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10th ClassModel Question Papers
State Council of Educational Research and TrainingAndhra Pradesh
NON - LANGUAGES
10th ClassModel Question Papers
State Council of Educational Research and TrainingAndhra Pradesh
NON - LANGUAGES
I N D E X
1. MATHS 1 - 85
2. PHYSICS 86 - 150
3. BIOLOGY 151 - 212
4. SOCIAL STUDIES 213 - 261
MATHEMATICS
1
S.S.C. Public ExaminationsFrom March - 2017
Division of Syllabus
Paper-I
Ch. No. Chapter Name
1. y�d�ïe d�+K«\T (Real Numbers)
2. d�$TÔáT\T (Sets)
3. �V�Q|�<�T\T (Polynomials)
4. Âs+&�T #ásÁs�Xø�\ýË ¹sFjáT d�MT¿£sÁD²\ ÈÔá (Pair of Linear Equations in two variables)
5. esÁZ d�MT¿£sÁD²\T (Quadratic Equations)
6. çXâ&ó�T\T (Progressions)
10. ¹¿�çÔá$TÜ (Mensuration)
Paper-II
7. �sÁÖ|�¿£ C²«$TÜ (Co-ordinate Geometry)
8. d�sÁÖ|� çÜuó�TC²\T (Similar Triangles)
9. e�Ô�ï�¿ì d�ÎsÁô¹sK\T eT]jáTT #óû<�q ¹sK\T (Tangents and Secants to a circle)
11. çÜ¿ÃD$TÜ (Trigonometry)
12. çÜ¿ÃD$TÜ nqTesÁïH�\T (Applications of Trigonometry)
13. d�+uó²e«Ôá (Probability)
14. kÍ+K«¿£ Xæçd�ï+ (Statistics)
2
Division of Syllabus for SA-I, II & IIIClass : X Subject : Mathematics Paper - I & II
Name of theExam
Paper - I Paper - II
SA-I
upto
September
SA-II
December
SA-III
March
Real Numbers
Sets
Polynomials
Mensuration
Real Numbers
Sets
Polynomials
Pair of linear equations in twovariables
Quadratic equations
Mensuration
Real Numbers
Sets
Polynomials
Pair of linear equations in twovariables
Quadratic equations
Mensuration
Progressions
Similar Triangles
Statistics
Trigonometry
Similar Triangles
Statistics
Trigonometry
Tangents and Secants of Circles
Co-ordinate Geometry
Similar Triangles
Statistics
Trigonometry
Tangents and Secants of Circles
Co-ordinate Geometry
Application of Trigonometry
Probability
3
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|�³ d�eTd�«\T
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H �s��D²\T
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5
Real Numbers
1. Irrational Number (¿£sÁD¡jáT d�+K«)
1. ç¿ì+~ y��ýË ¿£sÁD¡jáT d�+K«\qT e Z¿£]+º s�jáT+&�. (R.P)
2 , 3 , 5, 5.75, 1.735 ........., 8 , 4 , 16
2. ¿£sÁD¡jáT d�+K«\qT �sÁǺ+#á+&� ? �<�V�²sÁD*eÇ+&� ? (Commu)
3. ¿£sÁD¡jáT d�+K«\Å£� n¿£sÁD¡jáT d�+K«\Å£� >·\ uóñ<�ýñ$ ? (R.P)
4. 2 , 3 , 5 \qT d�+U²«¹sK�|Õ #áÖ|¾+#á+&�. (V.R).R)
5. 2 ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�. (R.P)
6. 2 jîTT¿£Ø $\TeqT H�\TZ <�Xæ+Xø\ esÁÅ£� $\Te ¿£qT>=q+&�. (P.S)
7. ¿£sÁD¡jáT d�+K«\qT �ÈJ$Ôá+ýË m¿£Ø&� �|�jîÖÐkÍïsÁT ?
8. #áÔáTsÁçd�+ýË uó�TC²�¿ì ¿£s���¿ì >·\ d�+�+<ó�+ Ôî\T|�+&� ? (Commu)
9. P $\Te ¿£sÁD¡jáT d�+K« ýñ¿£ n¿£sÁD¡jáT d�+K« ¿±sÁD²\T #î|�Î+&�. (R.P)
Chapter : �V�Q|�<�T\T
Topic : �V�Q|�~ XøSH�«\T
1. x2 + 8x + 15 jîTT¿£Ø �V�Q|�~ XøSH�«\qT ¿£qT>=q+&�.
2. x2 + 8x + 5 �V�Q|�~¿ì >·]w�÷+>± »2µ XøSH�«\T �+&�Tq� mý² #î|�Î>·\eÚ ?
3. x2 + 8x + 5 �V�Q|�~ XøSH�«\qT ç>±|�t <�Çs� ¿£qT>=q+&�.
4. x2 + 8x + 5 Å£� »6µ ÿ¿£ �V�Q|�~ XøSq«eTeÚÔáT+<� ? ýñ<� ? m+<�Te\¢.
5. »»ÿ¿£ d�+K« jîTT¿£Ø esÁZeTTqÅ£� � d�+K«jîTT¿£Ø 8 Âs³T¢ ¿£*|¾q |��*Ôá+ »`5µ n>·TqT. B�
qT|�jîÖÐ+º esÁZd�MT¿£sÁDeTT çy�d¾ � d�+K«qT ¿£qT>=qTeTT.
6. x2 + 8x + 5 �V�Q|�~ eç¿£eTT X`n¿�±�� >·]w�¼+>± m�� _+<�TeÚ\ e<�Ý K+&�+#áe#áTÌqT?
m+<�Te\¢.
7. x2 + 8x + 5 �V�Q|�~� 'y' #ásÁs�¥ <��cͼ« Ôî\Î+&�.
8. x2 + 8x + 5 �V�Q|�~ XøSH�«\Å£�, >·TD¿±\Å£� eT<ó�«>·\ d�+�+<ó��� Ôî\Î+&�.
6
Chapter : Âs+&�T #ásÁs�Xø�\ýË ¹sFjáT d�MT¿£sÁD²\ ÈÔá
Topic : ÈÔá ¹sFjáT d�MT¿£sÁD²\ kÍ<ó�q
1. »»>·DìÔá bÍsÄÁ«|�Úd�ï¿£eTT yî\, �+>·¢ |�Úd�ï¿£ K¯<�T jîTT¿£Ø 2 Âs³¢ ¿£H�� 10 sÁÖöö\T ÔáÅ£�Øeµµ B��
¹sFjáT d�MT¿£sÁD+>± çy�jáT+&�.
2. 2x + 3y = 12, 3x + 2y = 13 ¹sFjáT d�MT¿£sÁD²\qT eTÖ\¿±�� Ô=\Ð+#û |�<�ÆÜýË kÍ~ó+#á+&�.
3. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�qqT ç>±|�t <�Çs� kÍ~ó+#á+&�.
4. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�q e«ed¾�Ôá+ neÚÔáT+<�? ýñ<�? >·TD¿±\
�w�ÎÔáTï\ �<ó�sÁ+>± Ôî\Î+&�.
5. »»2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\Å£� kÍ<ó�q\T nq+ÔáeTTµµ neÚH�? ¿±<�? Ôá>·T
¿±sÁD²\ÔÃ Ôî\Î+&�.
6. 2x + 3y = 12, 3x + 2y = 13 \qT ç|�ܹ¿�|�D |�<�ÆÜýË kÍ~ó+#á+&�.
7. 2x + 3y = 12 ¹sKÅ£� nq+ÔáyîT®q kÍ<ó�q\T �+{²sTT. m+<�Te\¢?
8. 2x + 3y = 12, 3x + 2y = 13 d�MT¿£sÁD²\ kÍ<ó�qÅ£� úeÚ @ |�<�ÆÜ� �|�jîÖÐkÍïeÚ? m+<�Te\¢?
úÅ£� qºÌq |�<�ÆÜýË x, y $\Te\qT ¿£qT>=qTeTT.
Chapter : çXâ&ó�T\T
Topic : n+¿£çXâ&ó�ýË 'n' e |�<�eTT
1. 2, 7, 12, ..... n+¿£çXâ&ó�ýË »13µe |�<�eTT ¿£qT>=qTeTT.
2. n+¿£çXâ&ó�ýË |�<�+ÔásÁeTT »6µ, 7e |�<�eTT 36. B�qT+&� n+¿£çXâ&ó�� çy�jáT&��¿ì M\eÚÔáT+<�?
ýñ<�? m+<�Te\q?
3. n+¿£çXâ&ó�ýË 'n' e |�<�+ 6n + 2 nsTTq yîTT<�{ì H�\T>·T |�<�\qT çy�jáT+&�.
4. n+¿£çXâ&ó�ýË 7e |�<�+ 13, 3e |�<�eTT 7. nsTTq eTÖ\¿±�� Ô=\Ð+#û |�<�ÆÜ <�Çs� a, d \qT
¿£qT>=q+&�.
7
5. n+¿£çXâ&ó�ýË 'n' e |�<��� ýÉ¿ìØ+#áT³Å£� eTqÅ£� @jûT |�<�\T Ôî* �+&�eýÉqT?
6. |�<�+ÔásÁeTT XøSq«+ nsTTq#à � çXâ&ó�ýË yîTT<�{ì |�<��¿ì, 'n' e |�<��¿ì >·\ d�+�+<ó�+
Ôî\Î+&�.
7. 2016 ýË sÁÖ. 10,000/` JÔá+Ôà �<ë>·+ bõ+~q e«¿ìï¿ì ç|�Ü d�+eÔáàsÁ+ sÁÖ.1500/` JÔá+
�|]Ðq#à 2020e d�+eÔáàsÁ+ýË � �<ëРJÔá+ ¿£qT>=q+&�.
8. �+&�� �\T|�Ú d��\+ýË ÿ¿£sÃEÅ£� sÁÖ.10/` ��|Õ ç|�ÜsÃEÅ£� sÁT.2/` n<�q+>± #î*¢+#áe\d¾q#Ã
15 sÃE\ Ôás�ÇÔá #î*¢+#áe\d¾q yîTTÔáï+ m+Ôá?
Chapter : �sÁÖ|�¿£ ¹sU²>·DìÔáeTT
Topic : Âs+&�T _+<�TeÚ\ eT<ó�« <�ÖsÁ+
1. (5, 7), (7, 5) _+<�TeÚ\ eT<ó�« <�ÖsÁ+ ¿£qT>=q+&�.
2. (5, 7), (7, 5) _+<�TeÚ\qT �sÁÖ|�¿£Ôá\+�|Õ >·T]ï+º \+�¿ÃD çÜuó�TÈ+ @sÁÎsÁº y�{ì eT<ó�«
<�ÖsÁ+ ¿£qT>=q+&�.
3. (5, 7), (7, 5) _+<�TeÚ\T d�eÖqeÖ? ¿±<�? m+<�Te\¢?
4. (5, 7), (7, 5) \Å£� d�eÖq <�ÖsÁ+ýË >·\ X`n¿£�+�|Õ >·\ _+<�TeÚqT ¿£qT>=qTeTT.
5. (5, 7), (`5, 7), (5, `7), (`5, `7) _+<�TeÚ\T @jûT bÍ<�\ýË �+&�THÃ Ôî\Î+&�.
6. |�³+ýË X`n¿�±�¿ì d�eÖ+ÔásÁ+>± >·\ ¹sK\ bõ&�eÚ\T
�dØ\T �|�jîÖÐ+#áÅ£�+&� ¿£qT>=qTeTT-4 -3 -2 -1 1 2 3 4
8
Chapter : ¹¿�çÔá$TÜ
Topic : Xø+Å£�eÚ yîÕXæ\«eTT
1. 7 �d+.MT. uó�Ö y�«kÍsÁ�eTT, 24 �d+.MT. mÔáTï>·\ Xø+Å£�eÚ �¿±sÁ {Ë|Ó\T »10µ ÔájáÖsÁT
#ûjáT&��¿ì ¿±e\d¾q >·T&�¦ yîÕXæ\«+ ¿£qT>=q+&�.
2. »21µ �d+.MT. y�«kÍsÁ�+ >·\ ÿ¿£ e�Ô�ï�� »3µ d�eÖq uó²>±\T>± $uó��+º Xø+Å£�eÚ\T @sÁÎsÁºq,
Xø+Å£�eÚ uó�Öy�«kÍsÁ�+ m+Ôá?
3. ç¿£eT Xø+Å£�eÚqT �sÁǺ+º, Xø+Å£�eÚ @³y�\T mÔáTïqT ¿£qT>=qT³Å£� d�ÖçÔáeTTqT �Ô�Î~+#áTeTT.
4. Xø+Å£�eÚ �¿±sÁ |�³+ ^º y�«kÍsÁ�+, mÔáTï, @³y�\T mÔáTï\T d�Öº+#á+&�.
5. ç¿ì+~ @ çÜuó�TC²\T çuó�eTD+ #ûd¾q#à @sÁ¿£yîT®q Xø+Å£�eÚqT @sÁÎsÁ#áTqT
m) d�eTuó²V�Q çÜuó�TÈ+ _) \+�¿ÃD çÜuó�TÈ+ d¾) $w�eTu²V�Q çÜuó�TÈ+
Chapter : d�sÁÖ|� çÜuó�TC²\T
Topic : çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+ÔáeTT
1. çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+ÔáeTTqT �sÁǺ+º, �sÁÖ|¾+#á+&�.
2. AB R 6 �d+.MT. ¹sU²K+&��� 3:2 �w�ÎÜïýË $uó�Èq #ûd¾ �s��Dç¿£eT+ çy�jáT+&�.
3. D ABC ýË AB, AC \�|Õ _+<�TeÚ\T esÁTd�>± E, F nsTTq ç¿ì+~ ç|�Ü d�+<�sÁÒÛ+ýË EF P BC
neÚHÃ ¿±<Ã Ôî\Î+&�.
a) AE = 3.9 cm, EB = 3 cm, AF = 3.6 cm, CF = 2.4 cmb) AE = 4 cm, BE = 4.5 cm, AF = 8 cm, CF = 9 cm
4. D ABC ýË BC P DE eT]jáTT AD = DB = 3:4 eT]jáTT
AC = 14 cm nsTTq AE, EC \ bõ&�eÚ\T ¿£qT>=qTeTT.
5. D ABC ýË AB, AC \ eT<ó�« _+<�TeÚ\T D, E eT]jáTT BC = 6 cm nsTTq DE bõ&�eÚqT
¿£qT>=qTeTT.
A
D E
CB
9
Chapter : e�Ô�ï\Å£� d�ÎsÁô¹sK\T eT]jáTT #óû<�q¹sK\T
Topic : e�Ôáï K+&� yîÕXæ\«eTT
1. ç|�¿£Ø |�³+ýË e�Ôáï y�«kÍsÁ�+ 21 �d+.MT, nsTTq AOBÐ R 120
nsTTq AYB e�ÔáïK+&� yîÕXæ\«+ ¿£qT>=qTeTT
2. ÿ¿£ >·&�jáÖsÁ+ýË 7 �d+.MT. bõ&�eÚ >·\ �$TcÍ\ eTT\T¢#û 10 �öö\ýË @sÁÎ&û ç|�<ûXø yîÕXæ\«+
Å£qT>=qTeTT.
3. 14 �d+.MT. y�«kÍsÁ�+ >·\ e�Ôáï+ýË n+Ôá]¢Ï+#á�&�q ç¿£eT nw�¼uó�T� yîÕXæ\«+ ¿£qT>=qTeTT.
4. 3 �d+.MT. y�«kÍsÁ�+ >·\ »4µ ¿±«sÁy�TuËsÁT¦ bÍH�\T ÿ¿£<��¿=¿£{ì Ô�Å£�q³T¢ neT]Ìq#à y�{ì
eT<ó�« yîÕXæ\«eTTqT ¿£qT>=qTeTT.
Chapter : d�$TÔáT\T (Sets)
Topic : d�yûT�Þøq+ (Union)
1. A, B d�$TÔáT*ºÌ d�eT�Þøq+ ¿£qT>=qeTq&�+.
2. AÌ B njûT«ý² d�$TÔáT*ºÌ ¿£qT>=qeTq&�+. @$T >·eT�+#�sÁT?
3. B Ì A njûT«ý² d�$TÔáT*ºÌ ¿£qT>=qeTq&�+. @$T >·eT�+#�sÁT?
4. A, B \T $jáTT¿£ï d�$TÔáTýÉÕq|�ð&�T AÈ B ¿£qT>=q&�+.
5. yîH� ºçÔ�\ <�Çs� AÈ B � #áÖ|�+&�.
