mathematics

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1. ¥À±ÀßPÉÆÃpAiÀÄ GzÉݱÀåUÀ¼ÀÄ:
• ¸ÁPÀµÀÄÖ ªÉÊ«zsÀå¥ÀÇtð, G¢ÝµÀÖUÀ¼À£ÀÄß ºÉÆA¢PÉÆAqÀAvÉ «µÀAiÀÄUÀ¼À ªÉÄÃ¯É ¥Àæ±ÉßUÀ¼À£ÀÄß ¸ÀAUÀ滸ÀÄ«PÉ.
• «±Áé¸À¤ÃAiÀÄ, ºÁUÀÆ CxÀð¥ÀÇtðªÁzÀ ¥ÀjÃPÀëtUÀ¼À£ÀÄß ¸ÁªÀÄxÁåðzsÁjvÀ eÉÆÃr¸ÀÄ«PÉ.
• ««zsÀ ªÀÄlÖzÀ PÁp£ÀåvÉUÀ£ÀÄUÀÄtªÁV ¥Àæ±ÉßUÀ¼À eÉÆÃqÀuÉ.
• ¤gÀAvÀgÀ ¥Àjòî£ÉUÉ M¼À¥Àr¸ÀĪÀ CªÀPÁ±À ºÉÆA¢gÀ¨ÉÃPÁVzÉ.

2. ¥Àæ±ÀßPÉÆÃpAiÀÄ gÀÆ¥ÀgÉÃSÉ:
• «µÀAiÀÄ «±ÉèõÀuÉ - «µÀAiÀÄUÀ¼À ºÀAaPÉ
• ¥ÀæwWÀlPÀzÀ°è G¢Ý±ÀåªÁgÀÄ ºÀAaPÉ - ¸ÁªÀÄxÁåðªÁgÀÄ ºÀAaPÉ
• ¥Àæ±ÉßAiÀÄ «zsÁ£À ºÀAaPÉ
- §ºÀÄ DAiÉÄÌ (1 CAPÀ)
- QgÀÄ GvÀÛgÀ (2 CAPÀUÀ¼ÀÄ)
- ¢ÃWÀð GvÀÛgÀ (3-4 CAPÀUÀ¼ÀÄ)
• PÀptvÉAiÀÄ ªÀÄlÖ - (¸ÀÄ®¨sÀ, PÀµÀÖ, ¸ÁzsÁgÀt)
• §ºÀÄDAiÉÄÌ GvÀÛgÀ ¥ÀnÖ, ºÁUÀÆ ¸ÀtÚ GvÀÛgÀ ªÀÄvÀÄÛ ¢ÃWÀð GvÀÛgÀUÀ¼À CAPÀ «vÀgÀuÉ.
3. ¥Àæ±ÀßPÉÆÃpAiÀÄ G¥ÀAiÉÆÃUÀUÀ¼ÀÄ:
• ªÉÊW¯Ó W¯Ó W¯Ó W¯Ó¤PÀªÁV ¥Àæ±ÀߥÀwæPÉUÀ¼À£ÀÄß vÀAiÀiÁj¸ÀĪÀ°è ²PÀëPÀjUÉ £ÉgÀªÀÅ.
• ¨ÉÆÃzsÀ£Á UÀÄtªÀÄlÖ ºÉaѸÀĪÀÅzÀÄ.
• ««zsÀ GzÉÝñÀUÀ½UÀ£ÀÄUÀÄtªÁV ¥Àæ±ÀßPÉÆÃp vÀAiÀiÁjPÉ (GzÁ: ¸ÁzsÀ£É, DAiÉÄÌ, ¥ÉÇæªÉÆõÀ£À¯ï ºÁUÀÆ £ÀÆå£ÀvÁ ¥Àj±ÉÆzsÀ£À, EvÁå¢).
• «µÀAiÀÄ «±ÉèõÀuÉAiÀÄ£ÀÄß PÀÆ®APÀıÀªÁV CxÀð¥ÀÇtðªÁV ªÀiÁqÀĪÀÅzÀgÀ°è ²PÀëPÀjUÀÆ ºÁUÀÆ «zÁåyðUÀ½UÀÆ ¸ÀºÁAiÀÄPÀ.
• ²PÀëPÀgÀÄ vÀªÀÄä YõÁÕ£ÀªÀ£ÀÄß ¨ÉÆÃzsÀ£ÁP˱À®åªÀ£ÀÄß ºÉaѹPÉƼÀî®Ä ¸ÀºÀPÁj.
• EµÉÆÖAzÀÄ C£ÀÄPÀÆ®vÉUÀ½gÀĪÀ ¥Àæ±ÀßPÉÆÃpUÀ¼À£ÀÄß ¸ÀAWÀn¸ÀĪÀ°è M¼ÉîAiÀÄ £ÀªÀÄÆ£É ¥Àæ±ÉßUÀ¼À£ÀÄß eÉÆÃr¸ÀÄvÁÛºÉÆÃUÀĪÀÅzÀÄ ªÁrPÉ.
• ¥ÀAiÀiÁðAiÀÄ ¥ÀjÃPÀëtUÀ¼À£ÀÄß ºÉÆA¢¹PÉƼÀî®Ä ¸ÀºÁAiÀÄPÀ.

4. M¼ÉîAiÀÄ ¥Àæ±ÉßUÀ¼À£ÀÄß Dj¸ÀĪÀ°è F CA±ÀUÀ¼À£ÀÄß UÀªÀÄ£ÀzÀ°èqÀĪÀÅzÀÄ ¸ÀÆPÀÛ:
• ¥Àæ±ÉßUÀ¼ÀÄ ¸ÀªÀÄ¥ÀðPÀªÁV «µÀAiÀiÁA±ÀUÀ½UÉ ºÀAaPÉ DVzÉAiÉÄÃ?
• ªÀAiÉÆêÀiÁ£ÀPÀÌ£ÀÄUÀÄtªÁzÀ ¥Àæ±ÉßUÀ¼ÁVªÉAiÉÄÃ?
• ¥ÀgÀ¸ÀàgÀ ªÀÄPÀ̼À°è ¸ÁªÀÄxÀåð ªÀåvÁå¸ÀUÀ¼À£ÀÄß JwÛ vÉÆÃj¸ÀĪÀÅzÉÃ?
• ¥Àæ±ÉßAiÀÄ ¨sÁµÉ ªÀÄPÀ̽UÉ w½AiÀÄĪÀAwzÉAiÉÄÃ?
• §ºÀÄDAiÉÄÌUÀ¼ÀÄ ¸ÀªÀÄAd¸ÀªÁVªÉAiÉÄÃ?
• ¥Àæ§AzsÀ ¥Àæ±ÉßUÀ¼ÀÄ CzÀgÀ ¸ÀÆZÀ£ÉUÀ¼ÀÄ ¸ÀàµÀÖªÁVzÉAiÉÄÃ?
• ªÀÄPÀ̽UÉ ¥ÉÇæÃvÁìºÀzÁAiÀÄPÀªÁVzÉAiÉÄÃ?

5. GvÀÛªÀÄ §ºÀÄ DAiÉÄÌ ¥ÀjÃPÀëtzÀ ®PàëtUÀ¼ÀÄ »ÃVgÀ¨ÉÃPÀÄ:
(qÁ:r.J¸ï.²ªÁ£ÀAzÀ)
• F £ÀªÀÄÆ£É ¥Àæ±ÉßUÀ¼À°è ªÀÄÆ® ªÁPÁåA±À(stem) / ¥Àæ±Éß JA§ ªÉÆzÀ® ¨sÁUÀ ºÁUÀÆ F ¥Àæ±ÉßUÉ ¸ÀÆavÀ 4 DAiÉÄÌUÀ¼ÀÄ EgÀĪÀªÀÅ.
• ¥Àæ±ÉßAiÀÄ ªÀÄÆ®ªÁPÁåA±À ¥Àæ±ÉßAiÀÄ gÀÆ¥ÀzÀ°ègÀĪÀÅzÉà ¸Àj. PÉ®ªÉǪÉÄä C¸ÀA¥ÀÇtð ªÁPÀå«gÀ§ºÀÄzÀÄ, ºÁVzÁÝUÀ C¸ÀA¥ÀÇtð¥ÀzÀ ªÁPÀåzÀ
PÉÆ£ÉAiÀįÉèà EgÀ¨ÉÃPÀÄ.
• 4 DAiÉÄÌUÀ¼ÀÆ ¸À«ÄÃ¥À / GvÀÛgÀUÀ¼ÁVzÀÄÝ MAzÀÄ ªÀiÁvÀæ ¸ÀªÀÄAd¸À GvÀÛgÀªÁVgÀĪÀAvÉ gÀa¸À¨ÉÃPÀÄ. 4 DAiÉÄÌUÀ¼ÀÄ «©ü£Àß «ZÁgÀUÀ½UÉ
ºÉÆA¢gÀ¨ÁgÀzÀÄ.
• F DAiÉÄÌUÀ¼À°è E¸À«UÀ¼À£ÀÄß / CAPÀUÀ¼À£ÀÄß §gÉAiÀÄĪÀÅzÁzÀgÉ CzÀÄ KjPÉ CxÀªÁ E½PÉ PÀæªÀÄzÀ°ègÀ¨ÉÃPÀÄ.
• ¥Àæ±ÉßUÀ¼ÀÄ ¥ÀŸÀÛPÀ¢AzÀ DAiÀÄÝ£ÉÃgÀ ªÁPÀåªÁVgÀ¨ÁgÀzÀÄ ºÁUÀÆ Cw GzÀÝ«gÀ¨ÁgÀzÀÄ. ªÀÄPÀ̼ÀÄ AiÉÆÃa¹ GvÀÛj¸ÀĪÀAvÉ CªÀgÀ
UÀæ»PÉUÀ£ÀÄUÀÄtªÁVgÀ¨ÉÃPÀÄ.
• DAiÉÄÌUÀ¼À°è ¥ÀÅ£À: ¥ÀÅ£À: MAzÉà ¸ÀAUÀw CxÀªÁ ºÉ¸ÀgÀÄ §gÀ¨ÁgÀzÀÄ.
• UÀtÂvÀzÀ ¥Àæ±ÉßUÀ¼À°è PÉêÀ® GvÀÛgÀUÀ¼À£ÀÄß DAiÉÄÌAiÀiÁV PÉÆqÀ¨ÁgÀzÀÄ.
• §ºÀÄ DAiÉÄÌUÀ¼À°è «±Éèö¸ÀĪÀ, PÁgÀtÂÃPÀj¸ÀĪÀ ¸Ë®¨sÀåUÀ½gÀ¨ÉÃPÀÄ.
• avÀæUÀ¼À£ÀÄß CxÀªÁ £ÀPÉëUÀ¼À£ÀÄß §ºÀÄ DAiÉÄÌUÉ §¼À¸À§ºÀÄzÀÄ. (DzÀgÉ ¸ÀªÀÄAd¸ÀªÁVgÀ¨ÉÃPÀÄ).
• §ºÀÄ DAiÉÄÌAiÀÄ ªÀiÁzÀj PÉêÀ® UÀÄgÀÄw¸ÀĪÀ CxÀªÁ ºÉ¸Àj¸ÀĪÀ ¸ÁªÀÄxÀåðªÀ£ÀÄß ªÀiÁvÀæ ¥ÀjÃQë¸ÀÄvÀÛzÉ J£ÀÄߪÀÅzÀÄ vÀ¥ÀÅöà PÀ®à£É.
• ¨sÁµÉUÀ¼À°è ¨sÁµÁP˱À®å ¥ÀjÃQë¸À®Ä ¥ÀoÉåÃvÀgÀ «µÀAiÀÄPÉÆlÄÖ UÀæ»PÉ ªÀÄvÀÄÛ C©üªÀåQÛvÀéªÀ£ÀÄß ¥ÀjÃQë¸ÀvÀPÀÌzÀÄÝ.

