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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: • • • • • • •
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4.
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5.
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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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F PÁAiÀÄðPÉÌ ¸ÀjAiÀiÁzÀ MvÀÄÛ PÉÆlÄÖ, ªÀÄÄAzÀÆr ±Àæ«Ä¸ÀÄwÛgÀĪÀ r.J¸ï.E.Dgï.n ¤zÉðñÀPÀgÁzÀ r.dUÀ£ÁßxÀgÁªï ºÁUÀÆ PÀ£ÁðlPÀ ¥ÀjÃPÁë ªÀÄAqÀ½ ¤zÉðñÀPÀgÁzÀ ²æÃ.n.JªÀiï. PÀĪÀiÁgï gÀªÀjUÀÆ £ÀªÀÄä ºÀÈvÀÆàªÀðPÀ C©ü£ÀAzÀ£ÉUÀ¼ÀÄ ºÁUÀÆ ªÀAzÀ£ÉUÀ¼ÀÄ. EzÉà jÃw r.J¸ï.E.Dgï.n AiÀÄ PÀbÉÃjAiÀÄ°è£À D¦üøÀgï DzÀ ²æêÀÄw. ¹jAiÀÄtÚªÀgï ®°vÁ ZÀAzÀæ±ÉÃRgï gÀªÀgÀÄ ºÁUÀÆ J®è gÀZÀ£Á ¸À«Äw ¸ÀzÀ¸ÀågÀÄUÀ½UÀÆ £ÁªÀÅ F ªÀÄÆ®PÀ ªÀAzÀ£ÉUÀ¼À£ÀÄß ¸À°è¸ÀÄvÉÛêÉ. qÁ:n.PÉ.dAiÀÄ®Që÷ qÁ: r. J¸ï.²ªÁ£ÀAzÀ ************
List of Abbreviations Used Part I Multiple Choice Questions Part II Short and Long Answer type Questions Abbreviations Meaning Item Number Code KF Languages L.No Lesson Number KS PR Prose EF PO Poem ES Gr Grammar HF Comp Comprehension HT SF Core Subjects Ch.No Chapter Number ST B Biology U Ma Social Studies H History Ta C Civics Te G Geography M E Economics SC SS UÀ Obj Objectives ¥À K Knowledge G Languages YõÁÕ C Comprehension ¨sÁ A Appreciation UÀæ E Expression ¥Àæ Core Subjects C U Understanding PÀ.ªÀÄlÖ A Application ¸ÀÄ S Skill ¸Á Diff.level Difficulty level PÀ E Easy G A Average D Difficult
Meaning Kannada First Language Kannada Second/Third Language English First Language English Second Language Hindi First Language Hindi Third Language Sanskrit First Language Sanskrit Third Language Urdu Marathi Tamil Telugu Mathematics Science Social Studies
UÀzÀå ¥ÀzÀå G¢ÝµÀÖ YõÁÕ£À÷ ¨sÁµÉ UÀæ»PÉ ¥Àæ±ÀA¸É C©üªÀåQÛ PÀp£ÀvÉAiÀÄ ªÀÄlÖ ¸ÀÄ®¨sÀ ¸ÁzsÁgÀt PÀµÀÖ G¢ÝµÀÖ
D.S.E.R.T #4, 100 fT ring road, Banashankari III stage, Bangalore – 85
Sample Items of X Standard Question Bank
tem No.
