò–

Write the equation 4x=6 (1−y)+3x in the form ax+by=c and also find the coordinates of the

points where its graph cuts the two axes ?

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13 ŒË „È߸ •Ê∑ΧÁà ◊¥, PQRS ∞∑§ ‚◊Ê¥Ã⁄U øÃÈ÷È¡̧ „Ò, Á¡‚∑§ Áfl∑§áʸ PR •ÊÒ⁄U SQ ¬⁄US¬⁄U O ¬⁄ ¬Á̋Ãë¿UŒ ∑§⁄Uà „Ò¥–

Œ‡Êʸß∞ Á∑§ ar (∆SOR) = ar (∆POQ) „Ò–

In the given figure, PQRS is a parallelogram in which diagonals PR and SQ intersect each

other at O. Show that ar (∆SOR) = ar (∆POQ).

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14 ŒË „È߸ •Ê∑ΧÁà ◊¥, Á’¥ŒÈ A, D, P, C •ÊÒ⁄U B ∑§ãŒ˝ O flÊ‹ ∞∑§ flÎûÊ ¬⁄U ÁSÕà „Ò¥– ÿÁŒ ∠BOD=150� „Ò, ÃÊ

∠BPD, ∠BCD •ÊÒ⁄U ∠BAD ∑§ ◊ʬ ôÊÊà ∑§ËÁ¡∞–

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In the given figure, points A, D, P, C and B lie on a circle with centre O. If ∠BOD=150�, find

the measures of ∠BPD, ∠BCD and ∠BAD.

15 7 cm ◊ʬ ∑§Ê ∞∑§ ⁄UπÊπ¥«U PQ πË¥Áø∞– ß‚∑§ ‹¥’ ‚◊Ám÷Ê¡∑§ ∑§Ë ⁄UøŸÊ ∑§ËÁ¡∞ ÃÕÊ flÊSÃÁfl∑§ ◊ʬŸ mÊ⁄UÊ ‚àÿʬŸ ∑§ËÁ¡∞– Draw a line segment PQ of measure 7 cm. Construct its perpendicular bisector and verify it by actual measurement.

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16 ∞∑§ ‚◊Ê¥Ã⁄U øÃÈ÷ȸ¡ PQRS ◊¥, ∠P=( 2x+45)� •ÊÒ⁄U ∠Q=(3x−15)� „Ò– x ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞– ß‚ ‚◊Ê¥Ã⁄U

øÃÈ÷ȸ¡ PQRS ∑§ ‚÷Ë ∑§ÊáÊ ÷Ë ôÊÊà ∑§ËÁ¡∞–

In a parallelogram PQRS, ∠P=( 2x+45)� and ∠Q=(3x−15)�⋅ Find the value of x. Also, find

all the angles of the parallelogram PQRS.

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17 L§‹⁄U ÃÕÊ ¬⁄U∑§Ê⁄U ∑§Ë ‚„ÊÿÃÊ ‚ 52

1

2

� ∑§Ê ∑§ÊáÊ ’ŸÊß∞–

Construct angle of 521

2

�, using compass and ruler.

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18 ŒÊ ªÊ‹Ê¥ ∑§ •Êÿßʥ ◊¥ 27 : 8 ∑§Ê •ŸÈ¬Êà „Ò– ©Ÿ∑§ ¬Îc∆UËÿ ˇÊòÊ»§‹Ê¥ ∑§Ê •ŸÈ¬Êà ôÊÊà ∑§ËÁ¡∞– 3

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The ratio of the volumes of two spheres is 27 : 8. Find the ratio of their surface areas.

πá«U-Œ / SECTION-D

¬˝‡Ÿ ‚¥ïÿÊ 19 ‚ 28 ◊¥ ¬˝àÿ∑§ ∑§ 4 •¥∑§ „Ò¥–

Question numbers 19 to 28 carry four marks each.