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************









List of Abbreviations Used
Part I Multiple Choice Questions
Part II Short and Long Answer type Questions
Abbreviations Meaning Item Number
Code
Meaning
Languages KF Kannada First Language
L.No Lesson Number KS Kannada Second/Third Language
PR Prose EF English First Language
PO Poem ES English Second Language
Gr Grammar HF Hindi First Language
Comp Comprehension HT Hindi Third Language
Core Subjects SF Sanskrit First Language
Ch.No Chapter Number ST Sanskrit Third Language
B Biology U Urdu
Social Studies Ma Marathi
H History Ta Tamil
C Civics Te Telugu
G Geography M Mathematics
E Economics SC Science
SS Social Studies
Obj Objectives
UÀ UÀzÀå
K Knowledge
¥À ¥ÀzÀå
Languages
G G¢ÝµÀÖ
C Comprehension
YõÁÕ YõÁÕ£À÷
A Appreciation
¨sÁ ¨sÁµÉ
E Expression
UÀæ UÀæ»PÉ
Core Subjects
¥Àæ ¥Àæ±ÀA¸É
U Understanding
C C©üªÀåQÛ
A Application
PÀ.ªÀÄlÖ PÀp£ÀvÉAiÀÄ ªÀÄlÖ
S Skill
¸ÀÄ ¸ÀÄ®¨sÀ
Diff.level Difficulty level
¸Á ¸ÁzsÁgÀt
E Easy
PÀ PÀµÀÖ
A Average
G G¢ÝµÀÖ
D Difficult


D.S.E.R.T
#4, 100 fT ring road, Banashankari III stage, Bangalore – 85
Sample Items of X Standard Question Bank Subject: Mathematics
o:r I Part I
Item
No.
Questions Ch.No Obj Key Diff.
Level
M001
· ct .: / - . ·o.·c.¬ = t - ^. ¯c..¬.¬ .. ¬ · c· - (P∪Q)∪R = R∪(P∪Q)
A. · ¬ ¬ : =. ¯c..¬. B. ..:.t ¯c..¬. C. ¬ c¬ : =. ¯c..¬. D. .¬.:/o=.. . ¯c. .¬.
Name the law that is symbolically stated as (P∪Q)∪R = R∪(P∪Q)
A. Associative Law B. Distributive Law C. Commutative Law D. De Morgan’s Law



1 K C E
M002
/ ~ A = {1,2,3,4,5}, B={0,1,2,3,4} ¬.:. / ~ C= {-2, -1, 0, +1, +2} :¬ c , :o./ ~¬ t - ^. c..:¬ / ~/ -
.¬ / ~¬:^¬ ¯
A. B ¬.:. C B. A ¬.:. C C. A ¬.:. B D. A, B ¬.: . C
If set A = {1,2,3,4,5}, B={0,1,2,3,4} and C= {-2, -1, 0, +1, +2},empty set is a subset of which of the following sets?
A. B and C B. A and C C. A and B D. A, B and C



1 K D E
M003

t - ^. ¬ .. t / - . c..:¬¬. (B-A) .. ¬.¯: ·.: ¬ ¯

Which of the following Venn diagrams represents B-A?





1



U



D



E

Item
No.
Questions Ch.No Obj Key Diff.
Level
M004
PÉÆnÖgÀĪÀ ªÉ£ï£ÀPÉëUÀ¼À°è PÀ£ÀßqÀ ªÀÄvÀÄÛ EAVèµï ¢£À ¥ÀwæPÉUÀ¼À£ÀÄß NzÀĪÀªÀgÀ ¸ÀASÉåAiÀÄ£ÀÄß vÉÆÃj¸ÀÄvÀÛzÉ. EªÀÅUÀ¼À°è AiÀiÁªÀ avÀæªÀÅ JgÀqÀÄ
¨sÁµÉUÀ¼À°è NzÀĪÀªÀgÀ ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä ¸ÀºÁAiÀÄPÀªÁVzÉ?

Given venn diagrams shows the number of people who read Kannada and English newspapers. Which
diagram helps in finding the number who read both the news papers?


Given Venn diagrams shows the number of people who read Kannada and English newspapers. Which diagram
helps in finding the number who read both the news papers?








1



A



C E
M005 U={0, 1, 2, 3, 4, 5,6}, A= {0,2,4} B= {0,2,3,5} :¬ c (A∪ B)

/ ~¬
A. {1, 6} B. {0, 2, 4} C. Ø D. {0,2,3,5}
If U={0, 1, 2, 3, 4, 5,6}, A= {0,2,4} B= {0,2,3,5} (A∪ B)

is :
A. {1, 6} B. {0, 2, 4} C. Ø D. {0,2,3,5}



1 U A A
M006 t - ^. · c.:/ ~/ - . c. .:¬¬. :.. c..:^¬ ¯
A. 4, 5, 7, 1, 13 B. 4, 3, 4, 3, 4 C. 10, 8, 3, 2, 1 D. 1, 4, 3, 5, 2
Which of the following set of numbers form a sequence?
A. 4, 5, 7, 1, 13 B. 4, 3, 4, 3, 4 C. 10, 8, 3, 2, 1 D. 1, 4, 3, 5, 2



1 K B E
E K

Item
No.
Questions Ch.No Obj Key Diff.
Level
M007 4+7+10+13+-----+ n :.. c.. .c.: . c.. ¬ ¬
A. 19 B. 28 C. 40 D. 50
The ninth term of the series : 4+7+10+13+-----+ n
A. 19 B. 28 C. 40 D. 50



1 K B A
M008 t- ^. c..:¬ ·o::c¬ , · ¬.:c: c :.. c.. n. . ¬ ¬ ¬ .. t c¬...c...¬ .¬.¯
A. T
n
= a + n-d B. T
n
= a + (n-1)d C. T
n
= a (n-1)d D. T
n
= a + n-1 d
Which of the following is the formula to find the n
th
term of an arithmetic progression?
A. T
n
= a + n-d B. T
n
= a + (n-1)d C. T
n
= a (n-1)d D. T
n
= a + n-1 d


1 K B E
M009
.c¬. · ¬.:c: c :.. c.. ¬o¬ .. ¬ ¬ 3 ¬.:. ·:¬.:. ¬ ::· 5 :¬:/ , n. . ¬ ¬ ¬,
A. n- 2 B. 5n -2 C. 5n +8 D. 3n
The first term of an A.P is 3 and common difference is 5 then the n
th
term is
A. n- 2 B. 5n -2 C. 5n +8 D. 3n


1 S B E
M010 t - ^. c..:¬¬. ¯.¬:¬ / ~ : · c. c¬ ¬:^¬ ¯
A. S
n
+ T
n
= S
n-1
B. S
n
– S
n+1
= T
n
C. S
n
– S
n-1
=T
n
D. S
n
+ T
n
= S
n+1
Which of the following is a true mathematical relation?
A. S
n
+ T
n
= S
n-1
B. S
n
– S
n+1
= T
n
C. S
n
– S
n-1
=T
n
D. S
n
+ T
n
= S
n+1




1 K C A
M011 .c¬. ¬.:: t c... -¬ c ·-:c: c·¬ ¬.:: t / · ¬..:¬ c -¬. = ¬.::t c..:/.: ¬ .
A. -¬ ·:.. B. t c.·:.. C. -· ¬.... D. · ¬....
If a matrix is equal to its transpose then the matrix is:
A. Row B. Column C. Skew symmetric D. symmetric

1 K D E

Item
No.
Questions Ch.No Obj Key Diff.
Level
M012 x ¬.:. y / - c..:¬ . c / -. ¬.:: t 1 x 3 c.... · ¬.... ¬.::t ¬.:¬.¬¬.¯
2 3 4
3 y 5

A. 3, 3 B. 1, 5 C. 2, 4 D. 4, 2

What values of x and y makes the matrix 1 x 3 a symmetric matrix?
2 3 4
3 y 5

A. 3, 3 B. 1, 5 C. 2, 4 D. 4, 2

1 U C E
M013 .c¬. · ¬.:c: c :.. c... T
10
=20 ; T
20
=10 :¬ c ·:¬.:. ¬ ::· .¬.¯
A. 2 B. 15 C. +1 D. –1
If T
10
=20 and T
20
=10 in an A.P, what is the common difference?
A. 2 B. 15 C. +1 D. -1


1 U D A
M014
. . ¬./ . ¬ c..·. , . . : c¬ c.. ¬ c..·. ¬.:. . . ¬ c..·. :¬/ - c: · ¬.:c: c :.. c... ¬ . . . ¬ c..·. 40,
¬:/o . . ¬./ . ¬ c..·. 10 ¬ ¬ =/ -:¬ c , . . : c¬ c.. ¬ c..· ¬.¯
A. 50 B. 60 C. 70 D. 80
My son’s age, father’s age and my age are in AP. If my age is 40 and my son’s is 10, what is the age of my father?
A. 50 B. 60 C. 70 D. 80


1 A C A

Item
No.
Questions Ch.No Obj Key Diff.
Level
M015
A+I = 2 1 :¬:/ , ¬.::t A / · ¬..:¬.¬.,
1 0

1 0 1 1 1 0 1 1
A. 0 1 B. 1 -1 C. 0 -1 D. 0 -1


If A+ I = 2 1 then, matrix A is equal to
1 0

1 0 1 1 1 0 1 1
A. 0 1 B. 1 -1 C. 0 -1 D. 0 -1 1 S B A

M016 t¬. c.o... c.. -¬ =¬ .. to¬.¬ ¬ .-t
A. :o..:c¬ c o.:: ¬ o/ - .. :c·.¬¬. B. ...c... c.¬ ¬o¬/ - .. :c·.¬¬.
C. t:¬.. .. . . c.¬ .~ / - :o.¬ ¬ D. /c¬:.c..¬ . . ¬.· t / - :c..
The statement which gives the meaning of permutation is :
A. Picking flowers in the rose garden B. Choosing different flowers in a basket
C. Arrangement of colours in a rainbow D. Selecting the books in a library




2




K




C




E
M017
5 ..¬ ¬.· t / - .. . .c . .c c..c... :o..·.¬¬ .. ../ ·o.· .¬.¬.¯
A.
5
P
2
B.
5
P
3
C.
5
P
4
D.
5
P
5

Arrangement of 5 different books in different ways can be denoted as:
A.
5
P
2
B.
5
P
3
C.
5
P
4
D.
5
P
5
2 K D E

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M018
n
C
8
=
n
C
12
:¬:/ n = 20 :¬ .. c -· .. .¬ c.o.^·.¬ · ...t c ~
A.
n
C
1
= n B.
n
C r = nPr /r! C.
n
C
r
=
n
C
n-r
D.
n
C
n
= 1
If nC
8
= nC
12
then n = 20. this can be calculated using the relation:
A.
n
C
1
= n B.
n
C r = nPr /r! C.
n
C
r
=
n
C
n-r
D.
n
C
n
= 1



2 K C A
M019
nC
15
= nC
11
. . ‘n’ . . c c.... t c¬...c...¬ ¬o¬ . ¬ c: nCr .. nC
n-r
/ ¬ c¬ .=·.¬¬. .c ¬ . . ¬ c:
A. n+15=n+11 B. 15=n+11 C. 15=n-11