6. AÈ B, B È A \qT ¿£qT>=� @$T >·eT�+#�sà çy�jáT+&�.
7. A, B \T AÈ B ¿ì �|�d�$TÔáT\eÚÔ�jáÖ? m+<�TÅ£�?
O
A
Y
B
10
Chapter : çÜ¿ÃD$TÜ
Topic : nqTesÁïH�\T
1. uó�Ö$T¿ì 30 MT. mÔáTïqT+&� 60+ ¿ÃD+Ôà C²sÁ&��¿ì C²sÁT&�T�\¢ yûjáTeýÉqT. nsTTq C²sÁT&�T�\¢
bõ&�eÚ m+Ôá �+&�eýÉqT.
2. �{²sÁT>± �\�&�q B|�d��+uó�eTT �|qT>±*¿ì |�P]ï>± $]Ð B|�d�ï+uó�+ ¿=quó²>·+ <�ÖsÁ+>± >·\
e«¿ìï� Ô�¿ìq~ nsTTq $sÁ>·¿£ eTTqT|�Ú � e«¿ìï B|�|�Ú d�ï+uó�eTTÔà #ûjáTT ¿ÃD+ ¿£qT>=qTeTT.
3. ÿ¿£ h MT. mÔáTï>·\ uó�eq+�|Õq bõ&�y�{ì çÔ�&�T d�V�äjáTeTTÔà m>·TsÁTÔáTq� >±*|�{²�� uó�eq+
ç¿ì+<� x MT. <�ÖsÁ+ýË >·\ u²\T&�T >±*|�{²��, çÔ�&�TqT m>·TsÁyûd�Tïq� e«¿ìï� esÁTd�>± , a b
¿ÃD+Ôà |�]o*+#�&�T. � <�Ô�ï+Xæ�� Ôî\T|�Ú |�³+ ^jáT+&�.
4. Âs+&�T uó�eH�\Å£� d�eÖq <�ÖsÁ+ýË >·\ e«¿ìï � uó�eH�\qT esÁTd�>± 35+, 46
+ ¿ÃD²\ÔÃ
|�]o*+ºq#Ã, � Âs+&�T uó�eH�\ýË @~ mÔáïsTTq~? m+<�Te\¢?
5. �<�jáT+ 8 >·+³\ d�eTjáT+ýË 15 MT. mÔáTï>·\ d�ï+uó�+ ú&�bõ&�eÚ 5 3 MT³sÁT¢ nsTTq �
d�eTjáT+ýË d�ÖsÁ«¿ìsÁD²\T uó�Ö$TÔà #ûjáTT ¿ÃD+ ¿£qT>=qTeTT.
Chapter : d�+uó²e«Ôá
Topic :
1. ÿ¿£ d�+ºýË 3 mçsÁ�+ÔáT\T, 4 Ôî\¢�+ÔáT\T ¿£\eÚ. jáÖ<��ºÌÛ¿£+>± rd¾q �+Ü (i) mçsÁ�+Ü
n>·T³Å£� (ii) Ôî\¢�+Ü n>·T³Å£� d�+uó²e«ÔáqT ¿£qT>=qTeTT.
2. ÿ¿£ d�+eÔáàsÁeTTýË »53µ �~y�s�\T n>·T³Å£� d�+uó²e«Ôá m+Ôá?
3. 1`20 esÁÅ£� n+¿\ >·\ d¾Øq�sYýË
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25
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A B
26
28. a , b , g \T eTÖ\¿±\T>± >·\ p(x) = ax3 + bx2 + cx + d (a ¹ o) �V�Q|�~ýË ( )
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3) d�Ö�|�eTT jîTT¿£Ø d�+|�PsÁ�Ôá\ yîÕXæ\«eTT ( ) c) P rl
A) 1-a, 2-b, 3-c B) 1-c, 2-a, 3-b ( )
C) 1-b, 2-c, 3-a D) 1-b, 2-a, 3-c
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C) 100 jîTT¿£Ø ¿±sÁD²+¿±\ d�$TÜ D) 100 jîTT¿£Ø >·TDC²\ d�$TÜÿ¿£
31. ÿ¿£ CË¿£sÁT jîTT¿£Ø Ôá\{Ë|¾ ç¿£eTXø+KTeÚ �¿±sÁeTTýË �q�~. <��jîTT¿£Ø uó�Öy�«kÍsÁ�eTT ( )
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>·T&�¦ yîÕXæ\«eTT m+Ôá ?
A) 528 cm2 B) 550 cm2 C) 550 cm D) 620 cm3
32. ÿ¿£ ç¿£eTe�Ô�￱sÁ Xø+KTeÚ jîTT¿£Ø y�«kÍsÁ�eTT eT]jáTT mÔáTï\T 2:3 �w�ÎÜïýË �q� ( )
y�{ì |��Tq|�]eÖDeTT\ �w�ÎÜï
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33. �ç¿ì+~y��ýË @~ 3D �¿±sÁeTTqT d�Öº+#áTqT ( )
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27
Weightage Table (Paper-II) forAcademic Standard wise
Academic Standard L.A. S.A. V.S.A. M.C.Q. Total %4m 2m 1m 1/2m
PS 2 (4) 2 (2) 1 (1) 6 (1/2) 11 (16) 40%
R.P 1 (4) 1 (2) - 4 (1/2) 6 (8) 20%
Communication - 1 (2) 1 (1) 2 (1/2) 4 (4) 10%
Connections - 1 (2) 2 (1) 4 (1/2) 7 (6) 15%
Representation & 1 (4) - - 4 (1/2) 5 (6) 15%Visual Form
Total 4 (4) 5 (2) 4 (1) 20 (1/2) 33 (40) 100%
28
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�|Õ |�{켿£qT+&� $<�«sÁT�\ d�s�d�] �sÁTeÚqT ¿£qT>=q+&�.
�d¿£�H� ` III
d�Ö#áq\T : 1. n�� ç|�Xø�\Å£� Èy��T\T s�jáT+&�.
2. ç|�Ü ç|�Xø�Å£� 4 eÖsÁTØ\T. 4I4 R 16 eÖsÁTØ\T
10 (a) çbÍ<�$T¿£ nqTbÍÔá d¾<�Æ+Ôá+ �sÁǺ+º �sÁÖ|¾+#á+&�
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10 (b) çÜuó�TÈ\+ ABD ýË \+�¿ÃDeTT A e<�Ý ¿£\<�T
eT]jáTT AC ^ BD nsTTq
(i) AB2 = BC.BD (ii) AC2 = BC.DC
(iii) AD2 = BD.CD n� #áÖ|�+&�.
$<�«sÁT�\ �sÁTeÚ Kg\ýË 20 25 30 35
d�+K« 2 7 10 6
B A
D
C
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11 (a) (Sin A + Cosec A)2 + (Cos A + Sec A)2 = 7 + tan2A + Cot2A n� #áÖ|�+&�.
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11 (b) Sec q + Tan q = P nsTTq Sin q $\Te ¿£qT>=q+&�.
12 (a) |¾\¢\ sÃEy�] Cñ�T KsÁTÌ\T $es�\T ç¿ì+~ båq'|�Úq« $uó²È¿£ |�{켿£ýË �eÇ�&�q$. |¾\¢\
d�>·³T #ûÜKsÁTÌ 18 sÁÖöö nsTTq ç¿ì+~ |�{켿£ýË ýË|¾+ºq båq'|�Úq«eTT ( f ) qT ¿£qT>=qTeTT.
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12 (b) ç¿ì+~ båq'|�Úq« $uó²Èq |�{켿£Å£� eT<ó�«>·Ôá+ ¿£qT>=q+&�?
13 (a) 5 �d+.MT., 6 �d+.MT., 7 �d+.MT. ¿=\Ôá\Ôà çÜuó�TC²�� �]�+º B�¿ì d�sÁÖ|�+>± �+³Ö �
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13 (b) 3 �d+.MT, 4 �d+.MT uó�TC²\T>± >·\ \+�¿ÃD çÜuó�TC²�� �]�+º B�¿ì d�sÁÖ|�+>± �+³Ö �
çÜuó�TÈ uó�TC²\Å£� 53 Âs³T¢ nqTsÁÖ|� uó�TC²\T ¿£*Zq çÜuó�TC²�� �]�+#á+&�?
|¾\¢\ #ûÜKsÁTÌ 11`13 13`15 15`17 17`19 19`21 21`23 23`25
|¾\¢\ d�+K« 7 6 9 13 f 5 4
$\Te\T < 100 100`200 200`300 300`400 > 400
båq'|�Úq«+ 50 90 158 68 134
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d�+ç>·V�²D²Ôá�¿£ eTÖý²«+¿£qeTT`1
eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT �||�sY-II
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2. ç|�Ü ç|�Xø�Å£� d�+�+~ó+ºq Èy��TqT d�Öº+#áT �+>·¢ �|<�Ý n¿£�sÁeTTqT ç|�¿£Øq sTTºÌq
çu²Â¿³¢ýË çy�jáT+&�.
3. ¿={ì¼yûÔá\T, ~<�TÝu²³¢Å£� eÖsÁTØ\T sTTeÇ�&�eÚ.
4. n�� ç|�Xø�\Å£� eÖsÁTØ\T d�eÖqeTT.
�d¿£�H� ` IV
d�Ö#áq\T : 1. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ. 20I
1/2 R 10 eÖsÁTØ\T
14. DABC ~ DDEF eT]jáTT ÐA R 37+, ÐE R 64
+ nsTTq ÐC R ? ( )
A) 59+ B) 69
+ C) 79+ D) 101
+
15. 4 �d+.MT uó�TÈeTT ¿£*Zq ÿ¿£ s�+�dt jîTT¿£Ø ¿£sÁ�eTT\ jîTT¿£Ø es�Z\ yîTTÔáïeTT ( )
A) 16 �d+.MT. B) 36 �d+.MT. C) 56 �d+.MT. D) 64 �d+.MT
16. �ç¿ì+~ y��ýË d�sÁÖbÍ\T ¿±�$ ( )
A) @yîÕH� Âs+&�T q\¢�\¢\T
B) eT�w¾ eT]jáTT nÔá� ú&�
C) |�]eÖD²\T ÔáÐZ+ºq eT]jáTT �|+#á�&�q b�þ{Ë\T
D) <�sÁÎDeTTýË� ed�TïeÚ eT]jáTT <�� ç|�Ü_+�eTT
17. ÿ¿£ çÜuó�TÈeTTq+<�T eT<ó�«>·Ôá ¹sK\ $T[Ôá_+<�TeÚ ................ ( )
A) n+ÔásÁe�Ôáï ¹¿+ç<�eTT B) |�]e�Ôáï ¹¿+ç<�eTT
C) >·TsÁTïe¹¿+ç<�eTT D) \+�¹¿+ç<�eTT
32
18. ÿ¿£ çÜuó�TÈeTTq+<�T eTÖ&�T uó�TC²\ es�Z\ yîTTÔáïeTT <��jîTT¿£Ø eT<ó�«>·Ôá¹sK\ es�Z\ ( )
yîTTÔáïeTTqÅ£� .................... Âs³T¢
A) Âs{ì¼+|�Ú B) H�\T>·T C) d�>·eTT D) d�eÖqeTT
19. ÿ¿£ e«¿ìï 20 MT. ÔáÖsÁTÎ>± ç|�jáÖDì+º n¿£Ø&�qT+&� 15 MT. �ÔáïsÁ ~Xø>± yî[ßq#à ( )
ç|�d�TïÔáeTT yîTT<�{ì kÍ�qeTT qT+&� m+Ôá <�ÖsÁeTTýË �H��&�T
A) 5 MT. B) 35 MT. C) 25 MT. D) 10 5 MT.
20. ABC çÜuó�TÈeTTq+<�T 'C' osÁüeTT e<�Ý \+�¿ÃDeTT @sÁÎ&�q~. CD ^ AB eT]jáTT ( )
�ç¿ì+~ y��ýË @~ d�Ôá«eTT
A) 1 1 1p a b
= + B) p = a+b
C) 2 2 2
1 1 1p a b
= + D) p2 = a2+b2
21. Sin 2q = Cos 3q nsTTq Tan 2q R .............. ( )
A) 1 B) 0 C) 12 D) ¥
22. 'Sin q' qT 'Sec q' |�<�\ýË e«¿£ï|�sÁ#áTeTT. ( )
A) 2 1
Sec
Secq
q-
B) 2 1
SecSec
qq- C)
2
2
1
SecSec
qq- D)
1
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qq-
23. Sin2 30o, Sin2 45o, Sin2 60o \T .................... çXâ&ó�ýË �+{²sTT. ( )
A) n+¿£çXâ&ó� B) >·TDçXâ&ó�
C) n+¿£çXâ&ó� D) n+¿£çXâ&ó�, >·TDçXâ&ó�\T ¿±<�T
24.
2 2
2
18 7245
o o
o
Sin SinCos
+ R ................... ( )
A) 0 B) 1 C) 2 D) 3
25. Sin q . Sec q . Cos q . Cosec q R .............. ( )
A) Sin2 q B) Cos2 q C) Sec2 q D) Sin2 q+Cos2 q
A D B
a
C
b p
33
26. Cos405o R ................... ( )
A) 1 B) 12 C)
12 D) �|Õ @$jáTT ¿±eÚ
27. ç|�¿£Ø |�³eTTq+<�T tan C = ..................... ( )
A) 12 B)
13
C) 2 D) 3
28. 10`25 ÔásÁ>·Ü jîTT¿£Ø eT<ó�«$\Te ...................... ( )
A) 15 B) 17 C) 17.5 D) 19.5
29. yîTT<�{ì 15 ç|�<ó�q d�+K«\ jîTT¿£Ø eT<ó�«>·ÔáeTT ( )
A) 17 B) 19 C) 23 D) 29
30. �ç¿ì+<� sTTºÌq <�Ô�ï+XøeTTq+<�T d�]jî®Tq~ ( )
12, 9, 15, 15, 18, 7, 24
A) n+¿£ eT<ó�«eTeTT R eT<ó�«>·ÔáeTT B) n+¿£eT<ó�«eTeTT R 15
C) n+¿£eT<ó�«eTeTT R �V�QÞø¿£eTT D) eT<ó�«>·ÔáeTT R �V�QÞø¿£eTT
31. e Z¿£�Ôá <�Ô�ï+XøeTTq+<�T eT<ó�«>·ÔáeTT ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )
A) 2N f
l hF
-+ ´ B) 2
F Nl h
f
-+ ´ C) 2
N Fl h
f
-+ ´ D) 2
N hl h
f
-+ ´
32. ~>·Te båq'|�Úq« $uó²Èq |�{켿£ýË 10`15 ÔásÁ>·Ü u²V�QÞø¿£eTT m+Ôá ?
A) f = 15 eÖçÔáyûT B) f ³ 15 C) f < 7 D) f < 15 ( )
33. ÿ¿£ ÔásÁ>·ÜjáT+<�T 30 eT+~ u²\TsÁT, 20 eT+~ u²*¿£\T >·\sÁT. MsÁT >·DìÔá |� ¿£�Å£� ( )
V�äÈsÁT¿±>± u²\TsÁ d�>·³TeÖsÁTØ 15, u²*¿£\ d�>·³TeÖsÁTØ 10, nsTTq yîTTÔáïeTT ÔásÁ>·Ü
d�>·³TeÖsÁTØ m+Ôá?
A) 25 B) 30 C) 13 D) 20
A
B C
1 2
(
ÔásÁ>·Ü 0`5 5`10 10`15 15`20 20`25
båq'|�Úq«+ 11 14 f 10 07
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d�+ç>·V�²D²Ôá�¿£ eTÖý²«+¿£qeTT`2
eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT
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¿±\eTT : 2 >·+öö 15 �öö bÍsÁT¼ ` A >·]w�÷ eÖsÁTØ\T : 30
d�Ö#áq\T : 1. n�� ç|�Xø�\qT çXø<�Æ>± #á<�e+&�.
2. bÍsÁT¼ A Å£� d�+�+~ó+ºq ç|�Xø�\ Èy��T\qT MT¿ì#ûÌ Èy��T |�çÔá+ýË s�jáT+&�.
3. bÍsÁT¼ A eTÖ&�T �d¿£�H�\T>± �+³T+~.
4. n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT\T s�jáT+&�.
5. d�eÖ<ó�qeTT\T d�Îw�¼+>±qT, Xø�çuó�+>±qT s�jáT+&�.
6. �d¿£�H� III q+<�* ç|�Xø�\Å£� n+ÔásÁZÔá m+|¾¿£ �+³T+~.
�d¿£�H� ` I
d�Ö#áq\T : 1. n�� ç|�Xø�\Å£� Èy��T\T s�jáT+&�.
2. ç|�Ü ç|�Xø�Å£� 1 eÖsÁTØ. 4I1 R 4 eÖsÁTØ\T
1. (A - B) È (B - A) = AADB eT]jáTT N nHû~ d�V�²È d�+U²«d�$TÜ, W nHû~ |�Ps��+¿±\ d�$TÜ nsTTÔû
NDW qT ¿£qT>=q+&�.