19 Á∑§‚Ë ≈US≈U ◊¥, ÁŸÁ∑§ÃÊ Ÿ ªÁáÊà •ÊÒ⁄U •¥ª˝$¡Ë ◊¥ ∑˝§◊‡Ê— x •ÊÒ⁄U y •¥∑§ ¬Ê̋åà Á∑§∞– ÿÁŒ ©‚∑§ ∑ȧ‹ ¬Ê̋åÃÊ¥∑§ 70 „Ò¥, ÃÊ

ß‚∑§ Á‹∞ ŒÊ ø⁄UÊ¥ flÊ‹Ë ∞∑§ ⁄UÒÁπ∑§ ‚◊Ë∑§⁄UáÊ ’ŸÊß∞– ß‚∑§Ê •Ê‹π ÷Ë πË¥Áø∞– •Ê‹πËÿ M§¬ ‚ ©‚∑§ •ãÿ

Áfl·ÿ ◊¥ ¬˝Êåà •¥∑§ ôÊÊà ∑§ËÁ¡∞, ÿÁŒ ©‚∑§ —

(a) ªÁáÊà ◊¥ •¥∑§ 30 „Ò¥– (b) •¥ª˝$¡Ë ◊¥ •¥∑§ 20 „Ò¥–

In a certain test, Nikita scored marks x and y respectively in Mathematics and English. If her

total score is 70, then form a linear equation in two variables for this. Also, draw its graph.

Find graphically, her score in other subject if :

(a) score in Mathematics is 30. (b) score in English is 20.

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20 ŸËø ÁŒ∞ •Ê‹π ◊¥ ŒË ªß ̧⁄UπÊ•Ê¥ p •ÊÒ⁄U q ∑§ ‚◊Ë∑§⁄UáÊ Á‹Áπ∞ —

∞∑§ ÁfllÊÕ˸ Ÿ ⁄UπÊ q ∑§Ë ‚◊Ë∑§⁄UáÊ ∑§Ê x+y=1 ’ÃÊÿÊ– ÄÿÊ ©‚Ÿ ‚„Ë ©ûÊ⁄U ÁŒÿÊ? ⁄UπÊ•Ê¥ p, q •ÊÒ⁄U r ∑§

’Ëø ÁÉÊ⁄UÊ ˇÊòÊ»§‹ ÷Ë ôÊÊà ∑§ËÁ¡∞–

Write the equations of the lines p and r in following graph :

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A student answered equation of line ‘q’ as x+y=1. Did he answer correctly ? Also, find the

area enclosed between lines p, q and r.

21 ŒË „È߸ •Ê∑ΧÁà ◊¥, Á’¥ŒÈ D •ÊÒ⁄U E ÁòÊ÷È¡ ABC ∑§ •ÊœÊ⁄U BCU ∑§Ê ‚◊ÁòÊ÷ÊÁ¡Ã ∑§⁄Uà „Ò¥– ‚ÊÕ „Ë, AF=FB •ÊÒ⁄U

AM ⊥ EF „Ò– Á‚h ∑§ËÁ¡∞ Á∑§ ar (∆BEF)=ar (∆ADE) =3 ar (∆AOF) „Ò–

In the given figure, points D and E trisect the base BC of ∆ABC. Also, AF=FB and AM ⊥ EF.

Prove that ar (∆BEF)=ar (∆ADE) =3 ar (∆AOF).

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22 ÿÁŒ Á∑§‚Ë ø∑˝§Ëÿ øÃÈ÷¸È¡ PQRS ∑§ ‚ï◊Èπ ∑§ÊáÊÊ¥ P •ÊÒ⁄U R ∑§ ‚◊Ám÷Ê¡∑§ ‚¥ªÃ flÎûÊ ∑§Ê A •ÊÒ⁄U B ¬⁄U ¬˝ÁÃë¿UŒ 4

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∑§⁄Uà „Ò¥, ÃÊ Á‚h ∑§ËÁ¡∞ Á∑§ AB flÎûÊ ∑§Ê ∞∑§ √ÿÊ‚ „Ò–

In the bisectors of the opposite angle P and R of a cyclic quadrilateral PQRS intersect the

corresponding circle at A and B respectively, then prove that AB is a diameter of the circle.

23 ∞∑§ ‚◊’Ê„È ÁòÊ÷È¡ ∑§Ë ⁄UøŸÊ ∑§ËÁ¡∞ Á¡‚∑§Ê ‡ÊË·¸‹¥’ 5.5 cm „Ò–

Construct an equilateral triangle of altitude 5.5 cm.