D. 11= n-15
nC
15
= nC
11
to find the value of ‘n’ the first step is converting nCr into nC
n-r.
Second step is:
A. n+15=n+11 B. 15=n+11 C. 15=n-11

D. 11= n-15 2 K C E
M020 :c. .. c . -:o.t . o ... = /.c.¯c¬ -: o.t . .. · .c·¬ c: 4 .. c .. .¬. .¬ / - . :c· .¬.¬.¯
A. 10 B. 15 C. 20 D. 60
Ashok is one among 6 people. In how many ways can 4 people be selected from them, so as to include Ashok?
A. 10 B. 15 C. 20 D. 60 2 K A A
M021
to.c.¬ c..:¬ ¬ .-t / -. nCr = nC
n-r
¯.c¬ . c.... -..· c·.¬¬.¯
A. 10C
8
= 10C
4
B. 10C
8
= 10C
2
C. 10C
8
= 10C
3
D. 10C
5 =
10C
2

Which of the following satisfy the relation nCr = nC
n-r
?
A. 10C
8
= 10C
4
B. 10C
8
= 10C
2
C. 10C
8
= 10C
3
D. 10C
5 =
10C
2
2 K B E
M022
7 .~ / -c¬ ¬.¬ .¬ .o ¬.. c:¬ .=· ¬ ..¬ ¯: =¬ .~ / - .. · c¬oc¬.¬ c: 210 ¬ ./ - ..
¬.:¬ .¬.¬:¬ c ¬ . ¬ .¬ . . .~ / - · c.
A. 2 B. 3

C. 4 D. 5
Among 7 colours 210 different flags are formed with a certain equal number of colours without repetition. Number of colours
in each flag is:
A. 2 B. 3

C. 4 D. 5 2 A B A

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M023 nP
2
= 2 ×
n-1
P
3
, :¬cc¬ n(n-1) = 2 × -----------. :. : .¬o.^c.¬ ¬ ¬ ¬
A. n(n+1) (n+2) B. n(n-1) (n-2)

C. (n-1) (n-2) (n-3) D. (n-1) (n) (n+1)
nP
2
= 2 ×
n-1
P
3
, therefore n(n-1) = 2 × -----------. Here the missing term is:
A. n(n+1) (n+2) B. n(n-1) (n-2)

C. (n-1) (n-2) (n-3) D. (n-1) (n) (n+1) 2 A C A
M024
5 ..¬ ¯¬ c../ -. ¬.:. 4 ..¬ ¬:t c ~ ¬.· t / - .. .c¬ . c..c.. ¬.· t / -. ../ :c.¬ c: t ¬:.. .
:o..·¬:/ ·:¬¬:/.¬ :o.¬ ¬ / - .¬ / - · c.
A. 5! + 4! B. 5! × 4!

C. 5! + 4! + 2! D. 5! × 4! × 2!
5 different dictionaries and 4 different grammar books are arranged in a shelf such that same books are together. Number of
arrangements are:
A. 5! + 4! B. 5! × 4!

C. 5! + 4! + 2! D. 5! × 4! × 2! 2 U D D
M025 5C
2
. c c.... t c¬. ..c...¬:/ -..· c·c.¬ : ¬. ¬ c: ¬ .. /.c..·
¬ c: 1 = 5! . ¬ c: 2 = 5! ¬ c: 3 = 5x4x3x2x1 ¬ c: 4 = 10
5-2! 3! 3x2x1
A. ¬ c: 1 B. ¬ c: 2

C. ¬ c: 3 D. ¬ c: 4
Identify the wrong step while finding the value of 5C
2
:
Step 1 = 5! . Step 2 = 5! Step 3 = 5x4x3x2x1 Step 4 = 10
5-2! 3! 3x2x1
A. Step 1 B. Step 2

C. Step 3 D. Step 4 2 A A A
M026
.c¬. -t. · c¬ ¬ . 10 : c¬ / -. .:/ ¬ .· .. ¬ . ¬. : c¬ ¬ .c ¬ c ¬. .:c :: c : c¬ ¬ o¬ . :¬ . .t:¬ c ,
:.¬ :./ - · c.
A. 2×
10
P
2
B. 2×
10
C
2
C. 2+
10
P
2
D. 2+
10
C
2

In a cricket league there are 10 teams competing. Each team has to play with every other team twice. The number of games to
be played is :
A. 2×
10
P
2
B. 2×
10
C
2
C. 2+
10
P
2
D. 2+
10
C
2
2 U B A

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M027
‘n’ .:¬./ -c.¬ .¬.. ..¬ . . t ~=/ - · c. [
n
c
2
– n] t ~=/ - .. .- /oc¬ c: 10 c ..::c¬ / -¬c :
.¬...::t.c...


A. ¬ c÷ ... B. ¬ ¬..

C. -¬... D. ¬ : ...
A polygon of ‘n’ sides has [
n
c
2
– n] diagonals. If number of line segments including diagonals are 10, the polygon is:
A. Pentagon

B. Hexagon

C. Octagon

D. Decagon

2 U A A
M028
5 · ¬.:c: c c .. / - /.c¬ .. 3 · ¬.:c: c c .. / -. t : c·¬:/ .c.:/.¬ · ¬.:c: c ÷ :...=./ - · c.
A. 120

B. 60 C. 30 D. 15
Number of parallelograms that can be formed by a set of 5 parallel lines intersecting with 3 other parallel lines are:
A. 120

B. 60 C. 30 D. 15 2 S C A
M029
.¬. .. ./¬ ¬ .:.. t¸/ - . , ¬ c¬ , ÷ t, : c: ¬.:. ¬ ¬/ -¬ . :c: ¬ 12 ./¬ / - .. ¬.:¬ . .t:¬ c t¸/ - . .
.¬/ - .. ¯¬ =.· .¬.¬:¬ .¬ / - .. ../ ¬.¯: · .¬.¬.
A. 4P
1
B. 4P
2
C. 4P
3
D. 4P
4

An idol of Vishnu has a mace, chakra, shanka and padma in each of the four hands. To make 12 such idols, the number of
ways in which the symbols in the hands have to be manipulated is represented as:
A. 4P
1
B. 4P
2
C. 4P
3
D. 4P
4
2 A B A
M030 σ = ¬· c ¬ c.. .÷ .. , = ¬:t¬ ·o.·.¬¬.
A. ¬.:. t .÷ .. B. ¬.:.=. /.¬:ct C. · c:· c D. · c:· c .÷ ..
The expression σ = variance, represents:
A. Standard deviation B. Coefficient of variation C. Mean D. Mean deviation 3 K A E
M031 ¬ /:=c: c 30-34 c ¬.¬ .c¬.
A. 30 +34 B. ½ ( 30 + 34) C. ½ ( 34 -30) D. 34 -30
Mid point of the class interval 30 – 34 is:
A. 30 +34 B. ½ ( 30 + 34) C. ½ ( 34 -30) D. 34 -30 3 K B E

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M032 to.c.¬ ¬ :: c: / - .. .¬ c.o.^·toc¬. ¬.:. t .÷ .. c.... c -·. N= 10, Σfx = 100 , Σfd
2
= 210
A. 4.6 B. 5 C. 2.1 D. 21
Using the given data, calculate standard deviation N= 10, Σfx = 100 , Σfd
2
= 210
A. 4.6 B. 5 C. 2.1 D. 21 3 S A E
M033 = t - ^. ¬ .-t / - . c..:¬¬. ¬.:.=. /.¬:ct t · c. c¬ ¬.. ¯
A. ·:¬.:.¬:^ : .t ¬: c..c... ¬ .- .¬.: ¬ . B. ¬ c .. :c.¬ . ·:¬ .t -- : c.. c..c. ..
C. :t ¬.:. / -. ¬ ¬ c¬.:~¬:^ D. t .c:.c.. ¬¬ . c.. -- :
Which of these statements is not related to co-efficient of variation
A. generally expressed in percentage B. relative measure of dispersion
C. independent of units D. measure of central tendency 3 U D E
M034 .c¬. ::c c.. 9. : c / .c.. A ¬.:. B · t . / -. / ~ : ¬ . / -·c.¬ · c:· c -ct / -. t¬.¬:^ 34.5 ¬.:. 28.5
:^¬., ¬ .:. t .÷ .. ¬ 6.21 ¬.:. 4.56:¬. , c..:¬ · t . ¯. ·:¬ . c... -·: : ¬ ÷. , t:c ~ .t c·
A. · t . A B. · t . B C. · t . A ¬.:. B .c ¬o D. · t . A ¬.:. B .c ¬ c . .c¬o -.
If the arithmatic mean in maths of a 9
th
std., A & B sections in a school are 34.5 and 28.5 respectively and the Standard deviation
are 6.21 and 4.56 respectively, in which section is the achievement unstable?
A. Section A B. Section B C. Both section A and B D. Neither section A nor section B 3 U A A
M035 ‘n’ ¬.-./ - · c:· c:.c¬:¬ .÷ .. / - ¬o: ¬ , c..:¬:/ .o
A. -1 B. 0 C. +1 D. 1-c: -: t
The sum of deviation of a set of ‘n’ values from the arithmetic mean is always :
A. -1 B. 0 C. +1 D. more than 1 3 K B A
M036 A, B ¬.:. C : c / ./ - -ct / - .. to¬ c:^¬ . : : c / ./ - .÷ . ¬¸.¬ : c.... .-c...., .¬ c. o.^· .¬.¬:¬.¬.
A. ¬.¬ t .÷ .. B. ¬.:.=. /.¬:ct C. ÷ :.¬ =t .÷ .. D. ÷ :.¬ =t .÷ .. c.. / ~t
Marks of three classes A, B and C are given. To find the heterogeneity of classes, the measure used is:
A. Mean deviation B. Coefficient of variation C. Quartile deviation D. Coefficient of quartile deviation 3 U B A

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M037 1,2,3,4,5 ¬.:. t .÷ .. c. .. 1.4 :¬ c , 11, 12, 13, 14, 15 / - ¬.:. t .÷ .. c...
A. 1.4 B. 2.8 C. 14 D. 28
If the standard deviation of 1,2,3,4,5 is 1.4, then the value of standard deviation of 11, 12, 13, 14, 15 is:
A. 1.4 B. 2.8 C. 14 D. 28 3 U A E
M038 .c¬. :¬ : =¬.:.c¬ , .. .¬::=c... X, d ¬.:. d
2
/ - .. t c¬ ...c...:: . . ¬.:. t .÷ .. c.... t c¬.
..c.... .:¬ c -· . .t:¬ ¬ c: ¬
A. Σfd
2
B. Σfd
2
C. √ Σfd
2
D. fd
2

N N
A student finds X, D and D
2
of a given frequency distribution. The next step in finding the S.D is to calculate.
A. Σfd
2
B. Σfd
2
C. √ Σfd
2
D. fd
2

N N 3 U D A
M039 .c¬. /.c.. .. c ¬ c..· .. :¬ : =¬.c... ¬. ¬.:¬ c:^¬ . :¬ c ¬ /:=c: c ¬ .. ¬ . ·¬:/ , = t - ^. ¬/ - .
c..:¬¬. ¬ ÷: /.: ¬ ¯
A. ... ¬ /:=c: c / - · c. B. .. c ¬ c..·.
C. ... :¬ : =ct: D. ¬ /:=c: c / - .- ^. :¬ .
The age of a set of people is tabulated in the form of a frequency distribution. Which one of the following increases, when the
size of the class interval is increased?
A. total number of class intervals B. ages of people
C. total frequency D. frequency within the class interval 3 U D D
M040 t - ^. ¬/ - . c..:¬¬. ‘3P’ c.... ·:¬.:. -¬ ¬ : =. ¬:^ ¬ oc:c.¬:. ¯
A. 3P
3
B. 6P
2
C. 9P
1
D. 12P
0