2. jáTÖ¿ì¢&� uó²>·V�äsÁ Xâw�$~ó qT|�jîÖÐ+º 90, 70\ >·.kÍ.uó². ¿£qT>=q+&�.
3. d�eÖq y�«kÍsÁ�eTT, mÔáTï >·\ d�Ö�|�eTT, >ÃÞøeTT\ |��Tq|�]eÖD²\ �w�ÎÜï� ¿£qT>=qTeTT.
4. Âs+&�T <ó�q eTÖý²\T �+&û ÿ¿£ esÁZd�eÖkÍ\qT çy�jáT+&�.
�d¿£�H� ` II
d�Ö#áq\T : 1. n�� ç|�Xø�\Å£� Èy��T\T s�jáT+&�.
2. ç|�Ü ç|�Xø�Å£� 2 eÖsÁTØ. 5I2 R 10 eÖsÁTØ\T
5. (2.3)x = (0.23)y R 1000 nsTTq 1 1x y
- $\Te ¿£qT>=q+&�.
6. p(x) = x3 - 8 nsTTq p(2), p( - 2), p(3), p( - 3) $\Te\T ¿£qT>=q+&�.
35
7. 4x - 6y = 15, 2x - 3y = 5 d�MT¿£sÁD²\Å£� kÍ<ó�q kÍ<ó�«eÖ? ¿±<�? |�]o*+º kÍ<ó�«eTsTTÔû ¿£qT>=q+&�.
8. XøSq«d�$TÜ¿ì Âs+&�T �<�V�²sÁD*eÇ+&�? MT Èy��TqT d�eT]�+#á+&�.
9. ç¿£eT e�Ô�￱sÁ Xø+KTeÚ �¿±sÁeTTýËqTq� CË¿£sY {Ë|¾ uó�Öy�«kÍsÁ�+ 7 �d+.MT. eT]jáTT mÔáTï 24
�d+.MT. �³Te+{ì 15 {Ë|Ó\qT ÔájáÖsÁT#ûjáT&��¿ì m+Ôá n³¼ ¿±eýÉqT.
�d¿£�H� ` III
d�Ö#áq\T : 1. n�� ç|�Xø�\Å£� Èy��T\T s�jáT+&�.
2. ç|�Ü ç|�Xø�Å£� 4 eÖsÁTØ. 4I4 R 16 eÖsÁTØ\T
10.2 3 17
3 2 3 2 5x y x y+ =
+ - eT]jáTT 5 1 2
3 2 3 2x y x y+ =
+ - \qT kÍ~ó+#á+&�.
(ýñ<�)
>·DìÔá+ýË CË«Üw�, Èd¾�Ôá\ eÖsÁTØ\ yîTTÔáï+ 50 ÿ¿£yûÞø CË«w¾ÔáÅ£� 3 eÖsÁTØ\T mÅ£�Øe>±qT Èd¾�ÔáÅ£�
3 eÖsÁTØ\T ÔáÅ£�Øe>±qT eºÌeÚ+fñ y�] eÖsÁTØ\ \�Æ+ 625 nsTTq y�] eÖsÁTØ\T m��?
11. 20 MT. ýËÔáT, 7 MT. y�«d�eTT �+&û³³T¢ ÿ¿£ u²$� çÔá$Ç]. çÔáeÇ>± eºÌq eT{ì¼� 22 MT I
14 MT. ¿=\Ôá\T >·\ ÿ¿£ bÍ¢{Ùb�Í+>± d�eÖq+>± (#á<�TqT>±) bþd¾q � b�Í¢{Ùb�ÍsÁ+ mÔáTï m+Ôá?
(ýñ<�)
11. ÿ¿£ |��Tq �V�Q|�~ jîTT¿£Ø XøSH�«\ yîTTÔáï+, Âs+&ûd¾ XøSH�«\ \u²Ý\ yîTTÔáï+ eT]jáTT XøSH�«\ \�Æ+\T
esÁTd�>± 2, - 7, - 14 nsTTq � |��Tq�V�Q|�~� ¿£qT>=q+&�.
12. (a) 5 2+ nHû~ ÿ¿£ ¿£sÁD¡jáT d�+K« n� �sÁÖ|¾+#á+&�.
(ýñ<�)
12. (b) ç¿ì+~ y��ýË d�$TÔáTýñ$? MT Èy��TqT d�eT]�+#á+&�.
(i) uó²sÁÔá<ûXø+ýË� 10 eT+~ n+<�yîT®q e«Å£�ï\ d�eTT<�jáT+.
(ii) uó²sÁÔá<ûXø+ýË� n�� q<�T\ d�eTT<�jáTeTT.
(iii) uó²sÁÔá ç¿ì¿{٠ȳ¢ýË� eT+º u²«{ÙàyîTH�\ d�eTT<�jáTeTT.
(iv) uó²sÁÔá eTV¾²Þ² ç�|d¾&î+{Ù\ (n<ó�«Å£��\) d�eTT<�jáTeTT.
36
13. (a) eTÖ&�T Å£�¯Ì\T, Âs+&�T fñ�TÞøß $\Te sÁÖ.2,250/`. Âs+&�T Å£�¯Ì\T eTÖ&�T fñ�TÞøß $\Te
sÁÖ. 2,750/`. ç|�r Å£�¯Ìyî\, fñ�TýÙ yî\\qT ç>±|�t <�Çs� ¿£qT>=qTeTT.
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13. (b) x2 - 2x - 8 �V�Q|�~� ç>±|�t |�<�ÆÜ <�Çs� kÍ~ó+#áTeTT.
37
d�+ç>·V�²D²Ôá�¿£ eTÖý²«+¿£qeTT`2
eÖ~] ç|�Xæ�|�çÔáeTT ` >·DìÔáeTT �||�sY-I
ÔásÁ>·Ü ` 10
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¿±\eTT : 30 �öö bÍsÁT¼ ` B >·]w�÷ eÖsÁTØ\T : 10
d�Ö#áq\T : 1. bÍsÁT¼ B q+<�* n�� ç|�Xø�\Å£� y�{ì ¿<�TsÁT>± sTTeÇ�&�q çu²Â¿³¢jáT+<�T �+>·¢ n¿£�sÁeTT\ýË�
�|<�Ý n¿£�s�\qT A, B, C, D çy�jáTeýÉqT.
2. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ ¹¿{²sTT+#á&�yîT®q~.
3. ¿={ì¼yûÔá\T, ~~ÝyûÔá\T eTÖý²«+¿£qeTT #ûjáT�&�eÚ.
4. n�� ç|�Xø�\Å£� d�eÖ<ó�qeTT sTTeÇeýÉqT.
�d¿£�H� ` IV
d�Ö#áq\T : 1. ç|�Ü ç|�Xø�Å£� 1/2 eÖsÁTØ. 20I
1/2 R 10 eÖsÁTØ\T
14. 632016log G 32
2016log jîTT¿£Ø $\Te R ................ ( )
A) 632016log B) 95
4032log C) 1 D) 0
15. 2 2 2 Sin+ + + ¥ R ...................... ( )
A) 2 B) 8 C) 2 2 D) 2
16. a, b \ eT<ó�« n¿£sÁD¡jáT d�+K« ( )
A) ab B) 2a b+
C) .a b D) ab
17. 3, 6, 9, 12, ......... 30 jîTT¿£Ø d�$TÜ �s��D sÁÖ|�eTT ( )
A) {3x | x = 1, 2, 3, 4, .......10, xÎn} B) {x : x nqTq~ ç|�<ó�qd�+K«}
C) {x2 | xÎn} D) {x : x nqTq~ 30 ¿£+fÉ ÔáÅ£�ØyîÕq uñd¾d�+K«}
18. P, Q nHû$ Âs+&�T $jáTT¿£ï d�$TÔáT\T nsTTq P - Q = ................... ( )
A) P È Q B) P Ç Q C) P D) Q
38
19. ç|�¿£Ø |�³eTT d�Öº+#áTq~ :` ( )
A) P Ç Q Ç R B) (P Ç Q)`R C) P`(Q Ç R) D) Q`(R Ç P)
20. 2017 jîTT¿£Ø |�]eÖDeTT ( )
A) 2017 B) 0 C) 1 D) 7
21. ax2 + bx + c esÁZ �V�Q|�~ jîTT¿£Ø XøSq«$\Te\ yîTTÔáïeTT eT]jáTT \�ÝeTT ( )
d�eTqeT>·T³Å£�
A) a = b B) a = c C) b = - c D) b = c
22. ç|�¿£Øq �q� ¹sU²ºçÔáeTT y = p(x) XøSq«$\Te\ d�+K« ( )
A) 2 B) 3 C) 0 D) 1
23. Âs+&�T <ó�qd�+K«\jîTT¿£Ø yîTTÔáïeTT 27, eT]jáTT y�{ì \�ÆeTT 180 nsTTq � ( )
<ó�qd�+K«qT
A) 11, 16 B) 10, 17 C) 12, 15 D) 10, 18
24. ax+by+c = 0, a, b, cÎr nqT ¹sFjáT d�MT¿£sÁDeTTýË a, b \qT Ôá�|¾ï|�sÁ#áTq~. ( )
A) a2+b2 = 0 B) a2+b2 ¹ 0 C) a+b ¹ 0 D) a+b = 0
25. ¹sFjáT d�MT¿£sÁD²\ ÈÔá d�+>·Ôá d�MT¿£sÁD²\T eT]jáTT |�sÁd�ÎsÁ �<ó�]Ôá d�MT¿£sÁD²\T ( )
nsTTq
A) 1 1
2 2
a ba b
= B) 1 1
2 2
a ba b
¹ C) 1 1 1
2 2
a b ca b c
= ¹ D) 1 1 1
2 2 2
a b ca b c
= =
26. lx2 - mx - n = 0 esÁZ d�MT¿£sÁDeTT jîTT¿£Ø eTÖý²\T a , b nsTTq a 2, b 2 = .......... ( )
A) 2
mnl B)
2lmn
C) 2
2
2m nll+
D) 2n
lm
27. 6x2 - px + 15 = 0 jîTT¿£Ø $#á¿ì�Dì 81 nsTTq p $\Te R ................... ( )
A) 21 B) 31 C) 18 D) 41
P Q R m
39
28. �ç¿ì+~ y��ýË b2 - 4ac Ü 0 ( )
A) B)
C) D)
29. yîTT<�{ì 'n' d�V�²È d�+K«\ yîTTÔáïeTT 465 nsTTq n $\Te m+Ôá ? ( )
A) 25 B) 29 C) 30 D) 31
30. ÿ¿£ uË\T >ÃÞøeTT jîTT¿£Ø |��Tq|�]eÖDeTT ¿£qT>=qT³Å£� d�ÖçÔáeTT ( )
A) ( )3 343
R rP - B) ( )3 323
R rP - C) ( )3 3R rP - D) ( )3 313
R rP -
31. d�eÖq y�«d�eTT eT]jáTT d�eÖq mÔáTï\T ¿£*Zq d�Ö�|�eTT, Xø+KTeÚ eT]jáTT >ÃÞøeTT\ ( )
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A D B
C
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120o
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cmP B) 298 5
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cmP
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A BCos +æ öç ÷è ø $\Te ................... ( )
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46
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
X CLASS MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
WEIGHTAGE TABLES & BLUE PRINT
TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage
Alloted1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15
TOTAL 40 100
S.No. Academic Standards No. of Marks PercentageQuestions Alloted
1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25
TOTAL 33 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS
TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL
1 Problem Solving 1 2 2 6 112 Reasoning Proof - 1 1 4 63 Communication 1 1 - 2 44 Connection 2 1 - 4 75 Visualization /Representation - - 1 4 5
TOTAL 4 5 4 20 33
TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL %
1 Real Numbers - 1 1 3 52 Sets 1 - 1 2 43 Polynomials 1 1 1 3 64 Linear Equations in 2 Variables 1 1 2 3 75 Quadratic Equations 1 1 1 3 6
6 Progressions - - 1 3 4
7 Mensuration - 1 1 3 5
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B = {x | 2x+1, xÎw eT]jáTT x£ 9} nsTTq
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SUMMATIVE ASSESSMENT - IIIMODEL PAPER
X CLASS MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
WEIGHTAGE TABLES & BLUE PRINT
TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage
Alloted1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15
TOTAL 40 100
S.No. Academic Standards No. of Marks PercentageQuestions Alloted
1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25
TOTAL 33 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS
TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL
1 Problem Solving 1 2 2 6 112 Reasoning Proof - 1 1 4 63 Communication 1 1 - 2 44 Connection 2 1 - 4 75 Visualization /Representation - - 1 4 5
TOTAL 4 5 4 20 33
TABLE (3) BLUE PRINT (X CLASS PAPER-I)S.No. Academic Standards VSA SA LA MCQ TOTAL %
1 Co-ordinate Geometry 1 2 2 3 72 Similar Triangles - 1 1 2 53 Tangents & Secants of circles 1 - 1 3 54 Trigonometry - 1 1 3 55 Application of trigonometry 1 - 1 2 4
6 Probability 1 1 1 3 5
7 Statistics - 1 1 3 5
54
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5. What is the relationship between the areas of two equilateral triangles those are constructed on side
of a square and its diagonal.
55
6. Mr. Gopal aged 70 lives in his house at (4, 5). He goes to shop which is located at (5, 2) and then
to a park located at (3, 6). Find the distance travelled by Gopal.
7. Simplify (1 - Sin q) (1+Sin q) (1+tan2 q)
8. Find the median of the following distribution
C.I 65-85 85-105 105-125 125-145 145-165 165-185 185-205
f 3 4 12 15 14 12 8
9. A box contain 25 balls numbered as 1, 2, 3, ......, 25 a ball is drawn at random. What is the
probability for getting the ball bearing the number
(i) is divisible by 6
(ii) is a prime number
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+ C) 60+ D) 90
+
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C) \+�¿ÃD d�eT~Çu²V�Q D) d�eTu²V�Q
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17. ABd çÜuó�TÈeTTq+<�T DE nqTq~ Bd ¿ì d�eÖ+ÔásÁeTT>± �q�~. D, AB �, AC �|Õq ( )
>·\ _+<�TeÚ\T
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AD AE 3) = AB AdDB Ed
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A(3, 2)B(0, 0)
58
18. DPQR eT]jáTT DXYZ \T d�sÁÖbÍ\T, eT]jáTT PQ : XY = 5:8 nsTTq � çÜuó�TC²\ ( )
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A) AB2+BC2`BD2
B) AB2+BC2
C) AB2+BC2+2BC.DB
D) AB2+BC2`2BC.DB
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C) 72 jáTÖ�³T¢ D) ( )
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1) cos (180+q) ( ) a) - cot q
2) sec (270+q) ( ) a) - cos q
3) tan (90+q) ( ) a) - cosec q
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C) 1 - a, 2 - b, 3 - c D) 1 - c, 2 - a, 3 - b
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17 D)
67
31. 25 n+XøeTT\ d�>·³T 40. n+<�TýË ÿ¿£ n+XøeTT 53 Å£��<�T\T>± »28µ n� ( )
ýÉ¿ìØ+#á�&�q~. nsTTq KºÌÔáyîT®q d�>·³T m+Ôá?
A) 26 B) 39 C) 41 D) 46
60
32. �ç¿ì+~ y��Ôà d�]nsTTq~ ( )
A) ÔásÁ>·Ü eT<ó�« $\Te R 2ÿ¿ £ ÔásÁ>Ü· m>·Te ne~ ó - ÿ¿ £ Ôsá >Á ·Ü ~>·Te ne~ó
B) ÔásÁ>·Ü eT<ó�« $\Te R 2Ôsá >Á ·Ü m>T· e ne~ ó G Ôsá >Á ·Ü ~>T· e ne~ó
C) ÔásÁ>·Ü eT<ó�« $\Te R m>·Te ne~ó - ~>·Te ne~ó
D) ÔásÁ>·Ü eT<ó�« $\Te R m>·Te ne~ó + ~>·Te ne~ó
33. �ç¿ì+<� sTTeÇ�&�q bå'q$uó²È¿£ |�{켿£ jîTT¿£Ø �V�QÞø¿£ ÔásÁ>·Ü ¿£qT>=qTeTT ( )
ejáTd�Tà 0`10 10`20 20`30 30`40 40`50 50`60
sÃ>·T\ d�+K« 12 09 05 10 25 18
A) 10`20 B) 20`30 C) 30`40 D) 40`50
61
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
X CLASS MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
SYLLABUS: 1. Real Number2. Sets3. Polynomials4. Linear Equations in 2 Variables5. Quadratic Equations6. Progressions10. Mensuration
TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15
TOTAL 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONSS.No. Academic Standards No. of Questions Marks Alloted Percentage1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25
Total 33 40 100
NOTE ; 1. There is weightage to only academic standards and type of questions.2. There is no fixed weightage to content, but all chapters must be covered in each question paper.3. Student should answer the questions as per the academic standard required.4. Answer scripts shall be in the view of achievement of academic standards.