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24 ABCD ∞∑§ øÃÈ÷ȸ¡ „Ò, Á¡‚∑§ Áfl∑§áʸ ’⁄UÊ’⁄U „Ò¥ ÃÕÊ ¬⁄US¬⁄U ‚◊∑§ÊáÊ ¬⁄U ‚◊Ám÷ÊÁ¡Ã ∑§⁄Uà „Ò¥– Á‚h ∑§ËÁ¡∞ Á∑§

ABCD ∞∑§ flª¸ „Ò–

ABCD is a quadrilateral whose diagonals are equal and bisect each other at right angles. Prove

that ABCD is a square.

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25 ∞∑§ ∑§Ê‹ÊŸË ÁŸflÊÁ‚ÿÊ¥ Ÿ ∑§Ê‹ÊŸË ∑§ ¬Ê∑§̧ ◊¥ ÉÊÊ‚ ∑§Ê≈UŸ ÃÕÊ ß‚∑§ øÊ⁄UÊ¥ •Ê⁄U ÃÊ⁄U ‹ªÊŸ ∑§Ê ∑§Êÿ¸ •¬Ÿ •Ê¬

Á∑§ÿÊ– ¬Ê∑¸§ •ÊÿÃÊ∑§Ê⁄U „Ò ‹Á∑§Ÿ ß‚∑§Ë ŒÊŸÊ¥ øÊÒ«∏Ê߸ÿÊ° •œ¸ ªÊ‹Ê∑§Ê⁄U „Ò–

(a) ß‚ ¬Ê∑§̧ ∑§Ë ÉÊÊ‚ ∑§Ê ` 100 ¬Á̋à 50 flª¸ ◊Ë≈U⁄U ∑§Ë Œ⁄U ‚ ∑§≈UflÊŸ ∑§Ê πø ̧ôÊÊà ∑§ËÁ¡∞–

(b) ß‚ ¬Ê∑§̧ ∑§ øÊ⁄UÊ¥ •Ê⁄U 3 ’Ê⁄U ÃÊ⁄U ‹ªflÊŸ ¬⁄U ÃÊ⁄U ∑§Ë ‹ï’Êß ̧ôÊÊà ∑§ËÁ¡∞–

(c) ∑§Ê‹ÊŸË ÁŸflÊÁ‚ÿÊ¥ Ÿ§ Á∑§Ÿ ◊ÍÀÿÊ¥ ∑§Ê Œ‡ÊʸÿÊ?

A colony decides to take care of their common park by cutting their grasses and fencing the whole

area. The park is in the shape of rectangle adjoint with the semicircle on the both width sides.

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(a) Find the cost of cutting the grass at rate of ` 100 per 50 m2.

(b) How much length of wire is used to fence the whole area if it is rounded 3 times ?

(c) Which value is depicted by colony ?

26 ∞∑§ 12 m ‹¥’ ∑§◊⁄U ◊¥ ŒËflÊ⁄UÊ¥ ¬⁄U 1.35 L§. ¬˝Áà m2 ∑§Ë Œ⁄U ‚ ¬¬⁄U ‹ªflÊŸ ∑§Ê √ÿÿ

340.20 L§. „Ò ÃÕÊ $»§‡Ê¸ ¬⁄U 85 ¬Ò‚ ¬Á̋à m2 ∑§Ë Œ⁄U ‚ ◊Ò≈U Á’¿UflÊŸ ∑§Ê √ÿÿ 91.80 L§. „Ò– ∑§◊⁄U ∑§Ë ™°§øÊ߸ ôÊÊÃ

∑§ËÁ¡∞–

The cost of papering the walls of the room 12 m long at the rate of Rs. 1.35 per m2 is Rs. 340.20

and the cost of matting the floor at the rate of 85 paisa per m2 is

Rs. 91.80. Find the height of the room.

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27 ∞∑§ •œ¸flÎûÊÊ∑§Ê⁄U ‡ÊË≈U ∑§Ë ÁòÊíÿÊ 21 cm „Ò– ß‚∑§Ê ◊Ê«∏∑§⁄U ∞∑§ πÈ‹Ê ‡Ê¥ÄflÊ∑§Ê⁄U ∑§¬ ’ŸÊÿÊ ªÿÊ „Ò– ß‚ ∑§¬ ∑§Ê

•Êÿß •ÊÒ⁄U ª„⁄UÊ߸ ôÊÊà ∑§ËÁ¡∞–

A semi- circular sheet of paper has radius 21 cm. It is bent to form an open conical cup. Find

the volume and depth of the cup.