Which of the following cannot have ‘3P’ as a common factor?
A. 3P
3
B. 6P
2
C. 9P
1
D. 12P
0
4 K D E

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M041 ax
2
-a
3
¬.:. bx-ab / - ¬ .¬ : ¬. ·:¬.:. -¬ ¬ : =. ¬
A. (x+a)

B. (x-a)

C. (x
2
-a
2
)

D. (x
2
+a
2
)
Highest common factor of ax
2
-a
3
and bx-ab is:
A. (x+a)

B. (x-a)

C. (x
2
-a
2
)

D. (x
2
+a
2
) 4 K B E
M042 x
3
y
4
z
6
¬.:. x
6
y
2
z
4
/ - ..·:.-. ¬
A. x
3
y
4
z
6
B. x
3
y
2
z
4
C. x
6
y
4
z
6


D. x
6
y
4
z
4

The L.C.M. of x
3
y
4
z
6
and x
6
y
2
z
4
is :
A. x
3
y
4
z
6
B. x
3
y
2
z
4
C. x
6
y
4
z
6


D. x
6
y
4
z
4
4 K C E
M043 ¬..·:.- ¬ .. t c¬...c...., 2x
4
– x
2
+ 3x
3
+ 1 .../.÷¬ .. .c ¬.to- .¬ · cc..:¬ t ¬.
A. 2x
4
+3x
3
–x
2
+1 B. 2x
4
-3x
3
–x
2
+1 C. 2x
4
+3x
3
–x
2
+0x+1 D. 2x
4
+3x
3
–x
2
+x+1
Correct arrangement of terms of the expression 2x
4
– x
2
+ 3x
3
+ 1 to find HCF is:
A. 2x
4
+3x
3
–x
2
+1 B. 2x
4
-3x
3
–x
2
+1 C. 2x
4
+3x
3
–x
2
+0x+1 D. 2x
4
+3x
3
–x
2
+x+1 4 K C E
M044 5x -10 ¬.:. 5x
2
-20 / - ¬..·:.-.¬
A. x-2 B. 5(x-2) C. 5x D. 5
HCF of 5x -10 and 5x
2
-20 is
A. x-2 B. 5(x-2) C. 5x D. 5 4 S B E
M045 t - ^. ¬/ - . c..:¬¬., ab (a+b)+bc(b+c)+ca(c+a) / ·:.s:õc.:Oc
A ∑ab (a+b) B. ∑c
2
(a+b)

C. ∑a
2
(b+c)

D. ∑b
2
(a+b)
Which of the following is not equal to ab (a+b)+bc(b+c)+ca(c+a)?
A ∑ab (a+b) B. ∑c
2
(a+b)

C. ∑a
2
(b+c)

D. ∑b
2
(a+b) 4 S D A
M046 ∑a=0 :¬:/ , ∑a
3
¬
A 0 B. abc

C. 3abc D. a
3
+b
3
+c
3
If ∑a=0, then ∑a
3
will be:
A 0 B. abc

C. 3abc D. a
3
+b
3
+c
3
4 S C A

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M047 ab
2
–ac
2
–a
2
b +bc
2
–cb
2
+ca
2
.. Σ · ct .: ¬ .. .¬ c.o.^· .c :.c
a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) d) Σ b(a-b)
Write ab
2
–ac
2
–a
2
b +bc
2
–cb
2
+ca
2
using Σ notation:
a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) d) Σ b(a-b) 4 S B E
M048 t - ^. ¬/ - . c..:¬¬ .. a
3
+b
3
+c
3
+3ab(a+b) / to.¬:/ , -¬. ÷ -.c.. · ¬....c..:/.: ¬ ¯
A bc(b+a)+ca(c+a) B. 3bc(b+c)+ca(c+a)

C. 3 [bc(b+c)+ca(c+a)] D. 3abc [(b+c) + (c+a)]

Which of the following has to be added to a
3
+b
3
+c
3
+3ab(a+b) to make it cyclically symmetric?
A bc(b+a)+ca(c+a) B. 3bc(b+c)+ca(c+a)

C. 3 [bc(b+c)+ca(c+a)] D. 3abc [(b+c) + (c+a)] 4 U C A
M049 ¬.oc. · c. / - ¬o: ‘¯’ :^¬ ¬.:. : ¬.oc. · c./ - ¬ . / - ¬o: ¬ 36 :¬ c , : · c./ -
/.~..¬
A. 6 B. 12 C. 20 D. 30
If the sum of three numbers is zero and sum of their cubes is 36, then the product of three numbers is:
A. 6 B. 12 C. 20 D. 30 4 U B E
M050 (a-b)
2
=0 :¬:/ , = t - ^. c..:¬ · c.c¬ ¬¯.¬:/.: ¬ ¯
A. 2(a
2
+b
2
) =(a+b)
2
B. 2(a
2
+b
2
) =(a-b)
2
C. 2(a
2
-b
2
) =(a+b)
2
D. (a
2
-b
2
) =(a-b)
2

When (a-b)
2
=0, which of the following relations become true?
A. 2(a
2
+b
2
) =(a+b)
2
B. 2(a
2
+b
2
) =(a-b)
2
C. 2(a
2
-b
2
) =(a+b)
2
D. (a
2
-b
2
) =(a-b)
2
4 U A A
M051 (x
2
+4x+4) (x
2
+6x+9) c ¬ / =¬.o./ - . c c.... t c¬...:.c
A. x
2
+5x+6 B. x
2
+6x+5 C. x
2
-5x+6 D. x
2
+5x-6
Find the square root of (x
2
+4x+4) (x
2
+6x+9) :
A. x
2
+5x+6 B. x
2
+6x+5 C. x
2
-5x+6 D. x
2
+5x-6 4 S A E

Item
No.
Questions
Ch.No Obj Key
Diff.
level
M052 1) √2 2) √12 3) √18 4) √200 = t c ~ / - . · ¬.co¬ t c ~ / -.
A. 1,2,3 B. 2,3,4 C. 1,2,4 D. 1,3,4
Like surds among the following are 1 ) √2 2) √12 3) √18 4) √200
A. 1,2,3 B. 2,3,4 C. 1,2,4 D. 1,3,4 4 K D A
M053 x √y = √80:¬ c , :/ ‘y’. . c c...
A. 4 B. 5 C. 8 D. 10
If x √y = √80, then the value of ‘y’ will be:
A. 4 B. 5 C. 8 D. 10 4 S B E
M054 2x√ x . -t c ~ .t:c t -¬ ¬ : =. ¬
A. 2x√ x B. 2x + √ x C. 2x - √ x D. √ x
Rationalizing factor of 2x√ x is
A. 2x√ x B. 2x + √ x C. 2x - √ x D. √ x 4 K D A
M056 .c ¬ . . ¬:: ¬ . c.¬ .c¬. -¬ t ¬ ¬ ¬ .o- /oc¬ .c¬. .¬.¬ ¬ ..: o.- c.... ../ c¬.
t c c...¬.¬..
A. :¬ ¬ ..:o.- B. · c - .¬.¬ ¬ ..:o.- C.¬ / = .¬.¬ ¬ ..:o.- D. .¬.¬ ¬ ..:o.-
A polynomial of degree two, in one variable is called:
A. a binomial B. a linear polynomial C. a quadratic polynomial D. polynomial 5 K C E
M057
¬ / =· ...t c ~¬ :¬ : = co¬ ¬:¬ ax
2
+bx+c=0 ¬ . b=0 :¬ c .c.:/.¬ · ...t c ~¬
A. :.¬ ¬ / =· ...t c ~ B. ..: ¬ / =· ...t c ~ C. . .c D. · c -
In the standard form of the quadratic equation ax
2
+bx+c=0, if b=0 then the resulting equation is:
A. Pure quadratic B. adfected quadratic C. linear D. simple 5 K A E
M058
ax
2
+bx+c=0, ¬ / =· .ot c ~¬ :o.¬ t
A. –b
2
-4ac B. b
2
-4ac C. b
2
+4ac D. –b
2
±√b
2
-4ac
The discriminant of the quadratic equation ax
2
+bx+c=0 is:
A. –b
2
-4ac B. b
2
-4ac C. b
2
+4ac D. –b
2
±√b
2
-4ac 5 K B A

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M059 4k (3 k -1) = 5 :¬ : = co¬ ¬
A. 12 k
2
-4k-5=0 B. 12 k
2
-k-5=0 C. 12 k
2
-4 k =5 D. 12 k
2
-k =5 Standard
from of 4k (3k -1) = 5 is:
A. 12 k
2
-4k-5=0 B. 12 k
2
-k-5=0 C. 12 k
2
-4 k =5 D. 12 k
2
-k =5 5 K A A
M060
¬o~=¬ / =¬ . ¬ .c¬. ¬ / =· ...t c ~ b
2
-4ac>0 :¬ c , -¬ c ¬.o./ -.
A. ¬:· ¬ B. · ¬. C. · c..: D. .:/ .. · c.
In a quadratic equation if b
2
-4ac>0 and not a perfect square, then the roots are :
A. Real B. Equal C. Imaginary D. Rational 5 K A E
M061 t - ^. · ...t c ~/ - . ¬.o./ -. · ¬..:^c.¬ ¬ / =· ...t c ~¬
A. x
2
-2x-1=0 B. x
2
-2x+1=0 C. 2x
2
-2x+1=0 D. x
2
-2x-3=0
Quadratic equation having equal roots among the following equation is :
A. x
2
-2x-1=0 B. x
2
-2x+1=0 C. 2x
2
-2x+1=0 D. x
2
-2x-3=0 5 U B A
M062
.¬.¬ ¬ x
2
-9
2
. t c.... .- ¬:/ c .. c... x- -t ¬ .. . t c.... · c: ·.¬ .c¬./ -.
A. (-3, 0) ¬.:. (3,0) B. (-2, 0) ¬.:. (2,0) C. (-2, -5) ¬.:. (2,-5) D. (1,-8) ¬.:. (-1,-8)
When the graph of the polynomial x
2
-9 is drawn, the graph intersects the x- axis at the points
A. (-3, 0) and (3,0) B. (-2, 0) and (2,0) C. (-2, -5) and (2,-5) D. (1,-8) and (-1,-8) 5 U A A
M063
3x
2
-10x+3=0

· ...t c ~¬ .c¬. ¬.o.¬ 1/3 :^¬ . :.oc¬. ¬.o.¬
A. 1/3 B. 3 C. 3 1/3 D. 7 1/3
One of the roots of the equation 3x
2
-10x+3=0 is

1/3. The other root is:
A. 1/3 B. 3 C. 3 1/3 D. 7 1/3 5 S B D


Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M064 m ¬.:. n / -. x
2
-6x +2 =0 .c. ¬ / = · ...t c ~¬ ¬.o./ -:¬ c , t - ^. ¬/ - . 3t
· ¬..:^c.¬¬.¯
A. m+n B. mn C. m+n D. m
2
n
2
mn
If m and n are the roots of the quadratic equation x
2
-6x +2 =0 then 3 is the value of
A. m+n B. mn C. m+n D. m
2
n
2
mn 5 S C E
M065
x
2
-x-c=0 · .ot c ~¬ . ’c’ c. .:¬ . c c..., · .ot c ~¬ ¬.o./ -. · c..: · c. / -:/.¬¬¯
A. 0 B. -1 C. +1 D. +2
In the equation x
2
-x-c=0 what value of ’c’ makes the roots of the equation imaginary?
A. 0 B. -1 C. +1 D. +2 5 U C A
M066 =/ ¬ .- 3 / c. :^¬c . 48 / c. / - .c:. ¬ .-
A. 3 / c. B. 6 / c. C. 9 / c. D. 12 / c.
At present the time is 3
’o’
clock then time before 48 hours was:
A. 3
’o’
’
clock