M001
M002
M003
Subject: Mathematics
¨sÁUÀ I
Part I Ch.No
Questions
Obj
Key
K
C
Diff. Level
¸ÀAPÉÃvÀU¼ À À°è ¸ÀÆa¹gÀĪÀ F PɼV À £À ¤AiÀĪÀĪÀ£ÀÄß ºÉ¸j À ¹ - (P∪Q)∪R = R∪(P∪Q) A. ¸Àºª À v À ð À £À ¤AiÀĪÀÄ B. «¨sÁdPÀ ¤AiÀĪÀÄ C. ¥ÀjªÀvð À £À ¤AiÀĪÀÄ D. rªÀiÁUÉÆðãÀ£À ¤AiÀĪÀÄ 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 UÀt A = {1,2,3,4,5}, B={0,1,2,3,4} ªÀÄvÀÄÛ UÀt C= {-2, -1, 0, +1, +2} DzÀg,É ±ÀÆ£ÀåUÀtªÀÅ PɼÀV£À AiÀiÁªÀ UàtUÀ¼À
E
G¥ÀUt À ªÁVzÉ? A. B ªÀÄvÀÄÛ C
B. A ªÀÄvÀÄÛ C
C. A ªÀÄvÀÄÛ B
D. A, B ªÀÄvÀÄÛ 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
PɼV À £À ªÉ£ É ï£ÀPÀ ÉëU¼ À ° À è AiÀiÁªÀÅzÀÄ (B-A) £ÀÄß ¥Àæw¤¢ü¸ÀÄvÀÛz?É
Which of the following Venn diagrams represents B-A?
1
U
D
E
Item No.
M004
M005
M006
Questions
Ch.No
Obj
Key
Diff. Level
1
A
C
E
1
U
A
A
1
K
B
E
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? E
K
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?
U={0, 1, 2, 3, 4, 5,6}, A= {0,2,4} B= {0,2,3,5} DzÀgÉ (A∪ B) A. {1, 6}
B. {0, 2, 4}
C.
Ø
UÀtªÀÅ :
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}
PɼV À £À ¸ÀASÁåUÀtUÀ¼° À è AiÀiÁªÀÅzÀÄ ±ÉæÃrüAiÀiÁVzÉ? A. 4, 5, 7, 1, 13 B. 4, 3, 4, 3, 4 C. 10, 8, 3, 2, 1 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 D. 1, 4, 3, 5, 2
tem No.
M007
M008
M009
M010
M011
Ch.No
Questions
Obj
Key
Diff. Level
4+7+10+13+-----+ n ±ÉæÃrüAiÀÄ MA§vÀÛ£A É iÀÄ ¥ÀzÀ 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
1
K
B
E
1
S
B
E
1
K
C
A
1
K
D
E
P¼ÀV£À AiÀiÁªÀ ¸ÀÆvÀæ¢AzÀ, ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ n£Éà ¥ÀzÀª£ À ÀÄß PÀAqÀÄ»rAiÀħºÀÄzÀÄ? A. Tn = a + n-d B. Tn = a + (n-1)d C. Tn = a (n-1)d D. Tn = a + n-1 d Which of the following is the formula to find the nth term of an arithmetic progression? A. Tn = a + n-d B. Tn = a + (n-1)d C. Tn = a (n-1)d D. Tn = a + n-1 d
MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ªÉÆzÀ®£É ¥ÀzÀ 3 ªÀÄvÀÄÛ ¸ÁªÀiÁ£Àå ªÀåvÁå¸À 5 DzÁUÀ, n£Éà ¥ÀzÀªÀÅ, A. n- 2 B. 5n -2 C. 5n +8 D. 3n th The first term of an A.P is 3 and common difference is 5 then the n term is A. n- 2 B. 5n -2 C. 5n +8 D. 3n
PɼV À £À AiÀiÁªÀÅzÀÄ ¤dªÁzÀ UÀtÂvÀ ¸ÀA¨sA À zÀªÁVzÉ? A. Sn + Tn = S n-1 B. Sn – S n+1 = Tn C. Sn – S n-1 =Tn Which of the following is a true mathematical relation? A. Sn + Tn = S n-1 B. Sn – S n+1 = Tn C. Sn – S n-1 =Tn
D. Sn + Tn = S n+1 D. Sn + Tn = S n+1
MAzÀÄ ªÀiÁvÀÈPÉAiÀÄÄ CzÀgÀ ¸ÀܼÁAvÀj¹zÀ ªÀiÁvÀÈPÉUÉ ¸ÀªÀÄ£ÁzÀgÉ CzÀÄ F ªÀiÁvÀÈPÉAiÀiÁUÀÄvÀÛz.É A. CqÀظÁ®Ä
B. PÀA§¸Á®Ä
C. C¸ÀªÀÄ«Äw
If a matrix is equal to its transpose then the matrix is: A. Row B. Column C. Skew symmetric
D. ¸ÀªÀÄ«Äw D. symmetric
tem No.