62
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
MATHEMATICS - PAPER-ITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 2 hrs 15 min. PART - A Max. Marks : 30
Instructions : 1. Read all questions.2. Part A answers should be written in separate answers book.3. There are three sections in Part A.4. Answer all questions.5. Every answer should write visibly and neatly.6. There is internal choice in Section-III.
SECTION - IInstructions : 1. Answer all questions.
2. Each question carries 1 mark. 4I1 R 4 marks
1. If a, b are zeroes of the polynomial 2x2 + 7x + 5, find the value of a+b+ab ?
2. If A = {1, 4, 9, 5, 16, 25, . . . . . .} then write it in set builder form.
3. The larger of two complimentary angles is double the smaller. Find the angles.
4. The height of a rectangular stockroom is 5m and perimeter of its floor is 50m. Find the outer area of thefour walls to be painted.
SECTION – IInstructions : 1. Answer all questions.
2. Each question carries 2 mark. 5I2 R 10 marks
5. Solve the equation 3x = 5x+2
6. Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing square.
7. A cone of height 24cm and radius of base 6cm is made up modeling clay. A child reshapes it into a
sphere. Find the radius of the sphere.
8. If a, b and g are the zeroes of a polynomial of degree 3, then give the relations between the zeroes and
the coefficients of the polynomial.
9. Find whether the equations x2 – 4x + 1.5 = 0 and 2x2 + 3 = 8x are consistent or not
63
SECTION - III
Instructions : 1. Answer all questions.
2. Choice any one from each question. 4I4 R 16 marks
Each question carries 4 marks
10a Solve the equations 10 2 4
x y x y+ =
+ - and 15 5 2
x y x y+ = -
+ -
(or)
10b An iron pillar consists of a cylindrical portion of 2.8 cm height and 20 cm in diameter and a cone of 42
cm height surmounting it. Find the weight of the pillar if 1cm3 of iron weighs 7.5 gram.
11a A contractor construction job specifies a penalty for delay of completion beyond a certain date asfollows. Rs. 200 for the first day. The penalty for each succeeding day being Rs.50 more than thepreceding day. How much money does the contractor pay as penalty if he has delayed the work by 30
days.
(or)
11b A Rectangular park is to be designed. Its breadth is 3m less than its length. Its area is to be 4 squaremeters more than the area of park that has already been made in the shape of an isosceles triangle with
base as the breadth of the rectangular park and altitude 12m. Find the length and breadth.
12a Proove that 3 2 5+ is irrational
(or)
12b If A = {x | x is a prime number and x 20}
B = {x | 2x+1, xew and x<9} then
Find (i) AB (ii) AB (iii) A-B (iv) B-A. What do you observe?
13a The Coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later he buys another bat and two
more balls of the same kind for Rs.1300. What is the cost price of each? Solve the situation graphically.
(or)
13b Solve the quadratic polynomial x2 - 3x - 4 graphically.
64
A) 6 B) 7 C) 8 D) 9
20. If a b+ is an irrational number, then which of the following is false ? ( )
A) ‘a’ and ‘b’ are prime B)’a’ or ‘b’ is primeC)’a’ and ‘b’ are any integers D)one of ‘a’ or ‘b’ is not a perfect square
21. If p(x) = g(x)q(x)+r(x) if deg {p(x)} = deg {q(x)} then deg {g(x)} = .............. ( )
A) 0 B) 1 C) 2 D) 3
22. The graph of y = ax+b is a straight line which intersects the X-axis at exactly one ( )
point namely, ..................
A) 0, ba
æ öç ÷è ø B) , 0b
aæ öç ÷è ø C) 0, b
a-æ ö
ç ÷è ø D) , 0ba-æ ö
ç ÷è ø
23. If x2+ax+b = 0; x2+bx+a = 0 have a common roots then ( )
A) a+b = 0 B) ab = 1 C) a+b = 1 D) a+b+1 = 0
24. Coefficient of x in a polynomial ax2 + bx + c is ‘o’. Then its zeroes are ( )
A) equal B)additive inverses to one anotherC)multiplicative inverses to one another D)none
25. The series (n-1), (n-2), (n-3), ................. is a type of ( )
A) AP B) GP C) may be both D) none
26. A metal cuboid of dimensions 22cm I 15cm I 7.5cm was melted and cast into a ( )
cylinder of height 14cm. Its radius is .............................
A) 15cm B) 7.5cm C) 22.5cm D) 7cm
27. If log a, log b, log c are in A.P. then a, b, c are ( )
A) A.P. B) G.P. C) Both A.P and G.P D) neither A.P. nor G.P.
28. To calculate the quantity of milk inside a bottle, we need to find out ............. ( )
A) Area B) Valume C) Density D) Total surface area
29. The height of right angle triangle is 7cm less than the base, the length of the diagonal ( )
is 17cm, then the length of remaining two sides are .........................
A) 15cm, 8cm B) 12cm, 5cm C) 24cm, 17cm D) All above
30. Length of the dark line given in the diagram ( )
A) 2 2l b+ B) l b h+ +
C) 2 2 2l b h+ + D) ( )2l b h+ +
65
31. The shaded area in the figure shows ( )
A) A-B B) B-A C) AÇB D) (AÈB)-(AÇB)
32. Solution of x-y = z; x+y = 0 lies in ................. quadrant. ( )
A) I B) IV C) II D) III
33. Inconsistent equations may represent. ( )
A) intersect line B) parallel lines C) coinciding lines D) B or C
66
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
X CLASS MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
SYLLABUS: 7. Co-ordinate Geometry8. Similar Triangles9. Tangents and Secants to a circle11. Trigonometry12. Applications of Trigonometry13. Probability14. Statistics
TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDSS.No. Academic Standards Marks Percentage1 Problem Solving 16 402 Reasoning Proof 8 203 Communication 4 104 Connection 6 155 Visualization /Representation 6 15
TOTAL 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONSS.No. Academic Standards No. of Questions Marks Alloted Percentage1 Very Short Answer 4 4 102 Short Answer 5 10 253 Essay/Long Answer 4 16 404 Multiple Choice 20 10 25
Total 33 40 100
NOTE ; 1. There is weightage to only academic standards and type of questions.2. There is no fixed weightage to content, but all chapters must be covered in each question paper.3. Student should answer the questions as per the academic standard required.4. Answer scripts shall be in the view of achievement of academic standards.
67
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 2 hrs 15 min. PART - A Max. Marks : 30
Instructions : 1. Read all questions.2. Part A answers should be written in separate answers book.3. There are three sections in Part A.4. Answer all questions.5. Every answer should write visibly and neatly.6. There is internal choice in Section-III.
SECTION - IInstructions : 1. Answer all questions.
2. Each question carries 1 mark. 4I1 R 4 marks
1. If C (2, P) is a point on the line segment joining the points A (6, 5) and B (2, 11). Explain condition for
the point C to become the mid point of AB.
2. A boy observes that the length of his shadow is equal to his height. What is the angle of elevation of the
Sun rays?
3. In a class of 35, 28 students brought Junk food for their lunch. What was the probability that a student
at random would have brought healthy food?
4. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.
SECTION - II
Instructions : 1. Answer all questions.
2. Each question carries 2 mark. 5I2 R 10 marks
5. Compare the areas of two equilateral triangles which are constructed on side of a square and its diagonal.
6. An ant is at (4, 5) on graph sheet mounted of a wall. If it moves to a point (5, 2) and turns to reach
another point (3, 6). Find the distance travelled by the ant.
7. Show that (1-Sin q) (1+Sin q) (1+tan2 q) =1
68
8. Find the median of the following distribution
CI 65-85 85-105 105-125 125-145 145-165 165-185 185-205
f 3 4 12 15 14 12 8
9. A box contains 25 balls numbered as 1, 2, 3, ......, 25. A ball is drawn from the box at random.What is the probability for getting the ball bearing the number, that
(i) is divisible by 6 (ii) is a prime number
SECTION - IIIInstructions : 1. Answer all questions.
2. Each question carries 4 mark. 4I4 R 16 marks
10a Prove that a line drawn through the mid-point of one side of a triangle parallel to another side
bisects the third side.
(OR)
10b Vertices of a triangle ABC are A (3, 5), B (7, 4) and C (10, 8). The mid point of the side BC, CA
and AB are D, E and F respectively. Are the centroids of DABC and DDEF are same or not?
11a If tan x = 512 , then find the value of sec x and x+1
x-1SecSec
(OR)
11b There is a tower beside the road, Rahim standing at the top of the tower observes two cars A and B oneither side of the tower at an angle of depression 30o and 60o are approaching the foot of the tower witha uniform speed of 10m/s and 5m/s respectively. If the height of the tower is 100 m, then find which
car reaches the tower first and how many seconds the other car is late by the first one.
12a A bag contains 6 yellow balls and some green balls. The probability of getting a green ball is triple thatof a yellow ball. Determine number of Green balls in the bag and find the probability of each colour ball
when a ball is drawn at time randomly.
(OR)
12b Ramu has a triangular site. He observes the corners of the triangular site are (2, 3), (4, 1), (�2, 5). Find
the area of the swimming pool dug by joining of the mid points of the sides of the site.
13a The following distribution gives the marks of 80 students in S.A-2 of Mathematics. Draw ogive curvefor the distribution.
69
Marks scored 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No.of Students 04 06 11 20 16 10 08 05
(OR)13b Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct the pair of
tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.
SUMMATIVE ASSESSMENT - IIIMODEL PAPER
MATHEMATICS - PAPER-IITime : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 30 min. PART - B Max. Marks : 10
Instructions : 1. Answer all the questions in Part-B.2. Each question has 4 options. Write the capital letter indicating the answer in the given
brackets.3. Marks are not awarded for over writing answers.4. All questions carry equal marks.
SECTION - IV
Instructions : 1. Answer all questions.
2. Each question carries 1/2 mark. 20I1/2 R 10 marks
14. If the slope of a line is »lµ then the angle made by it with X-axis in positive direction is ( )
A) 30+ B) 45+ C) 60+ D) 90+
15. If DPQR ~ DXYZ and PQ : XY = 5:8, then the ratio of their corresponding median is .. ( )
A) 5:8 B) 64:25 C) 25:64 D) 8:5
16.4 4
2 2
tantan
sec A Asec A A
--
= ........................ ( )
A) 0 B) 1/2 C) 1 D) 1
17. If the shadow of a tower is times its height then attitude of the Sun is ( )
A) 45o B) 30o C) 60o D) 90o
70
18. Three coins are tossed simultaneously, then probability of getting at least one tail is ( )
A) 3/4 B) 1/3 C) 7/8 D) 2/3
19. The mean of a data consisting 25 observations is 40. In doing so observation 53 ( )
was wrongly recorded as 28. Then the correct mean is
A) 26 B) 39 C) 41 D) 46
20. From the figure if ÐAPB = 70o then ÐAOB = ........................ ( )
A) 70o B) 90o
C) 160o D) 110o
21. The following line has only one point in common to the circle ( )
A) diameter B) tangent C) secant D) chord
22. Which of the following is not possible ( )
A) sin q = 0.5 B) cos q = 0 C) tan q = 2 D) sec q = 0.3
23. Which of the following is correct ? ( )
A) Class mark = Class Limit - Lower Class Limit2
Upper
B) Class mark = Class Limit + Lower Class Limit2
Upper
C) Class mark = Upper Boundary � Lower Boundary
D) Class mark = Upper Boundary + Lower Boundary
24. In the figure ÐB is an obtuse angle, then AC2 = ................ ( )
A) AB2+BC2�BD2 B) AB2+BC2
C) AB2+BC2+2BC.DB D) AB2+BC2�2BC.DB
25. Modal class of the following distribution is ( )
Age 0-10 10-20 20-30 30-40 40-50 50-60
No. of Patients 12 09 05 10 25 18
26. In the given figure, the radius of the outer circle is ‘7’ units; ( )
then the radius of the inner circle is
A) 7 2 units B) 7 2 1- units
C) 72 units D) ( )
142 1+ units
71
27. A Social Studies text book contains 250 pages. A page is selected at random. ( )
What is the probability that the number on the page selected is a perfect square?
A) 1
250 B) 1
125 C) 3
50 D) None
28. The probability of getting 53 Sundays in an ordinary year is .................... ( )
A) 5253 B) 1
52 C) 17 D) 6
7
29. Match the following
1) cos (180+q) ( ) a) cot q
2) sec (270+q) ( ) b) cos q
3) tan (90+q) ( ) c) cosec q
A) 1b, 2c, 3a B) 1c, 2b, 3a C) 1a, 2b, 3c D) 1c, 2a, 3b ( )
30. (0, 0), (1, 0), (0, 3) are vertices of a ......................... triangle. ( )
A) Right angle B) Isosceles C) Right isosceles D) Equilateral
31. Co –ordinates of second end of the diameter is ........................ ( )
A) (2, 3) B) (�2, �3) C) (�3, �2) D) (6, 4)
32. In a DABC, DE//BC and intersects AB at D and AC at E, then ( )
1) = AD AEDB Ed 2) =
AB ACAD AE 3) = AB Ad
DB Ed
A) 1�T, 2�T, 3�T B) 1�T, 2�F, 3�T C) 1�F, 2�T, 3�F D) 1�F, 2�F, 3�T
33. If the two trees of heights h1 and h2 subtended angles of 30o and 60o respectively ( )
at the mid point of the line joining their feet then h1 : h2 is ...........................
A) 3 :1 B) 1: 3 C) 3:1 D) 1:3
72
73
SUMMATIVE ASSESSMENT - III MODEL PAPER
X CLASS MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
SYLLABUS: 1. Real Number 2. Sets 3. Polynomials 4. Linear Equations in 2 Variables 5. Quadratic Equations 6. Progressions 10. Mensuration TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDS
S.No. Academic Standards Marks Percentage 1 Problem Solving 16 40 2 Reasoning Proof 8 20 3 Communication 4 10 4 Connection 6 15 5 Visualization /Representation 6 15 TOTAL 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS S.No. Academic Standards No. of
Questions Marks Alloted Percentage
1 Very Short Answer 4 4 10 2 Short Answer 5 10 25 3 Essay/Long Answer 4 16 40 4 Multiple Choice 20 10 25 Total 33 40 100
NOTE ; 1. There is weightage to only academic standards and type of questions.
2. There is no fixed weightage to content, but all chapters must be covered in each question paper.
3. Student should answer the questions as per the academic standard required.
4. Answer scripts shall be in the view of achievement of academic standards.
74
SUMMATIVE ASSESSMENT - III MODEL PAPER
MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 2 hrs 15 min. PART - A Max. Marks : 30
Instructions : 1. Read all questions. 2. Part A answers should be written in separate answers book. 3. There are three sections in Part A. 4. Answer all questions. 5. Every answer should write visibly and neatly. 6. There is internal choice in Section-III.
SECTION - I Instructions : 1. Answer all questions. 2. Each question carries 1 mark. 4I1 R 4 marks 1. If a, b are zeroes of the polynomial 2x2 + 7x + 5, find the value of a+b+ab ?
2. If A = {1, 4, 9, 5, 16, 25, . . . . . .} then write it in set builder form. 3. The larger of two complimentary angles is double the smaller. Find the angles. 4. The height of a rectangular stockroom is 5m and perimeter of its floor is 50m. Find the
outer area of the four walls to be painted. SECTION – I
Instructions : 1. Answer all questions. 2. Each question carries 2 mark. 5I2 R 10 marks 5. Solve the equation 3x = 5x+2 6. Find the roots of the equation 5x2 - 6x - 2 = 0 by the method of completing square. 7. A cone of height 24cm and radius of base 6cm is made up modeling clay. A child reshapes
it into a sphere. Find the radius of the sphere. 8. If a, b and g are the zeroes of a polynomial of degree 3, then give the relations between the
zeroes and the coefficients of the polynomial. 9. Find whether the equations x – 4y + 1.5 = 0 and 2x – 8y+ 3=0 are consistent or not
SECTION - III
Instructions : 1. Answer all questions. 2. Choice any one from each question. 4I4 R 16 marks Each question carries 4 marks
10a Solve the equations and
(or)
10 2 4x y x y
+ =+ -
15 5 2x y x y
+ = -+ -
75
10b An iron pillar consists of a cylindrical portion of 2.8m height and 20 cm in diameter and a cone of 42 cm height surmounting it. Find the weight of the pillar if 1cm3 of iron weighs 7.5 gram.
11a A contractor construction job specifies a penalty for delay of completion beyond a certain date as follows. Rs. 200 for the first day. The penalty for each succeeding day being Rs.50 more than the preceding day. How much money does the contractor pay as penalty if he has delayed the work by 30 days.