B. 6
’o’

clock

C. 9
’o’

clock

D. 12
’o’

clock

6 K A E
M067
2005c ¬.:÷= .c/ -. 4 ¬.:. 11. . :.:ct / -. :.t¬:c / -:/.: ¬ . = · c.c¬ ¬ .. ../
¬.¯: · .¬.¬.
A. 4<11 (¬o¬ 7) B. 11-4 (¬o¬ 7) C. 4>11 (¬o¬ 7) D. 4 ≡ 11(¬o¬ 7)
March 4
th
and 11
th
of 2005 are Fridays. This relation can be expressed as:
A. 4<11 (mod 7) B. 11-4 (mod 7) C. 4>11 (mod 7) D. 4 ≡11(mod 7) 6 K D A
M068
Y⊗
4
Y = 1 :¬ c , ‘Y’ . · cc..:¬ . c
A. 2 B. 4 C. 5 D. 6
If Y⊗
4
Y = 1 then value of ‘Y’ is:
A. 2 B. 4 C. 5 D. 6 6 K C E

Item
No.
Questions
Ch.No Obj Key
Diff.
Level
M069
2 ⊗
5
3 = 1 : : ____ ⊗
5
____ = 1
A. 4, 0 B. 2, 4 C. 3, 4 D. 4, 4
2 ⊗
5
3 = 1 : : ____ ⊗
5
____ = 1
A. 4, 0 B. 2, 4 C. 3, 4 D. 4, 4 6 S D E
M070
x+2≡4 (¬o¬ 5) :¬:/ , ‘x’ . . c c...
A. 3 B. 4 C. 5 D. 7
If x+2≡4 (mod 5), then the value of ‘x’ is :
A. 3 B. 4 C. 5 D. 7 6 S D E
M071
( 10⊕
12
2 ) ⊕
12
3 c.. . c
A. 2 B. 3 C. 10 D. 15
The value of ( 10⊕
12
2) ⊕
12
3 is
A. 2 B. 3 C. 10 D. 15 6 S B E
M072
-¬ =¬: ¬ . . .c ¬. ::/ - -..¬:: 1:1:¬c -¬/ -. .c..¬.:¬.¬ ¬: :c¬ / - .· .~=¬
-..¬::
A. 1:1 B. 1:3 C. 2:1 D. 1:3
In a semicircle, the ratio of the length of two chords is 1:1. The ratio of the area of the segments made by
them is:
A. 1:1 B. 1:3 C. 2:1 D. 1:3 7 K A E


Item
No.
Questions
Ch.No Obj Key
Diff.
level
M073 .:¬ . -:c: .t .¬. :c¬ ¬ .. ¬ ¬ c.... c. .:¬ ¬ : :c¬ t .~ ¬ ÷. .c¯
F E

A D A. ABC B. ABD
C. ACDF D. ACDEF
B C
In the given figure which segment would you shade to get the smallest minor segment?
F
E
A. ABC B. ABD
A D C. ACDF D. ACDEF

B C
7 U A E
M074 ¬ c · c . .:·.¬ c..:¬¬ . .c ¬. ¬:· / - :.:.c¬./ - . .- c.... ·: =t / -. .c..¬ .:¬.¬
:t.c... .c¬.
A. ÷ ÷- t B. :c..::t:c C. · ¬.:c: c ÷ :.. .=. D. ÷ :.. .=.
Tangents drawn at the end points of any two intersecting diameters always form a:
A. Square B. Rectangle C. Parallelogram D. Quadrilateral 7 K D E

O

O

Item
No.
Questions
Ch.No Obj Key
Diff.
level
M075
.:¬ . PABQ .c¬. · ¬.:.:¬. ::..¬:/ .. = · c.c¬ .¬:/ ¬.::

A B

P D C Q
A. PA ≥ CQ B. PB < CQ C. PD=CQ D. PB>CQ
In the figure PABQ will become an Isosceles trapezium only on the condition:

A B

P D C Q
A. PA ≥ CQ B. PB < CQ C. PD=CQ D. PB>CQ 7 K C E
M076
12· c... .¬¬ .c ¬. · ¬ .:.:c: c ::/ - ..‘x’· c... -c: c ¬ . ¬: t .c¬¬ .c.¬ .:/ - . .- :¬ .
:/ ..¬
A. √ 144 – x
2
B. √36 + x
2
C. √36-x
2
D. √144-x
2

4 4

If two parallel chords of length 12 cm each and x cm apart are drawn on either side of centre then radius of
the circle is:
A. √ 144 – x
2
B. √36 + x
2
C. √36-x
2
D. √144-x
2

4 4 7 S B E
M077 ABC ¬.:. DEF · ¬.co¬ ..../ - -..co¬ :c/ / -. A ¬.:. D, B ¬.:. E ¬:/o C ¬.:.
F / -. :^¬ c , = t - ^. ¬/ - . c..:¬¬. -..c o¬ .:¬./ - :o: c..:^¬
A. AB ¬.:. DF B. AC ¬.:. DE C. BC ¬.:. EF D. AC ¬.:. DF
Corresponding vertices of two similar triangles ABC and DEF are A & D, B & E, C &F
Which of the following pair are corresponding sides of these triangles
A. AB and DF B. AC and DE C. BC and EF D. AC and DF 8 K C E


C1

C2

C1

C2

R
Q

R
Q
Item
No.
Questions
Ch.No Obj Key
Diff.
level
M078
PQR ....¬ . ∠PQR = 90
0
, :¬:/ , · cc..:¬ · c.c¬ ¬ c..:¬¬.¯ ¬ : ¬ .:.c
A. PQ
2
= PR
2
+ QR
2
B. PR
2
= RP
2
+ QR
2

C. PR
2
= PQ
2
+ QR
2
D. QR
2
= PR
2
+ QP
2

For a triangle PQR where ∠PQR = 90
0
, which is the correct relation among the following
A. PQ
2
= PR
2
+ QR
2
B. PR
2
= RP
2
+ QR
2
C. PR
2
= PQ
2
+ QR
2
D. QR
2
= PR
2
+ QP
2
8 K C E
M079
.c¬. .c.to.. ....¬ .:¬./ - -..¬:: ¬ 3:4:5 = · c.c¬ ¬ .. / ¬.. ¬ ...toc¬., ..c.¬ ¬ ¬ ¬ .. :.c.·
5:12: -----
A. 19 B. 13 C. 17 D. 24
If the sides of a right-angled triangle are in the ratio 3:4:5 then the missing term in 5:12: ------ is:
A. 19 B. 13 C. 17 D. 24
8 U B E
M080 = .:¬ . c.¬ ¬ c:c.. to.. / - :o: c.... ¬ : ¬.:.c


A. ∟PRQ & ∟MRN
B. ∟QPR & ∟RMN
C. ∟PQR & ∟NMR
D. ∟RPQ & ∟RMN


In the given figure pair of alternate angles is

A. ∟PRQ & ∟MRN
B. ∟QPR & ∟RMN
C. ∟PQR & ∟NMR
D. ∟RPQ & ∟RMN




8 U C E

M
P
N
Q
R
M
P
Q
N
R
A
B
C
P
Q
A
B
C
P
Q
Item
No.
Questions
Ch.No Obj Key
Diff.
level

M081 .:¬ · ¬:c..:c¬ ¬o~= ¬.:.c


Complete the statement using the given figure

8 K C E


M082 .:¬ .. .o.. · cc..:¬ · c.c¬ ¬ .. ¬ : ¬.:.c
A. AP.AB = AQ.AC
B. AP.AC = AQ.AB
C. AP.AQ = AC.AB
D. AP.PQ = BC.AC

Which is the correct relation among the following
A. AP.AB = AQ.AC
B. AP.AC = AQ.AB
C. AP.AQ = AC.AB
D. AP.PQ = BC.AC
8 U A A


AB : AQ : : BC : ______


A. AQ B. AP C. PQ D. AC

AB : AQ : : BC : ______


A. AQ B. AP C. PQ D. AC

P
Q
P
Q

Item
No.
Questions
Ch.No Obj Key
Diff.
level
M083 .c ¬. · ¬.co¬ .. ../ - .· .~=¬ 392 ÷ .· c... ¬.:. 200÷ . · c... -¬/ - -..co¬
.:¬./ - -..¬:: ¬
A. 3:2 B. 49:25 C. 7:5 D. 14:10
Two similar triangles have areas 392 sq cm and 200 sq.cm respectively; What is the ratio of any pair of
corresponding sides.
A. 3:2 B. 49:25 C. 7:5 D. 14:10 8 U C A
M084 .c¬. ¬: ¬ ¬:· t · c.c¬ .. ¬ c: ¬ ¬ .-t c...
A. ¬: ¬ ..¬ .c ¬ c ¬ . B. ¬: ¬ -:c: ¬ o¬ ::
C. ¬: ¬ .. .c ¬. -¬ =¬: / -:^ -: =·.: ¬ D. .c¬. · c - c ..
The statement not related to the diameter of a circle is:
A. twice the radius of the circle B. longest chord of the circle
C. bisects the circle into two semicircles D. a straight line 8 K D E
M085 .:¬¬:^ ·:=·.¬ ¬ : / -/ · c.c: ·¬ · ...t c ~¬ .. ¬ : ¬.:.
A. d>R+r B. d = R + r C. d < R + r D. d = R - r
Which relation among the following refers to externally touching circles:
A. d>R+r B. d = R + r C. d < R + r D. d = R – r 8 K B E
M086 .c ¬. ..../ -. · ¬.to.¯c../ -:^¬ c , -¬/ - -..co¬ .:¬./ -.
A. · ¬. B. · ¬.:.:c: c C. .c. D. · ¬.:..¬::
If two triangles are equiangular, then their sides are:
A. equal B. parallel C. perpendicular D. proportional 8 U D E



Item
No.
Questions
Ch.No Obj Key
Diff.
level
M087 .c ¬. · ¬.:c: c ¬:^c.¬ ·: =t / - . ¬... , .c¬ . ·: =t . .¬ t ¬ ¬ : t .c¬¬ .
to.. ¬ .c..¬.:¬.: ¬ . : to.. ¬ -- : c...
A. .¬. B. .c. C. -: t D. · c -
The intercept of a tangent between two parallel tangents to a circle subtends an angle at the centre. The
measure of the angle is:
A. acute B. right C. obtuse D. straight 8 U B A
M088 .c¬. ¬: ·t ¬ . /o.- ¬ .. t c ^·, .c¬. / oc. c.... ¬.:.¬:/ -¬ c . .¬ c:/ ¬ :c.¬¬.
A. :t:c B. .¬ C. ¬..c¸.· .~= D. ¬ . ¬ .
A solid plastic sphere is melted and a doll is made. There will be no change in its:
A. shape B. length C. area D. volume 9 K D E
M089 to.c.¬ ·.c¬ c. . , .c ¬. .c¬./ - . ¬... -:c: ¬ oc


A o D A. AB B. AD
C. AC D. OC


B C

The farthest distance between the two points on the given cyclinder:


