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DISTRICT COMMON EXAMINATION BOARD

PRE-FINAL EXAMINATIONS, FEBRUARY,2015

MATHEMATICS - PAPER - II

(URDU VERSION)

Class: X ( Marks: 40 ) Time:2 .45min.

XÎZD6,pÆeg~VÆÓxÎZÑ]Æ�Z[Š£X 1 ¬x@Zc*]:X~ŠZ½�ŠwŠc*ŠHìX III XÜsœ 2

ÆÎZßVÆ�Z[Ì�Z!Òn~„KX IV Xv 3

X¬Gg{4~ÎZD6,p»_·gЙ,XCÙÎZwÃZh§b 4

]~�Z!*]KX 2.30 −Zkƈ!*¹

Section - I

7x1=7 XfsÆÓxÎZßVÆ�Z[Š£X 1 @Zc*]:XXCÙÎZwÆaZq-�–HŠHìX 2

ªìX 5 XŠZ],}ÆÃðŠzáZi~k»Ã,¥x<T»Û¢ 1

pÐ9L»ãCŠ~XÒy<X X2

ªìX 9 ªìZzg—~ 7 XZ2Z:ÅÈR»gK¥x<T»Û¢ 3

qŠ{iZz��A$U*"$< B Zzg A ˜V tan A = Cot B XZ¤/ 4

A + B = 90

X¬ÈZLkyÅ«2wÅ!*?ÐRi}6,ñ�ŠYw»x@{™CìT» 5

¢aìXZkÆaZq- x iZztÝáCìXZkqg]Å«2wÅ—~

™{Z@*g�X

X&jVÃ7VZYáYä6,ÜsZq-%ûh#Wäƪk¥x<X 6

ÅŠg¥x<X p ìA$ 7 »Zz‰ 3, 5, 9, p, 11 X!š‹5éG] 7

Section-II

6x2=12 XfsÆÓxÎZßVÆ�Z[Š£X 1 @Zc*]:X

XCÙÎZwÆaŠz�–K‰�X 2

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™{ZzgkÆÒgÕ)z~�ÔZyÆ9A.ð EVÅÚ¥x<X X8

~ ABC X|[ 9

AD A$ DE // BC

¥x<X

X¤/z„!š‹5éG]ÆzT6»Ÿ‚sZzgZyÆZg»yÅzŸs#<X 10

F,KMzZgk� BC Zzg AD X11

�ë%œ/ŠZ],}6,¯ñ‰�

OA=AB=ª21 X»Û¢

ì‚tŠZg»gK¥x<X 750 ìZzgiZzt

XŠz0*²VÃZq-‚BZYÑŠHA$Zq-‰}òq݃äŪk¥x<X 12

1 + sinθθθθ Cos θθθθ = 2 Sec θθθθ XU*"$<X 13Cos θ θ θ θ 1+Sinθθθθ

Section-III

4x4=16 XŠZ½�ŠwŠc*ŠHìX 1 â^:X

XCÙÎZwÆaeg¶K**]–�X 2

ÆzV AB, BC, CA ZHq D, E, F ~Õo ABC Ë[ (a X14

ÆgJVÅÚ¥x<X ABC Zzg DEF Õo�Ô[

( c* )

|~‚tŠZg»gK¥x<X (b

Zq-%,ìTÆ PQRS Z¤/

Zzg PTS ªìZzg 8 I»îw

ŠzÛŠZ],}�X QTR

A$øDfsÃC[<X Šc*ŠHì (aX15

1+sinθθθθ (ii) (1+sinθθθθ)(1+sinθθθθ) (i)cosθθθθ (1+cosθθθθ)(1-cosθθθθ)

1.8cm

5.4cm7.2cm

8cmS

P Q

R

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( c* )

ªìZzgZk~âùeZÑŠHX 15 Zq-4™z~',@TÅZ0+gzãR»Û¢ (b

ª—~zZàZ2Zã1ŒV~½äÆaX1³ 6 ª¢Zzg 5 ZkâùÊg»gƒVÏX

¢aah}‘ 7 ¢a�~!*îàÅŠ~ˆXqÝÅèà 20 ¢a¢zZà 18 (aX16

¯c*ŠHX‘Å—~Òy<X

( c* )

3 »gzVÆ*gä»x@{HX~CÙ 100 Zq-¤DäZq-vu6, (b

46,Zq-»g*gCìXTÃ].zw~Šg`HŠHZy!š‹5éG]»c�¥x<X70-80 60-70 50-60 40-50 30-40 20-30 10-20 0-10 »gzV»*g

8 15 11 20 12 13 14 7 ®ZŠ

ªÛ¢ë%œ/ŠZ],{ÆyÐUZzgZk 7 ªÛ¢zZáŠZ],{»Zq- 5 (a X17

( c* ) îwC[u£X

ȯ�X Ogive fsÆeZN*Æa (b

z9)®) 10-15 15-20 20-25 25-30 30-35 35-40

®Š 10 15 17 12 10 8

Section-IV

10x1/2=5 XÓxÎZÑ]Æ�Z[Š£X 1 â^:XXÓx�Z!*]Ã�Z!Òn~Zq-„(sX 2

[ ] XI¤/Z°~¯IÅ�#ÖgKc*(,~ÅYCìtXXXXBCìX 18

Ãð7 (D §z (C )xË (B xË (A

[ ] 7ìX (central tendency) XZy~ÐÃK%œ/gsy 19

c� (D £g~Z�Zs (C zT6 (B Zz‰ (A

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[ ] = XZ�Z°§iÐZz‰¥x™ä»Ÿ‚ 20

(Ãð7 D (C (B (A

[ ] ÆZDsW仪k 2 X0*µÃZq-%ûZY%6, 21

2/3 (D 1/6 (C 1/3 (B 1/2 (A

XZq-2yÅMðZzgZkÆ‚t»îw)z~ìA$Îg`ÐiZzt݃ÇX 22

[ ] 600 (D 900 (C 450 (B 300 (A

[ ] ÅŠgHƒÏ? 2 sin 60 cos 60 X23

3/4 (D 4/3 (C 5/2 (B 1/3 (A

[ ] ìA$Zê9A.ð EVÅÚ 1:4 XŠzâV™zVÅÈRÆgÕÅÚ 24

1:16 (D 1:12 (C 1:64 (B 1:8 (A

[ ] %zo»¢ƒA$Zk»wXXXXXƒÇX ' d ' XZ¤/ 25

(D (C (B (A

[ ] XkŠZ],}ÆÛ¢6,XXXXXƒ@*ìX 26

ÃðÌ7 (D ÀŠzZg (C ¾é (B áZi~ (A

ƒA$ A = 50 x˃VZzg DEF Zzg[ ABC XZ¤/[ 27

[ ]

1800 (D 1300 (C 900 (B 600 (A

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