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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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