(or) 11b A Rectangular park is to be designed. Its breadth is 3m less than its length. Its area is to be
4 square meters more than the area of park that has already been made in the shape of an isosceles triangle with base as the breadth of the rectangular park and altitude 12m. Find the length and breadth of rectangular park.
12a Proove that is irrational (or)
12b If A = {x | x is a prime number and x < 20} B = {x | 2x+1, xew and x<9} then Find (i) AÈB (ii) AÇB (iii) A-B (iv) B-A. What do you observe? 13a The Coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later he buys another bat
and two more balls of the same kind for Rs.1300. What is the cost price of each? Solve the situation graphically.
(or) 13b Solve the quadratic polynomial x2 - 3x - 4 graphically.
3 2 5+
76
SUMMATIVE ASSESSMENT - III MODEL PAPER
MATHEMATICS - PAPER-I Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 30 min. PART - B Max. Marks : 10
Instructions : 1. Answer all the questions in Part-B. 2. Each question has 4 options. Write the capital letter indicating the answer in
the given brackets. 3. Marks are not awarded for over writing answers. 4. All questions carry equal marks.
SECTION - IV Instructions : 1. Answer all questions. 2. Each question carries 1/2 mark. 20I1/2 R 10 marks 14. The H.C.F. of 31, 43 and 47 is ....................... ( )
A) 121 B) 1 C) 31 D) 43
15. If x2 + y2 = z2 then ................... ( )
A) 1 B) 2 C) `2 D) `1
16. n(A) = 14; n(B) = 11; n(AÈB) = 19 then n(AÇB) = ............. ( )
A) 6 B) 16 C) 22 D) 25
17. If a fraction becomes 2 when 9 is added to its numerator and 1 when 2 is subtracts ( )
from its denominator then the fraction is ................................. A) 5/8 B) 8/5 C) 5/7 D) 7/9 18. The sum of squares of two consecutive positive even numbers is 340, then the ( )
numbers are ............................. A) 12, 14 B) 10, 12 C) 14, 16 D) 16, 18
19. Which term of the G.P 3,3 √3, 9, . . . .. is 243 ? ( )
A) 6 B) 7 C) 8 D) 9
20. If is an irrational number, then which of the following is false ? ( )
A) 'a' and 'b' are prime B)'a' or 'b' is prime C)'a' and 'b' are any integers D)one of 'a' or ‘b' is not a perfect square 21. If p(x) = g(x)q(x)+r(x) if deg {p(x)} = deg {q(x)} then deg {g(x)} = .............. ( )
A) 0 B) 1 C) 2 D) 3 22. The graph of y = ax+b is a straight line which intersects the X-axis at exactly one ( ) point namely, ..................
1 1log logx x
z y z y+ -
+ =
a b+
77
A) B) C) D)
23. If x2+ax+b = 0; x2+bx+a = 0 have a common roots then ( )
A) a+b = 0 B) ab = 1 C) a+b = 1 D) a+b+1 = 0 24. Coefficient of x in a polynomial ax2 + bx + c is ‘o’. Then its zeroes are ( )
A) equal B)additive inverses to one another C)multiplicative inverses to one another D)none 25. The series (n-1), (n-2), (n-3), ................. is a type of ( ) A) AP B) GP C) may be both D) none 26. A metal cuboid of dimensions 22cm I 15cm I 7.5cm was melted and cast into a ( )
cylinder of height 14cm. Its radius is .............................
A) 15cm B) 7.5cm C) 22.5cm D) 7cm
27. If log a, log b, log c are in A.P. then a, b, c are ( )
A) A.P. B) G.P. C) Both A.P and G.P D) neither A.P. nor G.P. 28. To calculate the quantity of milk inside a bottle, we need to find out ............. ( )
A) Area B) Volume C) Density D) Total surface area 29. The height of right angle triangle is 7cm less than the base, the length of the diagonal ( ) is 17cm, then the length of remaining two sides are .........................
A) 15cm, 8cm B) 12cm, 5cm C) 24cm, 17cm D) All above 30. Length of the dark line given in the diagram ( )
A) B)
C) D)
31. The shaded area in the figure shows ( )
A) A-B B) B-A C) AÇB D) (AÈB)-(AÇB) 32. Solution of x-y = 2; x+y = 0 lies in ................. quadrant. ( ) A) I B) IV C) II D) III 33. Inconsistent equations may represent. ( ) A) intersect lines B) parallel lines C) coinciding lines D) B or C
0, ba
æ öç ÷è ø
, 0ba
æ öç ÷è ø
0, ba-æ ö
ç ÷è ø, 0b
a-æ ö
ç ÷è ø
2 2l b+ l b h+ +
2 2 2l b h+ + ( )2l b h+ +
78
Q. No Chapter Academic standard wise marks
AS 1 AS 2 AS 3 AS 4 AS 5 Very short answer questions
1 Polynomials 1 2 Sets 1 3 Linear Equations in 2 Variables 1 4 Mensuration 1 Short answer questions
5 Real Number 2 6 Quadratic Equations 2 7 Mensuration 2 8 Polynomials 2 9 Linear Equations in 2 Variables 2 Essay answer type questions
10 Linear Equations in 2 Variables 4 Mensuration
11 Progressions 4 Quadratic Equations
12 Real Numbers 4 Sets
13 Linear Equations in 2 Variables 4 Polynomials
Part B: Objective type questions 14 Real Number 0.5 15 Real Number 0.5 16 Sets 0.5 17 Quadratic Equations 0.5 18 Quadratic Equations 0.5 19 Progressions 0.5 20 Real Number 0.5 21 Polynomials 0.5 22 Linear Equations in 2 Variables 0.5 23 Quadratic Equations 0.5 24 Polynomials 0.5 25 Progressions 0.5 26 Mensuration 0.5 27 Real Number 0.5 28 Mensuration 0.5 29 Mensuration 0.5 30 Mensuration 0.5 31 Sets 0.5 32 Linear Equations in 2 Variables 0.5 33 Linear Equations in 2 Variables 0.5
Total 16 8 4 6 6
79
SUMMATIVE ASSESSMENT - III MODEL PAPER
X CLASS MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
SYLLABUS: 7. Co-ordinate Geometry 8. Similar Triangles 9. Tangents and Secants to a circle 11. Trigonometry 12. Applications of Trigonometry 13. Probability 14. Statistics TABLE (1) WEIGHTAGE TO ACADEMIC STANDARDS
S.No. Academic Standards Marks Percentage 1 Problem Solving 16 40 2 Reasoning Proof 8 20 3 Communication 4 10 4 Connection 6 15 5 Visualization /Representation 6 15 TOTAL 40 100
TABLE (2) WEIGHTAGE TO TYPE OF QUESTIONS S.No. Academic Standards No. of
Questions Marks Alloted Percentage
1 Very Short Answer 4 4 10 2 Short Answer 5 10 25 3 Essay/Long Answer 4 16 40 4 Multiple Choice 20 10 25 Total 33 40 100
NOTE ; 1. There is weightage to only academic standards and type of questions.
2. There is no fixed weightage to content, but all chapters must be covered in each question paper.
3. Student should answer the questions as per the academic standard required.
4. Answer scripts shall be in the view of achievement of academic standards.
80
SUMMATIVE ASSESSMENT - III MODEL PAPER
MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 2 hrs 15 min. PART - A Max. Marks : 30
Instructions : 1. Read all questions. 2. Part A answers should be written in separate answers book. 3. There are three sections in Part A. 4. Answer all questions. 5. Every answer should write visibly and neatly. 6. There is internal choice in Section-III.
SECTION - I Instructions : 1. Answer all questions. 2. Each question carries 1 mark. 4I1 R 4 marks 1. If C (2, P) is a point on the line segment joining the points A (6, 5) and B (2, 11). Explain
condition for the point C to become the mid point of AB. 2. A boy observes that the length of his shadow is equal to his height. What is the angle of
elevation of the Sun rays? 3. In a class of 35, 28 students brought Junk food for their lunch. What was the probability
that a student at random would have brought healthy food? 4. The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of
the circle.
SECTION - II
Instructions : 1. Answer all questions. 2. Each question carries 2 mark. 5I2 R 10 marks 5. Compare the areas of two equilateral triangles which are constructed on side of a square
and its diagonal. 6. An ant is at (4, 5) on graph sheet mounted of a wall. If it moves to a point (5, 2) and turns
to reach another point (3, 6). Find the distance travelled by the ant. 7. Show that (1-Sin q) (1+Sin q) (1+tan2 q) =1 8. Find the median of the following distribution
CI 65-85 85-105 105-125 125-145 145-165 165-185 185-205
f 3 4 12 15 14 12 8
9. A box contains 25 balls numbered as 1, 2, 3, ......, 25. A ball is drawn from the box at random. What is the probability for getting the ball bearing the number, that
(i) is divisible by 6 (ii) is a prime number
81
SECTION - III Instructions : 1. Answer all questions. 2. Each question carries 4 mark. 4I4 R 16 marks 10a Prove that “ If a line is drawn parallel to one side of a triangle , will divide other to sides in
the same ratio. (OR)
10b Vertices of a triangle ABC are A (3, 5), B (7, 4) and C (10, 8). The mid point of the side BC, CA and AB are D, E and F respectively. Are the centroids of DABC and DDEF are same or not?
11a If tan x = , then find the value of sec x and
(OR) 11b There is a tower beside the road, Rahim standing at the top of the tower observes two cars
A and B on either side of the tower at an angle of depression 30o and 60o are approaching the foot of the tower with a uniform speed of 10m/s and 5m/s respectively. If the height of the tower is 100√3m, then find which car reaches the tower first and how many seconds the other car is late by the first one.
12a A bag contains 6 yellow balls and some green balls. The probability of getting a green ball is triple that of a yellow ball. Determine number of Green balls in the bag and find the probability of each colour ball when a ball is drawn at time randomly.
(OR) 12b Ramu has a triangular site. He observes the corners of the triangular site are (2, 3), (4, 1),
(`2, 5). Find the area of the swimming pool dug by joining of the mid points of the sides of the site.
13a The following distribution gives the marks of 80 students in S.A-2 of Mathematics. Draw ogive curve for the distribution. Marks scored 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No.of Students 04 06 11 20 16 10 08 05
(OR) 13b Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct the pair of
tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.
512
x+1 x-1
SecSec
82
SUMMATIVE ASSESSMENT - III MODEL PAPER
MATHEMATICS - PAPER-II Time : 2 hrs 45 min. PART - A & B Max. Marks : 40
Time : 30 min. PART - B Max. Marks : 10
Instructions : 1. Answer all the questions in Part-B. 2. Each question has 4 options. Write the capital letter indicating the answer in
the given brackets. 3. Marks are not awarded for over writing answers. 4. All questions carry equal marks.
SECTION - IV
Instructions : 1. Answer all questions. 2. Each question carries 1/2 mark. 20I1/2 R 10 marks 14. If the slope of a line is »lµ then the angle made by it with X-axis in positive direction is ( ) A) 30+ B) 45+ C) 60+ D) 90+
15. If DPQR ~ DXYZ and PQ : XY = 5:8, then the ratio of their corresponding median is .. ( ) A) 5:8 B) 64:25 C) 25:64 D) 8:5
16. = ........................ ( )
A) 0 B) 1/2 C) 1 D) 1
17. If the shadow of a tower is √3 times its height then attitude of the Sun is ( )
A) 45o B) 30o C) 60o D) 90o 18. Three coins are tossed simultaneously, then probability of getting at least one tail is ( )
A) 3/4 B) 1/3 C) 7/8 D) 2/3 19. The mean of a data consisting 25 observations is 40. In doing so observation 53 ( )
was wrongly recorded as 28. Then the correct mean is A) 26 B) 39 C) 41 D) 46
20. From the figure if ÐAPB = 70o then ÐAOB = ........................ ( ) A) 70o B) 90o C) 160o D) 110o
21. The following line has only one point in common to the circle ( )
A) diameter B) tangent C) secant D) chord 22. Which of the following is not possible ( )
A) sin q = 0.5 B) cos q = 0 C) tan q = 2 D) sec q = 0.3
4 4
2 2
tantan
sec A Asec A A
--
83
23. Which of the following is correct ? ( )
A) Class mark =
B) Class mark = C) Class mark = Upper Boundary ` Lower Boundary D) Class mark = Upper Boundary + Lower Boundary 24. In the figure ÐB is an obtuse angle, then AC2 = ................ ( )
A) AB2+BC2`BD2 B) AB2+BC2 C) AB2+BC2+2BC.DB D) AB2+BC2`2BC.DB
25. Modal class of the following distribution is ( )
Age 0-10 10-20 20-30 30-40 40-50 50-60
No. of Patients 12 09 05 10 25 18
A) 10`20 B) 20`30 C) 30`40 D) 40`50
26. In the given figure, the radius of the outer circle is '7' units; ( ) then the radius of the inner circle is
A) units B) units
C) units D) units 27. A Social Studies text book contains 250 pages. A page is selected at random. ( )
What is the probability that the number on the page selected is a perfect square?
A) 1
250 B)
1125
C) 3/50 D) None
28. The probability of getting 53 Sundays in an ordinary year is .................... ( )
A) B) C) D)
29. Match the following 1) cos (180+q) ( ) a) cot q 2) sec (270+q) ( ) b) cos q 3) tan (90+q) ( ) c) cosec q A) 1b, 2c, 3a B) 1c, 2b, 3a C) 1a, 2b, 3c D) 1c, 2a, 3b ( ) 30. (0, 0), (1, 0), (0, 3) are vertices of a ......................... triangle. ( )
A) Right angle B) Isosceles C) Right isosceles D) Equilateral 31. Co –ordinates of second end of the diameter is ........................ ( )
A) (2, 3) B) (`2, `3) C) (`3, `2) D) (6, 4)
32. In a DABC, DE//BC and intersects AB at D and AC at E, then ( )
Class Limit - Lower Class Limit2
Upper
Class Limit + Lower Class Limit2
Upper
7 2 7 2 1-
72 ( )
142 1+
5253
152
17
67
84
1) AD AEDB ED
= 2) 3) AB ADDB ED
=
A) 1`T, 2`T, 3`T B) 1`T, 2`F, 3`T C) 1`F, 2`T, 3`F D) 1`F, 2`F, 3`T
33. If the two trees of heights h1 and h2 subtended angles of 30o and 60o respectively ( ) at the mid point of the line joining their feet then h1 : h2 is ...........................
A) :1 B) 1: C) 3:1 D) 1:3
Q. No Chapter Academic standard wise marks
AS 1 AS 2 AS 3 AS 4 AS 5 Very short answer questions
1 Co-ordinate Geometry 1 2 Applications of Trigonometry 1 3 Probability 1 4 Tangents and Secants to a circle 1 Short answer questions
5 Similar Triangles 2 6 Co-ordinate Geometry 2 7 Trigonometry 2 8 Statistics 2 9 Probability 2 Essay answer type questions
10 Similar Triangles 4 Co-ordinate Geometry
11 Trigonometry 4 Applications of Trigonometry
12 Probability 4 Co-ordinate Geometry
13 Statistics 4 Tangents and Secants to a circle
Part B: Objective type questions 14 Co-ordinate Geometry 0.5 15 Similar Triangles 0.5 16 Trigonometry 0.5 17 Applications of Trigonometry 0.5 18 Probability 0.5 19 Statistics 0.5 20 Tangents and Secants to a circle 0.5 21 Tangents and Secants to a circle 0.5 22 Trigonometry 0.5 23 Statistics 0.5 24 Similar Triangles 0.5 25 Statistics 0.5
= AB ACAD AE
3 3
85
26 Tangents and Secants to a circle 0.5 27 Probability 0.5 28 Probability 0.5 29 Trigonometry 0.5 30 Co-ordinate Geometry 0.5 31 Co-ordinate Geometry 0.5 32 Similar Triangles 0.5 33 Applications of Trigonometry 0.5
Total 16 8 4 6 6
1
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( Ò<ë)
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4
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A) 121 B) 1 C) 31 D) 43
15. x2 + y2 = z2 nsTTq 1 1
log logx xz y z y+ −
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A) 1 B) 2 C) − 2 D) − 1
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5
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a B) , 0
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A) düe÷q+ B) ˇø£<ëìø=ø£{Ï dü+ø£\q $˝Àe÷\T
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ø£&û¶ì ø£]–+∫ 14 ôd+.MT m‘·TÔ>∑\ dü÷ú|ü+>± #dæq <ëì yê´kÕs¡ú+
A) 15 ôd+.MT. B) 7.5 ôd+.MT C) 22.5 ôd+.MT D) 7 ôd+.MT
27. log a, log b, log c \T A.P ˝À ñqï#√ a, b, c \T ñ+& ÁX‚&Ûç ( )
A) A.P B) G.P C) ¬s+&ÉTq÷ D) @Bø±<äT
6
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A) yÓ’XÊ\´+ B) |òüTq|ü]e÷D+ C) kÕ+Á<ä‘· D) dü+|üPs¡í‘·\ yÓ’XÊ\´+
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bı&Ée⁄ 17 ôd+.MT nsTTq $T–*q ¬s+&ÉT uÛÑTC≤\ bı&Ée⁄\T
A) 15 ôd+.MT, 8 ôd+.MT B) 12 ôd+.MT, 5 ôd+.MT
C) 24 ôd+.MT, 17 ôd+.MT D) ô|’eìïj·TT
30. Á|üø£ÿ |ü≥+˝À eTT<ä›>± ^∫q πsK bı&Ée⁄ ( )
A) 2 2l b+ B) l b h+ +
C) 2 2 2l b h+ + D) ( )2l b h+ +
31. Á|üø£ÿ |ü≥+˝À ùw&é #dæq Á|ü<X yÓ’XÊ\´+ ‘Ó ÒŒ~ ( )
A) A − B B) B − A
C) A∩ B D) (A ∪ B) − (A ∩ B)
32. x+y = 2 eT]j·TT x − y = 0 jÓTTø£ÿ kÕ<Ûäq @ bÕ<ä+˝À e⁄+≥T+~. ( )
A) I B) IV C) II D) III
33. e´ed”úø£è‘·+ ø±ì düMTø£s¡D≤\T ÁbÕ‹ì<Ûä |ü]#$ ( )
A) K+&ÉqπsK\T B) düe÷+‘·s¡ πsK\T C) @ø°uÛÑ$+# πsK\T D) B Ò<ë C
h
lb
A B
7
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT
>∑DÏ‘·eTT ù||üsY-II
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 2 >∑+ˆˆ 15 숈 bÕs¡Tº ` A >∑]wü e÷s¡Tÿ\T : 30
dü÷#·q\T : 1. nìï Á|üXï\qT ÁX<äΔ>± #·<äe+&ç.