A o D A. AB B. AD
C. AC D. OC


B C 9 U C E
O
O

Item
No.
Questions
Ch.No
Obj
B Key
Diff.
level
M090 .c¬. -¬ =¬ :: t:c ¬ c o.¬ ¬ ¬:- c...., .c¬. : c ¬ : ct .. ... :t:c ¬ . .^·¬ . :/
-¬ =¬: ¬ ¬:· ¬ :¬ t :/.: ¬ .
A. .... ¬ c: B. .... :c .: c
C. .... :- D. .... ¬:·
A semicircular sheet of a metal is bent into an open conical cup. The diameter of the semicircle becomes:
A. Circumference of the cup B. Slant height of the cup
C. Depth of the cup D. Diameter of the cup 9 U B E
M091 .c¬. ·.c¬ c:t:c ¬ ¬ ¯. . , .c¬. .:c ¬.· :.c.¬:/ , 22 ¬../ - ¬. .c c...¬.¬.. 100 cc
¬.·:.c¬ 1600 ¬../ -. .c c...¬.¬.. ¬ ¯. c..:¬ -- : c.... t c¬...c.... = ¬ :: c: ¬
· ¬:c..t ¬:^¬ ¯
A. .· .~= B. ¬ . ¬ . C. .: c D. ..
A cylindrical fountain pen, when filled with ink can be used to write 22 pages. With 100 cc of ink. 1600
pages can be written. Which of the following measures can we find through this data?
A. area B. volume C. height D. radius 9 U B E
M092 6· c... ..¬ - ::¬.¬ /o.-:t:c ¬ /.c¬ .. t c ^·¬ ¬.:. -¬ .. 0.06 · c... ...c.¬
: c.c...:^ .- :¬ . : c.c.. .¬¬
A. 600 .o B. 650 .o C. 800 .o D. 825 .o
A copper sphere of radius 6 cms is melted and drawn into a wire of radius 0.06 cm. The length of the wire is:
A. 600 m B. 650 m C. 800 m D. 825 m 9 S C A
M093 .c¬. /o.- ¬ ¬ . ¬ . ¬.:. ¬..c¸ .· .~=/ -. c t:÷:c ¬t:c .c¬ . :^¬:/ , -¬ c ¬:· ¬
A. 3 :t ¬.:. / -. B. 6 :t ¬.:. / -. C. 8 :t ¬.:. / -. D. 9 :t ¬.:. / -.
If the volume and surface area of a sphere are numerically equal, then, its diameter is :
A. 3 units B. 6 units C. 8 units D. 9 units 9 U A A

Item
No.

Questions

Ch.No
Obj
Key Diff.
level
M094 7 .o.c ¬:· ¬.:. 5 .o.c .¬¬- .c¬. co..c ¬.¸¬:. ¬ . .c .-· c:^¬ . co..c
¬.:.¬ ·.:. / - · c.c.... t c¬...c.... . .t:¬ ¬ :: c: ¬
A. co..c. ... ¬..c¸ .· .~= B. -¬ c ¬ t ¬..c¸.· .~=
C. co..c. · ¬.:.. ¬ .:.¬ .¬ D. co..c. ¬ . ¬ .
A roller of 5 m length and 7 m diameter, rolled on a field. To find the number of revolutions it makes, data
required is :
A. Total surface area of the roller B. Curved surface area of the roller
C. Total length covered by the roller D. Volume of the roller 9 U C A
M095 ¬..c¸/ - · c. ¬.:. :c/ / - · c. / -. c..:¬:/ .o .c¬ . · ¬..:^c.¬ ¬ . ¬
A. ¬ ~.:¬ . B. ¬.t C. /o.¬.c D. ¬: .o.¯t ¬ .
The solid in which number of faces are always equal to the number of vertices is:
A. Hexahedron B. Prism C. Pyramid D. Platonic solid 10 K C A
M096
= t - ^. ¬/ - . c..:¬¬ . -·:¬
A. ¬.oc. · c¬:: .c¬./ - ::c ¬:¬ t ::c:t. c .. B. .c ¬. . · · c¬:: .c¬./ - ¬:c ¬:¬ t
::c:t. c ÷ .
C. .c¬. . · · c¬:: .¬.¬..c.¬ ::c:t. c ÷ . D. .c ¬. . · · c¬:: .c¬..c.¬ ::c:t .
c ÷ .
Which one of the following is impossible to do?
A. drawing a traversable network of 3 nodes B. making a traversable network of 2 odd nodes
C. drawing a network of one odd node D. drawing a network of two odd nodes 10 A C E

Item
No.
Questions
Ch.No Obj Key
Diff.
level
M097 = ::c:t.c.. ¬.:: t c. .. .¬. ·.c.-/ -¬
0 1 2
1 4 3
2 3 0
A. 1 B. 2 C. 3 D. 4
How many loops are there in the network of matrix?
0 1 2
1 4 3
2 3 0
A. 1 B. 2 C. 3 D. 4 10 K B E
M098 = ¬ .:t .c.... ¬ · c·


A. ¬ / =¬:¬ /o.¬.c B. ¬ / =¬:¬ ¬ .t
C. ....¬:¬ ¬.t D. ¯c....: ¬ ~.: ¬ .
Name the polyhedra



A. square based pyramid B. square based prism
C. triangular prism D. regular hexahedron

10 K B E




A
B
C
D
A
B
C
D
Item
No.
Questions
Ch.No Obj Key
Diff.
level

M099
= ::c:t.c... ¬:c ¬:¬ t ::c:t .c... c..:t c¬ c

A. t .¬ . 4 · c¬:: .c¬./ -¬
B. .c ¬. . · · c¬:: .c¬./ -¬
C. .c: · c¬:: .c¬./ -. · ¬. · c¬:: .c¬./ -.
D. .c ¬ -c: ¬ ÷. . · · c¬:: .c¬./ -¬




The given network is not a traversable network because:

A. there are 4 nodes
B. there are two odd nodes
C. all nodes are even nodes
D. there are more than two odd nodes
10 U D E
M100 = t - ^. .:¬ .. -¬ c :.:/ - . ¬...¬:/ .c.:/.¬ ¯c....: .¬. ¬ .t ¬ .. ¬ · c·

A. ÷ :.=¬..: ¬ . B. ¬ ~.: ¬ .
C. -¬¬..: ¬ . D. ¬:¬ : ¬..: ¬ .


Name the regular polyhedron can be formed by
folding the given structure at its edges

A. Tetrahedron B. Hexahedron
C. Octahedron D. Dodecahedron
10 A B E

A
A
D.S.E.R.T
#4, 100 fT ring road, Banashankari III stage, Bangalore – 85

Subject : Mathematics
o:r II s. v: c·.:ct ·n>s
Instructions for answering Part II

t=õs ±tr=s., ·n>s r-r :tc: v: c..
Answer the following question as directed:
Item
No.
Questions Ch.No Obj Marks Diff.
Level
M001 .c¬. · ¬.:c: c :.. c.. ¬o¬ .. ¬.:. 129. . ¬ ¬ / -. t¬.¬:^ 2 ¬.:. 258 :^¬ . 65. . ¬ ¬ ¬ .. t c¬.
..:.c.
First and the 129
th
term of an A.P are respectively 2 and 258. Find the 65
th
term

1 K,S 1+1 E
M002
.c¬. /.¬o.: c :.. c... T
n-1
= 1 .c¬. :o.c·.
T
n+1
r
2

In a G.P show that T
n-1
= 1
T
n+1
r
2



1 K,U 1+1 A
M003
.c¬. ÷-t ¬ .. 16 .t ÷ ¬ c / -:^ .:/ ¬.:.¬ . .. ¬.¬./ .., ¬o¬ .. ÷-t ¬ . 2 /o../ - .. ¬.:.
-¬ c ¬..c:. ÷-t ¬ . 4 /o../ - .. :¬.:: . . ../ c... ¬. · .¬ 2 /o../ - .. ¬ . ·.::
¬..c¬.¬ c·.¬ ... .c: ÷-t / - .. :.c... -¬ ¯/ ... .¬. / o../ -. . .t:/.¬¬.¯
A square is divided into 16 smaller squares. A boy keeps 2 marbles in the first square, 4 in the next, and continues by
increasing 2 marbles each time. How many marbles are needed to fill all the squares?

1 U,S 1+1 A
M004 ¬.oc. :t t .c:c.. ¬: / - . ./ - -..¬:: ¬ .c¬ . · ¬.¬:: ¬ . c.¬ c: .- :¬ . .- ^. ¬.:. -:c:
¬oc ^. ¬ : / - ../ -. t¬.¬:^ 3 · c... , 12 · c... :^¬ . ¬.¬ ¬ ¬: ¬ ..¬ .. t c¬...:.c.
Three concentric circles are drawn in such a way that the ratio of their radii is same. If the radii of the inner and outer
circles are 3 cms and 12 cms respectively. Find the radius of the middle circle.

1 A,S 1+1 A
M005 1, 2, 3, 4 ¬.:. 5 -ct / - .. .¬ c.o.^·toc¬., ¬.. c:¬ .=· ¬ , 2000to ¬ . c.¬ c: .¬. · c./ - ..
¬.:¬ .¬.¬.¯
How many numbers, more than 2000 can be formed using digits 1, 2, 3, 4 and 5 without repeating the digits? 2 K,S 1+1 E


Item
No.
Questions Ch.No Obj Marks Diff.
Level
M006 10 .. c .: c ¬.:. :ot / - , · c:· c ¬.:. ¬ .:. t .÷ .. c.... t - ^. ¬.c... to¬ c:^¬ . -¬ c c..:¬ .t ~¬ ¬ ÷.
-·c ¬:^¬ ¯
/.~.t ~
X
൦
.: c
174 · c... 3.77
:ot
75 t .. 1.05
The table below contains the mean and standard deviation of the heights and weights of 10 persons. In which
characteristic do they vary more?

Characteristic X
൦
Height 174 cms 3.77
Weight 75 Kg 1.05 3 K,S 1+1 E

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M007 . .c . .c t ·.../ - . . .. c /.c¬., .c¬. ¯/ : : -¬ : c... / -·¬ :. /o.c.., ¬.:. t .÷ .. c....
c t:÷:c ¬.:., . t c... :o.c·¬ . c..:¬ /.c.. .. c to.c... ·c ¬:^¬ ¯
0
1
2
3
4
5
6
7
8
9
10
Carpenter Coolie Driver Painter Plumber
Occupations
S
.
D
's

o
f

w
a
g
e
s

Following graph shows the calculated S.D’s of wages of groups of people of different occupations for a certain period.
Which group of people have a steady income?
0
1
2
3
4
5
6
7
8
9
10
Carpenter Coolie Driver Painter Plumber
Occupations
S
.
D
's

o
f

w
a
g
e
s

3 A 2 A
M008 a
2
-b
2
, (a-b)
2
¬.:. a
3
-b
3
/ - ¬..·:.¬ .. t c¬. ..:.c
Find the H.C.F of a
2
-b
2
, (a-b)
2
and a
3
-b
3
4 S 2 E
M009 x+y+z=9 ¬.:. xy+yz+zx=11 :¬:/ x
3
+y
3
+z
3
-3xyz . c c.... t c¬...:.c.
When x+y+z=9 and xy+yz+zx=11, find the value of x
3
+y
3
+z
3
-3xyz 4 K,S 1+1 A