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28 ÃËŸ Á‚P§Ê¥ ∑§Ê ∞∑§ ‚ÊÕ 300 ’Ê⁄U ©¿UÊ‹Ê ªÿÊ– ¬Ê̋# ¬Á⁄UáÊÊ◊Ê¥ ∑§Ê ’¥≈UŸ ß‚ ¬˝∑§Ê⁄U „Ò — (i) ÃËŸ ¬≈U —40, (ii) ŒÊ ¬≈UU ; 90 (iii) ∞∑§ ¬≈U ; 90, (iv) ∑§Ê߸ ¬≈U Ÿ„Ë¥ — 80, ¬˝àÿ∑§ ¬Á⁄UáÊÊ◊ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ ôÊÊà Á∑§Á¡∞ •ÊÒ⁄U ¡Ê°ø Á∑§Á¡∞ Á∑§ ‚÷Ë ¬Ê̋Áÿ∑§ÃÊ•Ê¥ ∑§Ê ÿʪ 1 „Ò– Three coins are tossed simultaneously 300 times. The distribution of various outcomes is listed below. (i) Three tails : 40 (ii) Both tails :90, (iii) one tail :90, (iv) No tails : 80 Find the respective probability of each event and check that the sum of all probabilities is 1.

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πá«U-य/SECTION-E

(◊ÈQ ¬Ê∆ /Open Text)

(·Ñi;k lqfuf'pr dj ysa fd miÿ¸ÈDr fo"k; dh eqDr ikB~;lkexzh bl iz'ui=k ∑ lkFk layXu gS)

(* Please ensure that open text of the given theme is supplied with this question paper.)

fo"k; % vfrfFk nsoks Hko% Theme : Atithidevo Bhavah

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29 ÁøòÊ 2 ‚ ÁŸïŸ ¬˝‡ŸÊ¥ ∑§ ©ûÊ⁄U ŒËÁ¡∞ —

(i) ÷ÍÁ◊ mÊ⁄UÊ ÁflŒ‡ÊË ¬ÿ¸≈U∑§Ê¥ ∑§Ê •Êª◊Ÿ ∑§◊ „Ò– ©‚∑§ ÄÿÊ ∑§Ê⁄UáÊ „¢Ò ?

(ii) Á∑§Ÿ Œ‡ÊÊ¥ ‚ ÁflŒ‡ÊË ¬ÿ¸≈U∑§ ÷ÍÁ◊ ÿÊÃÊÿÊà ‚ ‚’‚ •Áœ∑§ •Êà „Ò¢?

Refer to Table-2 and answer the following questions :

(i) The percentage of people travelling by land is less. What do you think are the factors responsible for it ?

(ii) FTA by land route is mostly from which countries ?

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30 fl·¸ 2006-2011 ◊¥ •Á¡¸Ã ÁflŒ‡ÊË ◊ÈŒÊ̋ (∑§⁄UÊ«∏ ∑§Ê Œ‚ „$¡Ê⁄U ∑§ ªÈáÊÊ¥∑§ ◊) ∑§Ê Œá«U ÁøòÊ mÊ⁄UÊ Œ‡Êʸß∞–

Draw a bar graph to represent Foreign exchange earnings (in Rs. Core to the nearest ten thousand) during the years 2006-2011.

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31 (a) vfrfFk nsoks Hko% ds ikB ls vkidks fdu fdu ckrksa dk Kku gqvk gS\ xf.kr blds fy, fdruk

lgk;d gS \

(b) lkj.kh 2 ls 2011 rFkk 2012 esa vyx vyx {ks=kksa ls fons'kh i;ZVd vkxeu dk ekè; Kkr dhft,

A 2012 ds ekè; esa 2011 ds ekè; ls fdrus izfr'kr dh of̀¼ gqbZ gS \ (a) What insight does this text gives to the reader? How is mathematics relevant to it ? (b) Refer to table-2 : Calculate mean of foreign tourists arrivals from different regions in 2011 and 2012. Find the percentage increase of mean in 2012 as compared to 2011 ?

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