2. bÕs¡Tº A ≈£î düe÷<ÛëqeTT\qT MTøÏe«ã&çq »yêãT |üÁ‘·+˝À sêj·T+&ç.
3. bÕs¡Tº A q+<äT eT÷&ÉT $uÛ≤>±\T e⁄HêïsTT.
4. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
5. Á|ü‹ »yêãTqT <ädü÷ÔØ>±, ns¡úeTjT´$<Ûä+>± sêj·T+&ç.
6. ôdø£åHé III q+<ä* Á|üXï\≈£î n+‘·s¡Z‘· m+|æø£ ñ+≥T+~.
ôdø£åHé ` I
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1 e÷s¡Tÿ. 4I1 R 4 e÷s¡Tÿ\T
1. A(6, 5) eT]j·TT B(2, 11) _+<äTe⁄\qT ø£*ù| πsU≤K+&É+ô|’q C(2, p) nH _+<äTe⁄ ø£\<äT. AB jÓTTø£ÿ
eT<Ûä _+<äTe⁄ 'C' n>∑T≥≈£î ø±e*‡q ìã+<Ûäq ‘Ó\Œ+&ç.
2. ˇø£ u≤\T&ÉT ‘·q ˙&É bı&Ée⁄, ‘·q jÓTTø£ÿ m‘·TÔ≈£î düe÷qyÓTÆq≥T¢>± >∑eTì+#ê&ÉT. Ä düeTj·T+˝À
dü÷s¡ øÏs¡D≤\ jÓTTø£ÿ }s¡ú«ø√D+ m+‘· ?
3. 35 eT+~ $<ë´s¡Tú\T >∑\ ‘·s¡>∑‹˝À 28 eT+~ $<ë´s¡Tú\T düeT‘·T\´+ø±ì ÄVü‰s¡+ eT<Ûë´Vü≤ï uÛÀ»q+>±
‹Hêïs¡T. nsTTq Äs√E düeT‘·T\´yÓTÆq ÄVü‰s¡+ rdüT≈£îqï $<ë´s¡Tú\ dü+uÛ≤e´‘· m+‘· ?
4. ˇø£ eè‘·Ô|ü]~Û <ëì yê´dü+ø£Hêï 16.8 ôd+.MT n~Ûø£yÓTÆq, Ä eè‘·Ô |ü]~Û m+‘· ?
ôdø£åHé ` II
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 2 e÷s¡Tÿ. 5I2 R 10 e÷s¡Tÿ\T
5. ˇø£ #·‘·Ts¡Ádü uÛÑT»+ô|’q eT]j·TT <ëì ø£s¡í+ô|’q ^j·Tã& ¬s+&ÉT düeTu≤VüQ Á‹uÛÑTC≤\ yÓ’XÊ˝≤´\qT
b˛\Ã+&ç.
8
6. ˇø£ >√&Éô|’q >∑\ Á>±|òt ø±–‘·+ô|’ ˇø£ NeT (4, 5) _+<äTe⁄qT+&ç (5, 2) _+<äTe⁄q≈£î yÓ[fl, ‹]–
(3, 6) _+<äTe⁄≈£î #]+~. nsTTq Ä NeT Á|üj·÷DÏ+∫q <ä÷s¡+ m+‘· ?
7. (1 − Sinθ) (1+Sinθ)(1+tan2θ) = 1 nì #·÷|ü+&ç.
8. øÏ+~ <ä‘êÔ+X+q≈£î eT<ä >∑‘·+ ø£qT>=q+&ç.
‘·s¡>∑‹ n+‘·s¡+ 65`85 85`105 105`125 125`145 145`165 165`185 185`205
bÂq'|ü⁄q´+ 3 4 12 15 14 12 8
9. ˇø£ ô|f…º À 1, 2, 3 ......... 25 dü+K´\T >∑\ 25 ã+‘·T\T e⁄HêïsTT. <ëìqT+&ç j·÷<äè∫äø£+>± ˇø£
ã+‹ì rdæq dü+<äs¡“¤+˝À
(i) 6 # uÛ≤–+#·ã&$ (ii) Á|ü<Ûëq dü+K´ njT´ dü+K´\ dü+uÛ≤e´‘· ø£qT>=q+&ç
ôdø£åHé ` III
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 4 e÷s¡Tÿ\T. 4I4 R 16 e÷s¡Tÿ\T
10 (a) ˇø£ Á‹uÛÑT»+˝À ˇø£ uÛÑTC≤ìøÏ düe÷+‘·s¡+>± ^j·Tã& πsK, $T–*q ¬s+&ÉT uÛÑTC≤\qT πø
ìwüŒ‹Ô À $uÛÑõdüTÔ+<äì ìs¡÷|æ+#·+&ç.
( Ò<ë)
10 (b) A(3, 5), B(7, 4) eT]j·TT C(10, 8) nH$ ABC Á‹uÛÑT» osê¸\T. D, E eT]j·TT F \T es¡Tdü>±
BC, CA eT]j·TT AB \ eT<ä _+<äTe⁄\T. ΔABC eT]j·TT ΔDEF Á‹uÛÑTC≤\ >∑Ts¡T‘·«πø+Á<ë\
ìs¡÷|üø±\T ˇø£fÒHê? ø±<ë? ‘Ó\Œ+&ç.
11 (a) tan x = 5
12 nsTTq#√ sec x $\Te ø£qT>=q+&ç. BìqT+&ç
sec x+1
sec x-1 $\Te >∑DÏ+#·+&ç.
( Ò<ë)
(b) ˇø£ s¡Vü≤<ë]ì ÄqTø=ì e⁄qï ≥esY ô|’qT+&ç s¡V”≤yéT, s¡Vü≤<ë]øÏ Çs¡TyÓ’|ü⁄\qT+&ç e#Ã ¬s+&ÉTø±s¡T¢
A eT]j·TT B \qT 30+ eT]j·TT 60
+ n<Ûä'ø√D+‘√ |ü]o*düTÔHêï&ÉT. ¬s+&ÉTø±s¡¢ À yÓTT<ä{Ï~ 10
MT/ôd y>∑+‘√q÷, ¬s+&Ée~ 5 MT/ôd y>∑+‘√q÷ ≥es¡TqT düMT|ædüTÔHêïsTT. ≥esY jÓTTø£ÿ m‘·TÔ
9
100 3 MTˆˆ nsTTq#√ @ø±s¡T ≥es¡TqT yÓTT<ä≥ #s¡T‘·T+~? ¬s+&Ée~, yÓTT<ä≥ #]q ø±s¡Tø£Hêï
mìï ôdø£qT¢ ‘·sê«‘· #s¡T‘·T+~?
12 (a) ˇø£ dü+∫˝À 6 |üdüT|ü⁄s¡+>∑T ã+‘·T\T eT]j·TT ø=ìï Ä≈£î|ü#·Ã ã+‘·T\T e⁄HêïsTT. dü+∫qT+&ç
rùd ã+‘·T\˝À Ä≈£î|ü#·Ã ã+‹ dü+uÛ≤e´‘·, |üdüT|ü⁄|ü#·Ã ã+‹ dü+uÛ≤e´‘·≈£î 3 ¬s≥T¢ nsTTq#√
Ä≈£î|ü#·Ãì ã+‘·T\ dü+K´ ø£qT>=q+&ç. n<$<Ûä+>± dü+∫qT+&ç j·÷<äè∫äø£+>± m+|æø£#ùd Á|ü‹
s¡+>∑T ã+‹jÓTTø£ÿ dü+uÛ≤e´‘· ‘Ó\|ü+&ç.
( Ò<ë)
(b) ABC Á‹uÛÑT» osê¸\T es¡Tdü>± (2, 3), (4, 1) eT]j·TT ( − 2, 5). Á‹uÛÑT» uÛÑTC≤\T AB, BC
eT]j·TT CA \ eT<Ûä _+<äTe⁄\T es¡Tdü>± D, E, F \T nsTTq#√, eT<Ûä _+<äTe⁄\‘√ @s¡Œ&
Á‹uÛÑT» yÓ’XÊ\´+ ø£qT>=q+&ç. Ç<$<Ûä+>± ΔABC eT]j·TT ΔDEF yÓ’XÊ˝≤´\ ìwüŒ‹Ô ‘Ó\Œ+&ç.
13 (a) ˇø£ ‘·s¡>∑‹˝À 80 eT+~ $<ë´s¡Tú\≈£î SA-2 |üØø£å À >∑DÏ‘·+˝À e∫Ãq e÷s¡Tÿ\T øÏ+~ Çe«ã&çq$.
á <ä‘êÔ+X+q≈£î bÂq'|ü⁄q´eÁø£+ (zõyéeÁø£+) ^j·T+&ç.
( Ò<ë)
(b) 6 ôd+.MT yê´kÕs¡ú+‘√ ˇø£ eè‘·Ô+ ^j·T+&ç. πø+Á<ä+qT+&ç 10 ôd+.MT <ä÷s¡+˝À>∑\ _+<äTe⁄
qT+&ç eè‘êÔìøÏ ˇø£ »‘· düŒs¡ÙπsK\qT ^∫, yê{Ï bı&Ée⁄\T ø£qT>=q+&ç. ô|’<∏ë>∑s¡dt dæ<ëΔ+‘·+
Á|üø±s¡+ dü]#·÷&É+&ç.
e÷s¡Tÿ\T 0`10 10`20 20`30 30`40 40`50 50`60 60`70 70`80
$<ë´s¡Tú\ dü+K´ 04 06 11 20 16 10 08 05
10
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT
>∑DÏ‘·eTT ù||üsY-II
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 30 숈 bÕs¡Tº ` B >∑]wü e÷s¡Tÿ\T : 10
dü÷#·q\T : 1. bÕs¡Tº B q+<äT nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 4 düe÷<ÛäqeTT\T ø£\e⁄. dü]jÓÆTq düe÷<ÛëqeTTqT m+|æø£#dæ, <ëì nø£åsêìï
Áu≤¬ø≥¢ À sêj·T+&ç.
3. ~~›y‘·\T, ø={Ϻy‘·\‘√ ≈£L&çq düe÷<ÛëqeTT\≈£î e÷s¡Tÿ\T Çe«ã&Ée⁄.
4. nìï Á|üXï\≈£î e÷s¡Tÿ\T düe÷q+.
ôdø£åHé ` IV
dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛäqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1/2 e÷s¡Tÿ πø{≤sTT+#·ã&çq~. 20I
1/2 R 10 e÷s¡Tÿ\T
14. x-nø£å+‘√ <ÛäHê‘·àø£ ~X˝À ø£<äT\T‘·Tqï ˇø£ πsK yê\T ª|μ nsTTq n~ #j·TT ø√D+ ( )
A) 30+ B) 45+ C) 60+ D) 90+
15. ΔPQR ∼ ΔXYZ eT]j·TT PQ : XY = 5:8 nsTTq yê{Ï düs¡÷|ü eT<ä >∑‘· πsK\ ìwüŒ‹Ô ( )
A) 5 : 8 B) 10 : 16 C) 25 : 64 D) 8 : 5
16.
4 4
2 2
sec tan
sec tan
A A
A A
−−
R ................. ( )
A) 0 B) 1
2C) 1 D) 2
17. ˇø£ düú+ã+ jÓTTø£ÿ ˙&É, <ëì m‘·TÔ≈£î 3 ¬s≥T¢ ø£\<äT. nsTTq dü÷s¡T´&ÉT <ëì m‘·TÔ‘√ ( )
#˚j·TT ø√D+
A) 45+ B) 30+ C) 60+ D) 90+
11
18. eT÷&ÉT HêD≤\T πøkÕ] m>∑Ts¡yj·Tã&çq$. nsTTq ø£ dü+ ˇø£ u§s¡TdüT (tail) e#Ã ( )
dü+uÛ≤e´‘·
A) 3
4B)
1
3C)
7
8D)
2
3
19. 25 |ü]o\Hê+XÊ\ dü>∑≥T 40. á dü+<äs¡“¤+˝À ˇø£ |ü]o\Hê+X+ 53 ≈£î ã<äT\T>± 28 >± qyÓ÷<Ó’q~
nsTTq dü]jÓÆTq dü>∑≥T ( )
A) 26 B) 39 C) 41 D) 46
20. Á|üø£ÿ |ü≥+˝À ∠APB = 70o nsTTq ∠AOB = ( )
A) 70+ B) 90+
C) 160+ D) 110+
21. øÏ+~ yêì˝À @πsK, eè‘·Ô+q≈£î πø _+<äTe⁄ e<ä› K+&çdüTÔ+~ ( )
A) yê´dü+ B) düŒs¡ÙπsK C) #Û<äqπsK D) C≤´
22. øÏ+~ yêì˝À @~ nkÕ<Ûä + ? ( )
A) sin θ = 0.5 B) cos θ = 0 C) tan θ = 2 D) sec θ = − 1
23. øÏ+~ yêì˝À @~ dü‘· + ? ( )
A) ‘·s¡>∑‹ e÷s¡Tÿ R
B) ‘·s¡>∑‹ e÷s¡Tÿ R
C) ‘·s¡>∑‹ e÷s¡Tÿ R m>∑Te Vü≤<äT› − ~>∑Te Vü≤<äT›
D) ‘·s¡>∑‹ e÷s¡Tÿ R m>∑Te Vü≤<äT› G ~>∑Te Vü≤<äT›
24. Á|üø£ÿ |ü≥+˝À ∠B n~Ûø£ ø√D+ nsTTq AC2 = ................. ( )
A) AB2 + BC2 − BD2
B) AB2 + BC2
C) AB2 + BC2 + 2BC.DB
D) AB2 + BC2 − 2BC.DB
)P
A
B
O
m>∑Te ne~Û ` ~>∑Te ne~Û
2
m>∑Te ne~Û G ~>∑Te ne~Û
2
A
D B C
)
12
25. øÏ+~ bÂq'|ü⁄q´ $uÛ≤»q+˝À u≤VüAfiø£ ‘·s¡>∑‹ ( )
A) 10`20 B) 20`30 C) 30`40 D) 40`50
26. Á|üø£ÿ|ü≥+˝À u≤Vü≤´eè‘êÔ\ yê´kÕs¡ú+ 7 j·T÷ˆˆ nsTTq n+‘·s¡eè‘·Ô yê´kÕs¡ú+ ( )
A) 7 2 j·T÷ˆˆ B) 7 2 1− j·T÷ˆˆ
C) 7
2 j·T÷ˆˆ D) ( )
14
2 1+ j·T÷ˆˆ
27. kÕ+|òæTø£XÊÁdüÔ |ü⁄düÔø£+˝À 250 ù|J\T ø£\e⁄. j·÷<äè∫äø£+>± @<ì ˇø£ù|Jì m+|æø£ #dæq|ü⁄&ÉT Ä ù|J
dü+K´ dü+|üPs¡íes¡Z+ njT´ dü+uÛ≤e´‘· m+‘·? ( )
A) 8
125B)
3
25C)
3
50D) 1
28. ˇø£ kÕ<Ûës¡D dü+e‘·‡s¡+˝À 53 Ä~yêsê\T e#à dü+uÛ≤e´‘· ( )
A) 52
53B)
1
52C)
1
7D)
6
7
29. øÏ+~ yêìì »‘· |üs¡Ã+&ç. ( )
1) cos (180+θ) ( ) a) cot θ
2) sec (270+θ) ( ) a) cos θ
3) tan (90+θ) ( ) a) cosec θ
A) 1(b), 2(c), 3(a) B) 1(c), 2(b), 3(a) C) 1(a), 2(b), 3(c) D) 1(c), 2(a), 3(b)
30. (0, 0), (1, 0), (0, 3) nH$ @ Á‹uÛÑT»eTTjÓTTø£ÿ osê¸\T ne⁄qT? ( )
A) \+ãø√D Á‹uÛÑT»eTT B) düeT~«u≤VüQ Á‹uÛÑT»eTT
C) düeT~«u≤VüQ \+ãø√D Á‹uÛÑT»eTT D) düeTu≤VüQ Á‹uÛÑT»eTT
31. Á|üø£ÿ |ü≥+˝À eè‘·Ôyê´dü+ jÓTTø£ÿ ¬s+&Ée ∫e] _+<äTe⁄ ( )
A) (2, 3) B) ( − 2, − 3) C) ( − 3, − 2) D) (6, 4)
ej·TdüT‡ 0`10 10`20 20`30 30`40 40`50 50`60
s√>∑T\ dü+K´ 12 09 05 10 25 18
13
32. ΔABC ˝À DE � BC eT]j·TT DE πsK AB ì D e<ä›, AC ì E e<ä› K+&ç+∫q#√ ( )
1) AD
DB R
AE
ED2)
AB
AD R
AC
AE3)
AB
DB R
AD
ED
A) 1-T, 2-T, 3-T B) 1-T, 2-F, 3-T C) 1-F, 2-T, 3-F D) 1-F, 2-F, 3-T
33. h1 eT]j·TT h
2 m‘·TÔ>∑\ ¬s+&ÉT #Ó≥T¢ yê{Ï bÕ<äeTT (yÓTT<ä\T) \T ø£\T|ü>± @s¡Œ&çq πsU≤ ( )
eT<ä _+<äTe⁄ e<ä› 30+ eT]j·TT 60
+ ø√DeTT\T #dæq, yê{Ï m‘·TÔ\ ìwüŒ‹Ô
A) 3 :1 B) 1: 3 C) 3 : 1 D) 1 : 3
14
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT
>∑DÏ‘·eTT ù||üsY I
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 2 >∑+ˆˆ 15 숈 bÕs¡Tº ` A >∑]wü e÷s¡Tÿ\T : 30
dü÷#·q\T : 1. nìï Á|üXï\qT ÁX<äΔ>± #·<äe+&ç.