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M010 .c ¬. ..:o.- / - ¬..·:.- ¬.:. ..·:.- / -. t¬.¬:^ (x-3) ¬.:. (x
3
-5x
2
-2x+24):^¬ . -¬/ - . .c¬.
..:o.- c... (x
2
-7x+12) :¬ c , ¬.:o c¬ .. t c¬...:.c.
The H.C.F and L.C.M of two expressions are (x-3) and (x
3
-5x
2
-2x+24) respectively. If one of the expressions is (x
2
-
7x+12), find the other 4 U,S 1+1 A
M011 2x
2
-3x+8=0 · .ot c ~¬ ¬.o./ - ./ .¬.:=·
Comment on the roots of the equation: 2x
2
-3x+8=0 5 K 2 E
M012 .c¬. ¬ / =· .ot c ~¬ :o.¬ t ¬ . c 16 :¬ c , ¬ / =· .ot c ~¬ ¬.o./ - ·.:¬ ¬ ...¯
If the value of the discriminant of a quadratic equation is 16. What is the nature of the roots of the equation? 5 K,S 1+1 E
M013 ¬.o./ -. (1-√5) ¬.:. (1+√5) :c.¬ c: .c¬. ¬ / =· ...t c ~¬ .. .c
Write the quadratic equation whose roots are (1-√5) and (1+√5) 5 K,S 1+1 E
M014 (6
8
7 )
8
5 = 6
8
(7
8
5).c¬. :o.c·
Show that (6
8
7 )
8
5 = 6
8
(7
8
5) 6 K.S 1+1 A
M015 Z
4
/.¬:t:c t · c.c: ·¬ c: to.¬t ¬ .. c .· .. ·:¬¬ .¯ t:c ~ .-·
2 4 6 8
2 4 8 2 6
4 8 6 4 2
6 2 - - -
8 6 - - -
Check whether construction of Cayley’s table is possible for Z
4
under multiplication. State the reason
2 4 6 8
2 4 8 2 6
4 8 6 4 2
6 2 - - -
8 6 - - -
6 U 2 A
Two congruent circles with centers A and B of 2 cm radius, touch two other
congruent circles with centers C and D of radius 4 cm as shown in the
figure. Find the perimeter of the rectangle ABCD


Item
No.
Questions Ch.No Obj Marks Diff.
Level
M016



7 U 2 A
M017



7 U 2 A
M018



8 U,S 1+1 A
4· c... ...c.¬ .:.. · ¬ =· ¬. ¬: / - t .c¬ / -. A, B, C ¬.:. D :^¬ .
= ¬ : / -. .:¬ . :o.c·c.¬ c: .c¬ .oc¬. ·:=·.. ¬ . ABCD ÷-t ¬
.· .~=¬ .. t c¬...:.c.
Four circles of radius 4 cm with centers A, B, C and D touch each other as
shown in the figure. Find the perimeter of the square ABCD
A ¬.:. B t .c¬ ¬:/.- .c ¬. · ¬ =· ¬. ¬: / - .. 2 · c... :^¬ . =
.c ¬. ¬ : / - , 4 · c... ...c.¬ C ¬.:. D t .c¬ / -:^c.¬ , .c ¬.
· ¬ =· ¬. ¬: / - .. .:¬ . :o.c·¬ c: ·:=·.. ¬ . :c..: ABCDc..
·.: - c.... c -·.
.:¬ . AP ¬.:. BP / - . ¬: ¬ t .c¬¬ O ¬.: . .:¬ .c¬. P ¯c¬
.- :c.¬ ·: =t / -., ∠APB=70
0
:¬ c t o.. ∠ACB c.. . c c.....¯
In the adjoining figure AP and BP are tangents drawn to the circle with
centre O from an external point P. If ∠APB=70
0
, Find ∠ACB


Item
No.
Questions Ch.No Obj Marks Diff.
Level
M019 = .:¬ . -c: ·¬:^ · :=·.¬ ¬: / - :o: .¬.¯



In the adjoining figure how many pairs of internally touching circles are there?

8 U 2 A
M020 APB ¬: ¬ . AB c... ¬:· ¬:^¬ . AH ¬.:. BK / -. t¬.¬:^ A ¬.:. B .c¬./ -c¬ , P :.c¬ .- ¬
·: =t t .c./ -:^¬ . AH + BK = AB .c¬. ·:: ·.
AB is a diameter of a circle APB. AH and BK are perpendiculars from A and B respectively to the tangent at P. Prove
that, AH + BK = AB 8 U,A 1+1 A
M021



8 K,A 1+1 A
M022 7.o. ¬:· ¬.:. 20.o.c :- .c.¬ .c¬. .:.c.... -/ :¬ . -¬ cc¬ ¬oc : ¬.~ .. · ¬.¬:^ ¬ c .
22.o x 14.o -- : c.. .c¬. ./..c.... ¬.:.¬ . ./..c.. .: c ¬ .. t c¬...:.c.
A well of diameter 7 m and depth 20 m is dug. The mud obtained is spread uniformly to form a platform measuring 22m
x 14 m. Find the height of the platform. 9 U,A 1+1 A
.:¬ . AB || DC .c¬. to.¬:/ , Δ DMU ||| Δ BMV .c¬.
·:: ·
In the figure, give that AB || DC,
Prove that Δ DMU ||| Δ BMV

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M023 10· c... .: c ¬.:. 6 · c... ¬:· .c.¬ .c¬. ¬ . ·.c¬ c .. t c ^·, .:~/ - .. ¬.:¬ . .t:^¬ . ¬ .
.:~¬ ¬:· ¬ 1.5 · c,.. ¬.:. 0.25 · c... ¬ ¬ .c.¬ c: .¬. .:~/ - . . ¬.:¬ .¬.¬.¯
A solid cylinder of height 10 cm and diameter 6 cm is melted to make coins. How many coins can be made of diameter
1.5cm with 0.25 cm thickness? 9 K,A 1+1 A
M024 .c¬. : ct.:t:c ¬ /.¬:c ¬ . 4 .. cc .. -¬ t:: .¬ . ¬.c. o.¯/o, . .¬ ¬..c 4¬ ..o . ¬. /:-
. .t:/.: ¬ . /.¬:c ¬ .: c ¬ .. t c¬...:.c.
A conical tent accommodates 4 persons. Each person requires 4 sq.m of space on the ground and 20 cu.m of air. Find
the height of the tent. 9 A,S 1+1 D
M025

.




.


10 K,S 1+1 A
¬:¬ : ¬..: ¬ . ¬ ¬..:/ - · c. , :c/ .c¬./ - · c. ¬.:.
-c÷./ - · c./ - .. .~ · .c :.c. :¬/ - .. :c.. .c .
·o:¬ -.c.. ::- .o...

Write the number of faces, vertices and edges of the given Dodecahedron
and verify Euler’s formula

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M026 .c¬. ::c:t.c.. ¬.:/ = · c.:c..: ¬ .. to.¬ . ::c:t.c.... c .· ¬ -¬ c . c.¬ t c· / - · c.c....
t c¬...:.c.

0 1 1 1 1 1
1 0 1 1 1 1
1 1 0 1 1 1
1 1 1 0 1 1
1 1 1 1 0 1
1 1 1 1 1 0
The network matrix of a network is as follows. Find the number of arcs present in the network without constructing the
network.
0 1 1 1 1 1
1 0 1 1 1 1
1 1 0 1 1 1
1 1 1 0 1 1
1 1 1 1 0 1
1 1 1 1 1 0
10 K,U 1+1 A
M027 t - ^. .:t :c.. c . ·o: -. :.· ::- .o.¬ .. ·:¬.. , t:c ~ .-·
A B


D C
It is not possible to verify Euler’s formula for the diagram given below. Give reason:

A B


D C 10 U 2 A
E

E


Item
No.
Questions Ch.No Obj Marks Diff.
Level
M028
.c¬. · ¬.:c: c :.. c.. 4. . ¬.:. 7. . ¬ ¬ / -. t¬.¬:^ ¬.:. 23 :^¬ . ‘d’ ¬.:. ‘a’./ - .. t c¬...:.c.
In an A.P the fourth and the seventh terms are 17 and 23 respectively. Find ‘d’ and ‘a’. 1 K,S 1+2 E
M029 n=7 ¬.:. r=3 :¬ c nC
r
+nC
r
-1 =
n+1
C
r
.c¬. :o.c·.
If n=7 and r=3 show that nC
r
+nC
r
-1 =
n+1
C
r
2 U,S 2+1 E
M030 A ¬.:. B .c. :.c. .:. ¬../ -. :c. :¯c// - . / -·c.¬ c ../ - .¬ c ..^¬
A 48 50 54 46 48 54
B 46 44 43 46 45 46
:¬ c . (a) .: ¬. c.: / -·¬ ¬ c..:c. (b) ¬ . . ·c : c...- :./:c .:c.¯
The runs scored by two Batsman A and B in six innings are given as follows:
A 48 50 54 46 48 54
B 46 44 43 46 45 46
Find: (a) who is a better run getter (b) who is a consistent player? 3 U,A 1+2 A
M031 .c ¬ . . ¬:: ¬ .c ¬. ..:o.- / - ¬..·:.- ¬.:. ..·:.- / -. t¬.¬:^ (p+2) ¬.:. p
3
-2p
2
-5p+6. .c¬.
..:o.- p
2
+p-2 :¬ c :.oc¬. ..:o.- c.... t c¬...:.c.
HCF and LCM of two expressions of second degree are (p+2) and p
3
-2p
2
-5p+6 respectively. If one of the expressions is
p
2
+p-2. Find the other. 4 K,S 1+2 A
M032 a
3
+7b
3
+6ab (a+2b) : ..:o.- c.... ¯¬./ .-:c.¬ .c¬. ·o: co¬ t : c¬., -¬ ¬ .=·.
Factorise a
3
+7b
3
+6ab (a+2b) by reducing the expression to a known formula 4 U,S 2+1 A
M033 /.~.. 224.. to¬.¬ .c ¬. t¬.:../ : ¬ . ¬o~= · c· c./ - .. t c¬...:.c.
Find two consecutive positive even integers whose product is 224 5 U,S 1+2 E
M034 .c ¬. · ¬. ../ -c.¬ ¬: / -/ . .c ·:¬.:. ·: =/ - .- :.c.
Draw the direct common tangents to two equal circles 7 A,S 1+2 A

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M035 2 · c... . ..c.¬ .c¬ . ¬: .- ¬., -¬ c . . OB c.... BX=2 · c,.. :c.¬ c: ¬ :·. AB c.... ‘x’
.c¬... . ·:=·.¬ c: c..o ¬.:. (¬o¬ .. .- ¬ ) ¬ : ¬ .. .:¬¬:^ ·:=·.¬ c: :.oc¬. ¬ : ¬ ..
.- :.c.
Draw a circle of radius 2 cms. Produce OB, a radius of this circle to ‘x’ so that BX=2 cms. Construct a circle to touch
AB at ‘x’ and to touch the circle (drawn earlier) externally. 7 A,S 2+1 D
M036 ∆ABC ¬ . BDc... ‘B’ ¬.o.t .- ¬ .: c ¬:^¬ ¬.:. AD : CD = 1:2. :^¬ . AC
2
=3 (BC
2
-AB
2
)
BD is the altitude through ‘B’ in the ∆ABC and AD : CD = 1:2. Prove that AC
2
=3 (BC
2
-AB
2
) 8 U,S 1+2 A
M037 = .:¬ . AB CD , AB = 9 · c..., DE = 4· c,.., CE = 5 · c... ¬.:. CD = 6 · c... :¬ c BE c..
-- : c.... t c¬...:.c. 9
A B
4
5
D C
6
In the adjoining figure AB CD, AB = 9 cm, DE = 4cm, CE = 5 cm and CD = 6 cm. Find BE
9
A B
4
5
D C
6 8 U,A 1+2 A
M038 .c ¬. · ¬.co¬ .. ..¬ -..c o¬ .:¬./ -. 9 · c... ¬.:. 6· c... :^¬ c . = .:¬./ -/ .- ¬
.c./ - -..¬:: ¬ .. t c¬. ..:.c.
Corresponding sides of two similar triangles are 9 cm and 6 cm. Find the ratio of their altitudes drawn to those two sides. 8 U,S 1+2 A