2. bÕs¡Tº A ≈£î düe÷<ÛëqeTT\qT MTøÏe«ã&çq »yêãT |üÁ‘·+˝À sêj·T+&ç.
3. bÕs¡Tº A q+<äT eT÷&ÉT $uÛ≤>±\T e⁄HêïsTT.
4. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
5. Á|ü‹ »yêãTqT <ädü÷ÔØ>±, ns¡úeTjT´$<Ûä+>± sêj·T+&ç.
6. ôdø£åHé III q+<ä* Á|üXï\≈£î n+‘·s¡Z‘· m+|æø£ ñ+≥T+~.
ôdø£åHé ` I
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1 e÷s¡Tÿ. 4I1 R 4 e÷s¡Tÿ\T
1. 6410log $\Te ø£qT>=q+&ç. ( 2
10log = 0.3010)
2. XSq´dü$T‹øÏ ì»J$‘·+˝À ¬s+&ÉT ñ<ëVü≤s¡D\T Çe«+&ç.
3. ª|üsêe\j·T+μ nq>±H$T?
4. ˇø£ {≤ø°‡øÏ yÓTT<ä{Ï øÏ ÀMT≥sY Á|üj·÷D≤ìøÏ r 40 #=|üq ‘·s¡Tyê‘· Á|ür øÏ.MT ≈£î r 10 #=|üq
#Ó*¢+#·e\dæj·TTqï~. yÓTT<ä{Ï 5 øÏ.MT es¡≈£î es¡Tdü>± #Ó*¢+#·e\dæq kıeTTà\qT sêj·T+&ç.
ôdø£åHé ` II
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 2 e÷s¡Tÿ. 5I2 R 10 e÷s¡Tÿ\T
5. 65 eT]j·TT 117 \ >∑.kÕ.uÛ≤ 65x − 117 nsTTq x $\Te ø£qT>=qTeTT.
6. A = {2, 5, 6, 8}, B = {1, 5, 7, 9} nsTTq n(A ∩ B) eT]j·TT n(A ∪ B) \qT ø£qT>=qTeTT.
15
7. ˇø£ Á‹uÛÑT» ø√DeTT\T x, y eT]j·TT 50+ ø√DeTT\T x, y \ uÛÒ<äeTT 30
+ nsTTq x, y $\Te\qT
ø£qT>=qTeTT.
8. es¡ZdüMTø£s¡D+ ax2 + bx + c = 0 (a≠0, a, b, c∈R) jÓTTø£ÿ eT÷˝≤\ dü«uÛ≤eeTTqT $e]+#·+&ç.
9. πø m‘·TÔ >∑\ ˇø£ dü÷ú|üeTT eT]j·TT X+≈£îe⁄\, uÛÑ÷yê´kÕsêú\T düe÷qeTT. yê{Ï |òüTq|ü]e÷D≤\ ìwüŒ‹Ô
3 : 1 nì ˙e⁄ m˝≤ #Ó|üŒ>∑\e⁄.
ôdø£åHé ` III
dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç. Á|ür Á|üXï≈£î n+‘·s¡Z‘·eTT>± a Ò<ë b m+|æø£
#˚düTø=qe#·TÃqT.
2. Á|ü‹ Á|üXï≈£î 4 e÷s¡Tÿ\T. 4I4 R 16 e÷s¡Tÿ\T
10 (a) A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 6, 8} \T ¬s+&ÉT dü$T‘·T\T nsTTq
(i) (A ∪ B) − (A ∩ B) (ii) (A − B) ∪ (B − A) \qT ø£qT>=qTeTT. @$T >∑eTì+#ês¡T?
( Ò<ë)
(b) es¡ZdüMTø£s¡D+ x2 + 2x − 143 = 0 jÓTTø£ÿ eT÷˝≤\qT, es¡ZeTTqT |üP]Ô#˚j·TT≥ <ë«sê
es¡ZdüMTø£s¡DeTTqT kÕ~Û+# |ü<äΔ‹˝À ø£qT>=qTeTT.
11 (a) ˇø£ bÕsƒ¡XÊ\˝À bÕsƒ¡ $wüj·Tø£ dü+ã+~Û‘· $wüj·÷\˝À n‘·T´qï‘· Á|ü‹uÛÑ ø£qã]∫q yê]øÏ yÓTT‘·Ô+
700 s¡÷bÕj·T\≈£î 7 ãVüQeT‘·T\T Çyê«\ì uÛ≤$+#ês¡T. Á|ü‹ ãVüQeT‹ $\Te <ëìeTT+<äTqï
<ëìøÏ r 20 ‘·≈£îÿe nsTTq Á|ü‹ ãVüQeT‹ $\TeqT ø£qT>=qTeTT.
( Ò<ë)
(b) ˇø£ Ä≥edüTÔe⁄ ns¡ú>√fieTTô|’ ì{≤s¡T>± ì\T|üã&çq X+KTe⁄ e … j·TTqï~. X+KTe⁄ jÓTTø£ÿ
uÛÑ÷´yê´dü+ 6 ôd+.MT. eT]j·TT m‘·TÔ 4 ôd+.MT. nsTTq#√ Ä≥edüTÔe⁄ jÓTTø£ÿ ñ|ü]‘·\
yÓ’XÊ\´eTT m+‘·? (π R 3.14 >± rdüTø=qTeTT)
12. (a) 2 ˇø£ ø£s¡D°j·T dü+K´ nì |üs√ø£å |ü<äΔ‹ <ë«sê ìs¡÷|æ+#·+&ç.
16
( Ò<ë)
(b) #·T≥Tºø=\‘· 80MT. yÓ’XÊ\´eTT 400 #·.MT ñ+&ÉTq≥T¢ ˇø£ Bs¡È#·‘·Ts¡ÁkÕø±s¡ bÕs¡TÿqT ‘·j·÷s¡T
#j·T>∑\e÷? #j·T>∑*–‘ <ëì bı&Ée⁄, yÓ&É\TŒ\qT ø£qT>=qTeTT.
13. (a) ˇø£ es¡Z ãVüQ|ü~ p(x) = x2 − 9 jÓTTø£ÿ πsU≤∫Á‘·eTTqT ^j·TTeTT. πsU≤∫Á‘·+ qT+&ç ãVüQ|ü~ p(x)
jÓTTø£ÿ XSHê´\qT ø£qT>=qTeTT. dü]#·÷&É+&ç.
( Ò<ë)
(b) düMTø£s¡D e´edüú x + y − 16 = 0, x − 2y + 2 = 0 qT πsU≤∫Á‘·|ü<äΔ‹ <ë«sê kÕ~Û+#·+&ç. kÕ<Ûäqô|’
˙ n_ÛÁbÕj·T+ yê´U≤´ì+#·+&ç.
17
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT
>∑DÏ‘·eTT ù||üsY-I
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 30 숈 bÕs¡Tº ` B >∑]wü e÷s¡Tÿ\T : 10
dü÷#·q\T : 1. bÕs¡Tº B q+<äT nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 4 düe÷<ÛäqeTT\T ø£\e⁄. dü]jÓÆTq düe÷<ÛëqeTTqT m+|æø£#dæ, <ëì nø£åsêìï
Áu≤¬ø≥¢ À sêj·T+&ç.
3. ~~›y‘·\T, ø={Ϻy‘·\‘√ ≈£L&çq düe÷<ÛëqeTT\≈£î e÷s¡Tÿ\T Çe«ã&Ée⁄.
4. nìï Á|üXï\≈£î e÷s¡Tÿ\T düe÷q+.
ôdø£åHé ` IV
dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛäqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1/2 e÷s¡Tÿ πø{≤sTT+#·ã&çq~. 20I
1/2 R 10 e÷s¡Tÿ\T
14. ¬s+&ÉT dü+K´\T 144 eT]j·TT 420 \ >∑.kÕ.uÛ≤. 12 nsTTq yê{Ï ø£.kÕ.>∑T. m+‘·? ( )
A) 6040 B) 5040 C) 4200 D) 1440
15. n(A) = 12, n(B) = 5 eT]j·TT A∩ B = φ nsTTq n(A ∪ B) = ................. ( )
A) 17 B) 7 C) 60 D) 0
16. ãVüQ|ü~ 2x2 − 9 jÓTTø£ÿ XSHê´\ yÓTT‘·Ô+ .............. ( )
A) 0 B) 1 C) − 1 D) 2
17. a + b = 5 eT]j·TT 3a + 2b = 20 nsTTq 3a + b R .............. ( )
A) 25 B) 20 C) 15 D) 10
18. n+ø£ÁX‚&Ûç 1
3,
1
2,
2
3, .........
11
6 ˝À >∑\ |ü<ë\ dü+K´ ................... ( )
A) 8 B) 10 C) 12 D) 13
18
19. x ôd+.MT, 6 ôd+.MT eT]j·TT 8 ôd+.MT yê´kÕsêú\T>± >∑\ eT÷&ÉT >√fieTT\qT ( )
ø£]–+#·>± 9 ôd+.MT yê´kÕs¡ú+>± >∑\ >√fieTT>± ‘·j·÷¬s’q~. yÓTT<ä{Ï >√fieTT
yê´kÕs¡ú+ x = ........................
A) 1
4ôd+.MT B)
1
3ôd+.MT C)
1
2ôd+.MT D) 1 ôd+.MT
20. ÁøÏ+~ yêì˝À n+‘·+ø±ì Äes¡ÔqeTjT´ <äXÊ+X_Ûqï+ @~ ? ( )
A) 24
1600B)
171
800C) 2 3
123
2 5× D) 3 2 2
145
2 5 7× ×
21. πsFj·T düMTø£s¡D≤\ »‘· 2x − 3y = 8 eT]j·TT 4x − 6y = 9 @ düMTø£s¡D e´edüú≈£î ( )
#Ó+~q~
A) dü+>∑‘· düMTø£s¡D e´edüú B) ndü+>∑‘· düMTø£s¡D e´edüú
C) ndü«‘·+Á‘· e´edüú D) dü«‘·+Á‘· düMTø£s¡D e´edüú
22. es¡ZdüMTø£s¡D+ ax2 + bx + c = 0 øÏ yêdüÔe eT÷˝≤\T Òe⁄. nsTTq#√ ÁøÏ+~ yêì˝À ( )
@~ dü‘· +
A) b2 − 4ac < 0 B) b2 − 4ac = 0 C) b2 − 4ac > 0 D) b2 − 4ac ≠ 0
23. 4 # ìX‚Ùwü+>± uÛ≤–+|üã& ¬s+&É+¬ø\ dü+K´\T mìï ø£\e⁄ ? ( )
A) 20 B) 16 C) 25 D) 22
24. dü$T‹ A = 1 1 1 1
1, , , , 2 4 8 16
jÓTTø£ÿ ìsêàDs¡÷|üeTT ( )
A) 1
: , y N, y 42
y
x x ε = ≤
B) 1
: , y W, y 42 yx x ε = ≤
C) { } : 2 , y W, y 4yx x ε= ≤ D) 1
: x N, y 5x
ε
≺
25. yÓTT<ä{Ï n uÒdædü+K´\ yÓTT‘·ÔeTT ( )
A) ( )12
nn + B) n2 C) n(n+1) D) [ ]2 ( 1)
2
na n d+ −
19
26. log2(5x+7) = 5 nsTTq x $\Te ( )
A) 5 B) 6 C) 7 D) 10
27. 3 ≈£îØÃ\T eT]j·TT 2 u…+N\ yÓ\ r 1850. 5 ≈£îØÃ\T eT]j·TT 3 u…+N\ yÓ\ ( )
r 2850. nsTTq#√ ˇø£ ≈£îØà eT]j·TT ˇø£ u…+N yÓ\ m+‘· ?
A) r 800 B) r 850 C) r 900 D) r 950
28. ˇø£ r>∑qT ñ|üjÓ÷–+∫ l ôd+.MT bı&Ée⁄, 1 ôd+.MT. yÓ&É\TŒ >∑\ Bs¡È#·‘·Ts¡ÁkÕ\qT ( )
‘·j·÷s¡T#düTÔHêïs¡T. Bs¡È#·‘·Ts¡ÁkÕ\ bı&Ée⁄qT 1 ôd+.MT. #=|üq ô|+#·T≈£î+≥÷ es¡Tdü>±
5 Bs¡È#·‘·Ts¡ÁkÕ\qT ‘·j·÷s¡T#dæq yê{ÏøÏ ø±e\dæq r>∑ bı&Ée⁄ m+‘·?
A) 10(l + 1) B) 10(l + 2) C) 10(l + 3) D) 5(l + 2)
29. ˇø£ |òüTq>√fieTT eT]j·TT ˇø£ |òüTq ns¡ú>√fieTT\T πø dü+|üPs¡í‘·\ yÓ’XÊ\´+qT ( )
ø£*–j·TTqï$. nsTTq yê{Ï |òüTq|ü]e÷D≤\ ìwüŒ‹Ô
A) 3 :1 B) 3 3 : 5 C) 3 3 : 4 D) 1: 3
30. |ü≥+˝À ùw&é #j·Tã&çq ÁbÕ+‘·eTT <ìì dü÷∫düTÔ+~? ( )
A) A − B B) B − A
C) A Δ B D) A ∩ B
31. ÁøÏ+~ yêì˝À @ πsU≤∫Á‘·eTT ˇø£ es¡ZãVüQ|ü~ì dü÷∫düTÔ+~ ? ( )
A) B) C) D)
32. πsU≤∫Á‘·+ qT+&ç ' l ' jÓTTø£ÿ düMTø£s¡D+ ( )
A) x = 2 B) y = 2 C) x = − 2 D) y = − 2
33. ˇø£ |òüTqedüTÔe⁄ jÓTTø£ÿ |òüTq|ü]e÷D+ 21
3V r h= Π nsTTq Ä |òüTqedüTÔe⁄ @~? ( )
A) B) C) D)
A
B
y
x
l
0
-2
r
h
h r
rh
20
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT `
>∑DÏ‘·eTT ù||üsY-II
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 2 >∑+ˆˆ 15 숈 bÕs¡Tº ` A >∑]wü e÷s¡Tÿ\T : 30
dü÷#·q\T : 1. nìï Á|üXï\qT ÁX<äΔ>± #·<äe+&ç.
2. bÕs¡Tº A ≈£î düe÷<ÛëqeTT\qT MTøÏe«ã&çq »yêãT |üÁ‘·+˝À sêj·T+&ç.
3. bÕs¡Tº A q+<äT eT÷&ÉT $uÛ≤>±\T e⁄HêïsTT.
4. nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
5. Á|ü‹ »yêãTqT <ädü÷ÔØ>±, ns¡úeTjT´$<Ûä+>± sêj·T+&ç.
6. ôdø£åHé III q+<ä* Á|üXï\≈£î n+‘·s¡Z‘· m+|æø£ ñ+≥T+~.
ôdø£åHé ` I
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1 e÷s¡Tÿ. 4I1 R 4 e÷s¡Tÿ\T
1. ( − 3, 2), (1, 5) eT]j·TT (11, − 19) \T osê¸\T>± >∑\ Á‹uÛÑT» >∑Ts¡T‘·«πø+Á<äeTT ø£qT>=q+&ç.
2. ÁbÕ<∏ä$Tø£ nqTbÕ‘· dæ<ëΔ+‘·eTTqT ìs¡«∫+|ü⁄eTT.
3. 50 MTˆˆ bı&Ée⁄ >∑\ <ës¡+‘√ ø£≥ºã&çq ˇø£ >±*|ü≥+ uÛÑ÷$T‘√ 60+ ø√D+ #dü÷Ô m>∑Ts¡T#·Tqï~.
nsTTq Ä >±*|ü≥+ uÛÑ÷$TqT+&ç m+‘· m‘·TÔ À ñqï<√ ø£qT>=q+&ç.
4. ¬s+&ÉT HêDÒ\qT m>∑Ts¡yùd Á|üjÓ÷>∑+˝À e#·Tà yÓTT‘·Ô+ |üs¡ ekÕHê\qT sêj·T+&ç.
ôdø£åHé ` II
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 2 e÷s¡Tÿ. 5I2 R 10 e÷s¡Tÿ\T
5. 15 Cot A = 8 nsTTq#√ sin A eT]j·TT sec A \qT ø£qT>=q+&ç.
6. ˇø£ ‘·s¡>∑‹˝À >∑\ q\T>∑Ts¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 72, eTT>∑TZs¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 78
eT]j·TT Ç<ä›s¡T $<ë´s¡Tú\ dü>∑≥T e÷s¡Tÿ\T 80. nsTTq Ä ‘·s¡>∑‹ jÓTTø£ÿ dü>∑≥T e÷s¡Tÿ m+‘· ?
21
7. Á|üø£ÿ |ü≥+ qT+&ç Á‹uÛÑT»eTT ABC eT]j·TT Á‹uÛÑT»eTT CPQ \T
@$<Ûä+>± düs¡÷bÕ˝À $e]+#·+&ç. x $\TeqT ø£qT>=q+&ç?
8. düeTdü+uÛÑe |òüT≥q\T nq>±H$T ? ˇø£ ñ<ëVü≤s¡D Çe«+&ç.
9. ˇø£ >∑&çj·÷s¡+ ì$TcÕ\ eTTfió¢ bı&Ée⁄ 14 ôd+.MT. ˇø£ 1
2 >∑+ˆˆ˝À Ä eTTfió¢ ‹]π> ÁbÕ+‘· yÓ’XÊ\´+
ø£qT>=q+&ç.
ôdø£åHé ` III
dü÷#·q\T : 1. nìï Á|üXï\≈£î »yêãT\T sêj·T+&ç.
2. Á|ür Á|üXï˝À n+‘·s¡Z‘·+>± a Ò<ë b m+|æø£ #düTø=qe#·TÃ.
2. Á|ü‹ Á|üXï≈£î 4 e÷s¡Tÿ\T. 4I4 R 16 e÷s¡Tÿ\T
10 (a) _+<äTe⁄\T (1, − 1), ( − 4, 6) eT]j·TT ( − 3, 5) \T osê¸\T>± >∑\ Á‹uÛÑT»eTT uÛÑTC≤\ eT<Ûä
_+<äTe⁄\qT ø£\T|ü>± @s¡Œ&ÉT Á‹uÛÑT» yÓ’XÊ\´+qT ø£qT>=qTeTT. Ä Á‹uÛÑT» yÓ’XÊ\´+, <ä‘·Ô Á‹uÛÑT»
yÓ’XÊ˝≤´\ ìwüŒ‹Ô ø£qT>=qTeTT.
( Ò<ë)
(b) ˇø£ ≥esY n&ÉT>∑TuÛ≤>∑+ qT+&ç uÛÑeq+ ô|’uÛ≤>∑+ 30+ }s¡ú«ø√D+ #düTÔ+~. uÛÑeq+ n&ÉT>∑TuÛ≤>∑+
qT+&ç ≥esY ô|’uÛ≤>∑+ 60+ }s¡ú«ø√D+ #düTÔ+~. ≥esY m‘·TÔ 30 MT≥s¡T¢ nsTTq uÛÑeq+ m‘·TÔ
ø£qT>=qTeTT.
11 (a) ˇø£ ø£sêà>±s¡+˝Àì 50 eT+~ ø±]à≈£î\ ~qdü] uÛÑ‘· eTT áÁøÏ+~ bÂq'|ü⁄q´ $uÛ≤»ø£ |ü{Ϻø£ À
Çe«ã&çq~.
‘·>∑T |ü<äΔ‹ì m+#·Tø=ì Ä ø£sêà>±s¡+˝Àì ø±]à≈£î\ dü>∑≥T uÛÑ‘· eTT\qT ø£qTø√ÿ+&ç.
C
P Q
A B5
3
3
70)
~qdü] uÛÑ‘· + (r) 200`250 250`300 300`350 350`400 400`450
ø±]à≈£î\ dü+K´ 12 14 8 6 10
22
( Ò<ë)
(b) ˇø£ ô|f…ºq+<äT 1 qT+&ç 90 es¡≈£î Áyêj·Tã&çñqï 90 |òü\ø±\T ñHêïsTT. yê{ÏqT+&ç j·÷<äè∫äø£+>±
ˇø£ |òü\ø±ìï mqTïø=+fÒ <ëìô|’ ÁøÏ+~ dü+K´\T ñ+&ÉT≥≈£î dü+uÛ≤e´‘· m+‘Ó+‘· ?
(i) ¬s+&É+¬ø\ dü+K´, (ii) K∫Ñ· es¡Zdü+K´, (iii) Á|ü<Ûëq dü+K´, (iv) 10# uÛ≤>∑+|üã&ÉT dü+K´.
12 (a) ˇø£ \+ãø√D Á‹uÛÑT»eTT˝À ø£s¡íeTT MT~ es¡ZeTT, $T–*q ¬s+&ÉT uÛÑTC≤\ esêZ\ yÓTT‘êÔìøÏ
düe÷q+ nì ìs¡÷|æ+#·+&ç.
( Ò<ë)
(b) Cosec θ cot θ = a nsTT‘ sec θ = 2
2
1
1
a
a
+−
nì #·÷|ü+&ç.
13 (a) Ç∫Ãq Á‹uÛÑT»eTT ABC øÏ düs¡÷|ü+>± ñ+≥÷, <ëì uÛÑTC≤\≈£î 4
3 ¬s≥T¢ ñ+& nqTs¡÷|üuÛÑTC≤\T
ø£*–q Á‹uÛÑTC≤ìï ì]à+#·+&ç. ìsêàDÁø£eTeTT Áyêj·T+&ç.
( Ò<ë)
(b) 3 ôd+.MT. yê´kÕs¡ú+‘√ ˇø£ eè‘êÔìï ^j·T+&ç. πø+Á<äeTT qT+&ç 5 ôd+.MT. <ä÷s¡+˝À >∑\ _+<äTe⁄
qT+&ç ˇø£ »‘· düŒs¡ÙπsK\qT ^∫ yê{Ï bı&Ée⁄\T ø=\e+&ç. ìsêàDÁø£eTeTT Áyêj·T+&ç.
23
dü+Á>∑Vü≤D≤‘·àø£ eT÷˝≤´+ø£qeTT`3
10e ‘·s¡>∑‹ ` e÷~] Á|üXÊï|üÁ‘·eTT
>∑DÏ‘·eTT ù||üsY-II
ø±\eTT : 2 >∑+ˆˆ 45 숈 bÕs¡Tº ` A & B >∑]wü e÷s¡Tÿ\T : 40
ø±\eTT : 30 숈 bÕs¡Tº ` B >∑]wü e÷s¡Tÿ\T : 10
dü÷#·q\T : 1. bÕs¡Tº B q+<äT nìï Á|üXï\≈£î düe÷<ÛëqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 4 düe÷<ÛäqeTT\T ø£\e⁄. dü]jÓÆTq düe÷<ÛëqeTTqT m+|æø£#dæ, <ëì nø£åsêìï
Áu≤¬ø≥¢ À sêj·T+&ç.
3. ~~›y‘·\T, ø={Ϻy‘·\‘√ ≈£L&çq düe÷<ÛëqeTT\≈£î e÷s¡Tÿ\T Çe«ã&Ée⁄.
4. nìï Á|üXï\≈£î e÷s¡Tÿ\T düe÷q+.
ôdø£åHé ` IV
dü÷#·q\T : 1. nìï Á|üXï\≈£î düe÷<ÛäqeTT\T sêj·T+&ç.
2. Á|ü‹ Á|üXï≈£î 1/2 e÷s¡Tÿ πø{≤sTT+#·ã&çq~. 20I
1/2 R 10 e÷s¡Tÿ\T
14. _+<äTe⁄\T A( − 4, 3) eT]j·TT B(2, 8) \qT ø£*ù| πsU≤K+&É+ô|’ _+<äTe⁄ P(m, 6) ( )
nsTT‘ m $\Te m+‘· ?
A) 1
2B)
3
2C)
2
5
−D)
1
3
15. ΔABC ˝À DE � BC, AD = 6 ôd+.MT., BD = 9 ôd+.MT., ( )
AE = 8 ôd+.MT. nsTTq AC bı&Ée⁄ m+‘· ?
A) 20 ôd+.MT. B) 12 ôd+.MT.
C) 15 ôd+.MT. D) 18 ôd+.MT.
16. |ü≥+˝À Bs¡È#·‘·Ts¡Ádü+ bı&Ée⁄ 20 ôd+.MT. n+‘·]¢œ‘· eè‘êÔ\T ( )
düs¡«düe÷Hê\T. nsTTq ùw&é #j·Tã&çq ÁbÕ+‘· yÓ’XÊ\´+
A) 40 cm2 B) 43 cm2
C) 25 cm2 D) 33 cm2
C
D E
A B
9 cm
6 cm 8 cm
20 ôd+.MT.
24
17. sin2 10o + sin2 15o + sin2 75o + sin2 80o $\Te ( )
A) 0 B) 1 C) 2 D) 3
18.1
2,
2
3,
3
4,
1
6 eT]j·TT
7
12 \ eT<ä >∑‘·eTT m+‘·? ( )
A) 3
4B)
7
12C)
2
3D)
1
6
19. ¬s+&ÉT bÕ∫ø£\qT πøkÕ] $dæ]q|ü⁄&ÉT bÕ∫ø£\ eTTU≤\ô|’ >∑\ n+¬ø\ yÓTT‘·Ô+ 14 ( )
njT´ dü+uÛ≤e´‘·
A) 1
2B) 1 C) 0 D)
2
3
20. ÁøÏ+~ yêì˝À ndü‘· Á|üe#·Hêìï >∑T]Ô+#·+&ç. ( )
A) ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\T>± 1, 1 eT]j·TT 2 \T ñ+&Ée#·TÃ.
B) 1, 2, 3 \T ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\ bı&Ée⁄\T.
C) 4:1 ìwüŒ‹Ô À yÓ’XÊ˝≤´\T >∑\ ¬s+&ÉT #·‘·Ts¡ÁkÕ\ nqTs¡÷|ü uÛÑTC≤\ ìwüŒ‹Ô 2:1
D) 17, 8 eT]j·TT 15 \T ˇø£ \+ãø√D Á‹uÛÑT» uÛÑTC≤\ bı&Ée⁄\T ne⁄‘êsTT.
21. x > 0, y < 0 nsTTq (x, − y) ñ+&ÉT bÕ<äeTT ( )
A) Q1
B) Q2
C) Q3
D) Q4
22. ªθμ jÓTTø£ÿ @ $\Te≈£î tan θ = cot θ dü‘· eT>∑TqT. (θ∈Q1) ( )
A) 60+ B) 45+ C) 90+ D) 0+
23. ªzJyé eÁø£eTTμ qT+&ç @ πø+ÁBj·T kÕúq$\TeqT ø£qT>=+{≤s¡T ? ( )
A) n+ø£eT<ä eT+ B) eT<ä >∑‘·+ C) u≤VüQfiø£+ D) yê´|æÔ
24. R eT]j·TT r yê´kÕsêú\T>± >∑\ @ø£πø+Á<ä eè‘êÔ\ eT<Ûä @s¡Œ&ÉT ÁbÕ+‘· yÓ’XÊ\´+ ( )
A) π (R − r)2 B) π (R2 − r2) C) π (R + r)(R − r) D) π R2 r2
25. ΔABC ˝À ∠B = 90o. θ n\Œø√DeTT. Sin θ = AB
AC nsTTq
AC
BC @ Á‹ø√D$Trj·T
ìwüŒ‹Ôì dü÷∫+#·TqT. ( )
A) cos θ B) tan θ C) sec θ D) cosec θ
25
26. _+<äTe⁄\T A(2a, 4a), B(2a, 6a) eT]j·TT C(2a + 3 a, 5a) \# @s¡Œ&ÉT Á‹uÛÑT»eTT ˇø£ ( )
A) \+ãø√D Á‹uÛÑT»eTT B) düeT~«u≤VüQ Á‹uÛÑT»eTT
C) düeTu≤VüQ Á‹uÛÑT»eTT D) n\Œø√D Á‹uÛÑT»eTT
27. ˇø£ dü+e‘·‡s¡+ »qe] HÓ\˝À X+ø£sY 165 bò Héø± Ÿ‡ #ôdqT. Ä dü+e‘·‡s¡+ »qe] ( )
1e ‘~ XóÁø£yês¡+. Ä HÓ\˝À Ä~yês¡+Hê&ÉT dü>∑≥Tq 7 f…*bò Héø± Ÿ‡ #XÊ&ÉT. $T–*q
s√E\˝À dü>∑≥Tq mìï bò Héø± Ÿ‡ #ôdqT ?
A) 165
31B) 5 C) 7 D)
137
27
28. ˇø£ ãT≥º À >∑\ e÷$T&ç|ü+&É¢ À 90% eT+∫$. j·÷<äè∫äø£+>± Ä ãT≥ºqT+&ç ˇø£ ( )
e÷$T&ç|ü+&ÉTqT mqTïø=+fÒ n~ bÕ&Ó’b˛sTTq e÷$T&ç|ü+&ÉT njT´ dü+uÛ≤e´‘·
A) 9
100B)
1
100C)
9
10D)
1
10
29. 30 ôd+.MT. >∑\ eè‘·Ô|ü]~Û À, 4 #·.ôd+.MT. ÁbÕ+‘· yÓ’XÊ\´+ ÄÁø£$T+# yÓTTø£ÿ\qT ( )
mìï Hê≥e#·TÃ ?
A) 18 B) 750 C) 24 D) 120
30. Á|üø£ÿ |ü≥+˝À ùw&é #j·Tã&çq ÁbÕ+‘·eTT <ìì ÁbÕ‹ì<ä |üs¡TÃqT ( )
A) n~Ûø£ eè‘·ÔK+&ÉeTT B) n~Ûø£ Á‹C≤´+‘·s¡eTT
C) n\Œ eè‘·ÔK+&ÉeTT D) n\Œ Á‹C≤´+‘·s¡eTT
31. nes√Vü≤D zJyé eÁø£eTT ì]à+#·T≥≈£î x`nø£å+ô|’ rdüTø=H$ ( )
A) ~>∑Te Vü≤<äT›\T B) m>∑Te Vü≤<äT›\T C) eT<ä $\Te\T D) bÂq'|ü⁄q´eTT
32. |ü≥+˝À #·÷|æq _+<äTe⁄ P(a, b) eT÷\_+<äTe⁄ qT+&ç >∑\ <ä÷s¡eTT ( )
A) 1
2ab B) 2 2a b+
C) a2 + b2 D) 2 2a b−
33. ΔABC ˝À BD ⊥ AC eT]j·TT ∠B = 90o qT ÁbÕ‹ì<ä |ü]# |ü≥eTT ( )
A) B) C) D)
A Bx
o
x
y
o
B D C
A A
B C B C
D E
A DB
C
A