E

E

Item
No.
Questions Ch.No Obj Marks Diff.
Level
M039 44....c .: c .c.¬ t .¬ ¬ 66 ....c .¬¬ . c - .. . .¬ ¬..c ..-.¬ c: ¬.:.¬ c -¬ . · ¬.c..¬ . 6
....c .: c ¬ ¬.c ¬ .c..¬.:¬.¬ . c -. .¬¬ .¬.¯
The length of the shadow cast by a building of height 44 mts is 66 mts on the ground. At the same time length of the
shadow cast by a tree is 6 mts. What is the vertical height of the tree? 8 U,S 1+2 A
M040
.c¬. ¬.c ¬ :.t c.. :t:c ¬, -¬ =/o- ¬ ¬..c , .c¬. : ct.¬ .. ¯. ·¬ c.¬ . -¬ =/o.- ¬.:. : ct ... ../ - .
: c: 4.2 · c... ¬.:. ... :.t c.. .: c ¬ 4.2 · c,.. :^¬ . :.t / . .t:/.¬ ¬.c ¬ /:¬ .. c -·.
A solid wooden toy is in the form of a cone mounted on a hemisphere. The radii of the hemisphere and the base of the cone are
4.2 cms each and the total height of the toy is 10.2 cms. Calculate volume of wood used in the toy. 9 K,S 1+2 A
M041 t¬.¬:^ 3 ,4 ¬.:. 3 ¬ /=.c.¬ A, B ¬.:. C · c¬:: .¬.¬./ -c.¬ ::c:t.c.... c .·.
Construct a network of 3 nodes A, B,C which are of the order 3 ,4 and 3 respectively 10 K,S 1+2 A
M042 .c¬. t c:. ¬:¬:c ¬ c.o... c... t:c .. to-.¬.¬:^¬ . ¬:c c. ¬ . 5co .¬. ¬.:., : .c/ - t o. c. .. 10c o
.. -.c: c ¬ ¬. .c/ - to. c... .c:. .c/ - t c.. ¬o..^. .c ¬c ¬c c: ¬ ~ t.. .t.. ¬:/ ... . 17.
t c.. . co. 3,27,680 t.¬ c , -¬ .. t .¬ ... ¬o: ¬ .. c..:¬¬:¬ co :.. c.. : :¬ .. .¬ c.o.^· t c¬ ...:.c.
In an instalment purchase scheme for cars, a buyer has to pay Rs.5 initially and Rs.10 at the end of that month. Further
he has to pay double the previous amount at the end of each month. If the 17
th
instalment paid is Rs. 3,27,680. Find total
amount paid using principles of progressions. 1 A,S 2+2 A
M043 .c¬. ¬:¬ . ¬ ·:¬.:.¬ ./ ¬ .. ¬ c. / 5 -... . ¬. : ^·¬ c , ¬:¬ . ¬ 300 -... ¬oc ¬ .. t..· .. 2¬ c.
¬ ÷. : / ¬.to-.: ¬ . ¬:/:¬ c -¬ c ·:¬.:.¬ ./ ¬ .. t c¬...:.c¯
If the usual speed of a vehicle is reduced by 5 km per hour, it takes 2 hrs more to cover a distance of 300 kms. Find the
usual speed. 5 K,S 2+2 E
M044 2.5 · c... ..¬- ¬ : t ‘P’ .c¬... . .c¬. QPR ·: =t ¬ .. c .·c. ¬ : ¬ ¬oc / ·: =t ¬ ¬.... ¬ .c¬.
.c¬. ‘S’ ¬ .. /.c..·. ¬:c.o.^t ¬ ¬:. :c¬ .c ¬ . . ·: =t SPT ¬ .. c .· .. ·:¬.. .c¬. :o.c·.
Draw a tangent QPR to a circle of radius 2.5 cms at any point ‘P’ on it. Mark a point ‘S’ outside the circle and not on
QPR. By practical method show that a second tangent SPT cannot be drawn. 7 A,S 2+2 A
M045 .c ¬. ..../ -. · ¬. t o.. / -:^¬c , -¬/ - -..co¬ .:¬./ -. · ¬.:..¬:: ¬ . c.: ¬ , ·:: ·.
Prove that if two triangles are equiangular, then their corresponding sides are proportional. 8 K,S 2+2 E

gÀZÀ£Á vÀAqÀ

Kannada Hindi
Sri.B.S.Gundu Rao, Deputy Director , Gandhi Centre for Peace and
Human Values Bangalore
Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum
Dr. Ispak Ali, Lalbahudar Sastry B.Ed College, Bangalore
Sri.C.S. Banashankariah, Bangalore Sri. Abdul Nazir, Q.Islam HS, Bangalore
Sri. P.Dharukaradhya, Basaveshwara Girls High School, B’lore Sri. G.H. Balakrishna, Bangalore
Sri.N.Gopal Krishna Udupa, Bangalore Smt. Shyalaja H.Naidu, DPH HS, Bangalore
Smt. Prema H.Tahsildar, Bharati Vidyalaya, Khasbag, Belgaum Smt. Urmilla Nahar, DPH HS, Bangalore
Smt.Bhuvaneshwari.G.S, Women’s Peace league, Bangalore Sri. Anand.S. Kalasad, KC PU College, Hirebagewadi, Belgaum
Smt. Bhagirathi Bhat, GHS, Ketamaranahalli, Bangalore Sri. Ashok.H.Balunnavar, MM Comp. PU College, Belgaum
Smt. Vasundhara M.G, Bharatamata Vidyamandir, Bangalore Smt. Geetanjali.P.Yogi, Benson’s HS, Belgaum
Sri. V. Krishnaiah, Sir M.V. Comp. PU College, Bangalore Dr.Bharati T.Savadattu, Govt. Saraswathi PU College, Belgaum
Smt. S. Padmavathi, Vidya Vardhaka Sangha, Bangalore Dr. K.L.Sattigeri, Principal, Dr. B.D. Jatti COE, Belgaum
Sri.Nagaraj.S, Vivekananda Vidya Kendra, Bangalore Urdu
Smt. Kannika, Sri Aravind Vidya Mandira, Bangalore Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum
Smt. Srilata G.S, MES Kishore Kendra, Bangalore Smt. Shaheda Perveen, BRP, Shankarapura, Bangalore
English Sri. Bahadur Khan, MO Girls HS, Bangalore
Prof. G.S. Mudambadithaya, Bangalore Sri.S.G. Deshnoor, Al-Ameen HS, Belgaum
Sri.A.P. Gundappa, Attibele Sri. F.A. Yallur, Islamai Girls High School, Belgaum
Smt. Umadevi, R.V.Girls High School, Bangalore Sri.D.M. Momin, Bashiban High School, Belgaum
Smt. Maya Ramchand, Bangalore Marati
Smt. Shobha Kulkarni, Govt. Sardar HS, Belgaum Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum
Sri.Sathya Prakash, Vidya Vardhaka Sangha HS, Bangalore Smt.Shaila.V.M, Mahila Vidyalaya HS, Belgaum
Smt. Asha, Saraswathi Vidya Mandir, Bangalore Smt. Sunitha.D. Mathad, Ushatai Gogate Girls HS, Belgaum
Smt. Prameetha Adoni, HM, GHS, KR Puram, Bangalore Sri. P.T. Malege, MM Comp. PU College, Belgaum
Sri.G.N. Deshpande, HM, BN Darbar GHS, Bijapur Sri. C.Y. Patil, Talakwadi HS, Belgaum
Sri. Shankaranarayana Rao.P , SS High School, Kadandale, DK Sri. A.L. Patil, MM Central HS, Belgaum
Smt. Lata Rao, HM, SJR High School, Bangalore Smt. Sheela Deshpande, LBS B.Ed College, Bangalore

Sanskrit Science
Dr. Satish Hegde, R.V. Girls High School, Bangalore Dr. Sameera Simha, Vijaya Teachers College, Bangalore
Sri. Shridhar Hegde, National High School, Bangalore Dr. S. Srikanta Swamy, R.V. Teachers College, Bangalore
Sri. Narayan Ananth Bhat,Govt PU College, Chamarajpet, B’lore Sri.P.G.Dwarakanath, Vidya Vardhaka Sangha, Bangalore
Sri.Venkataramana D.Bhat, Govt Jr. College, Vartur, B’lore Dr.R.Mythili, Associate Director, RVEC, Bangalore
Sri.Narasimha Bhagavat, Janaseva Vidya Kendra, Chennenahalli Smt. Shantha Kumari.B.S., Bangalore
Smt. Shylaja.V, Chamarajpet Jr. College, Bangalore Smt. Vasanthi Rao, Bangalore
Sri. Krishna V. Bhat, Vasavi Vidyaniketan, Bangalore Smt. Rekha Hegde, Vani High School, Bangalore
Sri. Mahesh Bhat, PTA High School, Bangalore Smt. K.S. Shyamala, HM, Vasavi High School, Bangalore
Sri. Balasubramanian, Methodist HS, Kolar Smt. R. Geetha, Vasavi High School, Bangalore
Smt. Geeta B.S, Seshadripuram GHS, Bangalore Smt. S.K. Prabha, Retd. Lecturer, DIET, Bangalore
Telugu Smt. Bhagyalakshmi, Stella Mari’s School, Bangalore
Dr. T.K. Jayalakshmi, Director, RVEC, Bangalore Smt. V. Padma, Vidya Vardhaka Sangha HS, Bangalore
Sri. Nagesam.C, RBANM High School, Bangalore Social Studies
Sri. G. Venkata Rama Reddy, Telugu Pandit, Bangalore Prof. G.P. Basavaraj, Retd Director, NCERT
Sri. P.Hema Chendra Babu, Telugu Pandit, Bangalore Sri. P.A. Kumar, HM, Vijaya High School, Bangalore
Tamil Prof. B.R. Gopal, MES Teachers College, Bangalore
Prof. Susheela Sheshadri, Principal, Amrita Shikshana M.Vidyala,Mysore Smt. Lorna Pinto, SAM High School, Bangalore
Sri. Pulavar V. Vishwanathan, Bangalore Smt. Radhika.S, Hymamshu Jyothi Kala Kendra, Bangalore
Sri.S.Ramalingam, Seva Ashram High School, Bangalore Smt. T.R. Sandhyavalli, Basaveshwara Jr. College, Bangalore
Sri.G. Sampath, Bangalore Smt. R. Vijayavalli, Nirmala Rani GHS, Bangalore
Mathematics Smt. Shamala Prasad, MES Kishore Kendra, Bangalore
Dr. D.S. Shivananda, Bangalore Smt. Sukanya.N.R, Sardar Patil HS, Bangalore
Sri. Kailash Nekraj, HM, Jnanamitra HS, Bangalore Smt. Meera, Vidya Vardhaka Sangha HS, Bangalore
Sri.N.C. Satyaji Rao, Bangalore Smt. N.S. Vyjayanthi, Vidya Bharathi Eng. School, Bangalore
Smt. K.S. Susheela, Bangalore Smt. Lakshamma, Bangalore
Smt. Subhadra.M.S, Bangalore
Smt. C. Nirmala, HM, MABL HS, Doddaballapura
Dr.T.K. Jayalakshmi, Director, RVEC, Bangalore
Dr. R. Mythili, Associate Director, Bangalore