M012
M013
M014
Ch.No
Questions x ªÀÄvÀÄÛ y UÀ¼À AiÀiÁªÀ ¨É¯ÉU¼ À ÀÄ ªÀiÁvÀÈPÉ
1 x 3
Obj
Key
Diff. Level
AiÀÄ£ÀÄß ¸ÀªÀÄ«Äw ªÀiÁvÀÈPÉ ªÀiÁqÀĪÀÅzÀÄ?
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
A. 3, 3
B. 1, 5
C. 2, 4
1 x 3 2 3 4 3 y 5
a symmetric matrix?
D. 4, 2
1
U
C
E
1
U
D
A
1
A
C
A
MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ°è T10=20 ; T20=10 DzÀgÉ ¸ÁªÀiÁ£Àå ªÉåvÁå¸À JµÀÄÖ? A. 2 B. 15 C. +1 D. –1 If T10=20 and T20=10 in an A.P, what is the common difference? A. 2 B. 15 C. +1 D. -1
£À£Àß ªÀÄUÀ£À ªÀAiÀĸÀÄì, £À£Àß vÀAzÉAiÀÄ ªÀAiÀĸÀÄì ªÀÄvÀÄÛ £À£Àß ªÀAiÀĸÀÄì EªÀÅUÀ¼¯ É Áè ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ°èª.É £À£Àß ªÀAiÀĸÀÄì 40, ºÁUÀÆ £À£Àß ªÀÄUÀ£À ªÀAiÀĸÀÄì 10 ªÀµð À UÀ¼ÁzÀg,É £À£Àß vÀAzÉAiÀÄ ªÀAiÀĸÉìµÀÄÖ? 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
tem No.
Ch.No
Questions
Obj
Key
Diff. Level
1
S
B
A
2
K
C
E
2
K
D
E
M015
M016
M017
A+I =
A.
1 0
A.
1
1
0
0 1
If A+ I =
1 0
2
DzÁUÀ, ªÀiÁvÀÈPÉ A UÉ ¸ÀªÀÄ£ÁzÀÄzÀÄ,
B.
2 1
1 0
0 1
1 1
1 -1
1 0
C.
0 -1
D.
1 1 0 -1
D.
1 1 0 -1
then, matrix A is equal to
B.
1 1
1 -1
1 0
C.
0 -1
PÀæªÀÄ AiÉÆÃd£ÉAiÀÄ CxÀðªÀ£ÀÄß PÉÆqÀĪÀ ºÉýPÉ A. vÉÆÃl¢AzÀ gÉÆÃeÁ ºÀÆUÀ¼£ À ÀÄß Dj¸ÀĪÀÅzÀÄ
B. §ÄnÖAiÀÄ°ègÀĪÀ ºÀƪÀÅUÀ¼£ À ÀÄß Dj¸ÀĪÀÅzÀÄ
C. PÁªÀÄ£À©°è£° À ègÀĪÀ §tÚU¼ À À eÉÆÃqÀuÉ
D. UÀæAxÁ®AiÀÄzÀ°è£À ¥ÀĸÀÛPU À ¼ À À DAiÉÄÌ
The statement which gives the meaning of permutation is : A. Picking flowers in the rose garden C. Arrangement of colours in a rainbow
B. Choosing different flowers in a basket D. Selecting the books in a library
5 ««zsÀ ¥ÀĸÀÛPU À ¼ À £ À ÀÄß ¨ÉÃgÉ ¨ÉÃgÉ jÃwAiÀÄ°è eÉÆÃr¸ÀĪÀÅzÀ£ÀÄß »ÃUÉ ¸ÀÆa¸À§ºÀÄzÀÄ? A. 5P2
B.
5
P3
C. 5P4
D. 5P5
Arrangement of 5 different books in different ways can be denoted as: A. 5P2
B.
5
P3
C. 5P4
D. 5P5
Item No.
M018
M019
M020
M021
M022
Questions n
Ch.No
Obj
Key
Diff. Level
2
K
C
A
2
K
C
E
2
K
C8 = nC12 DzÁUÀ n = 20 EzÀ£ÀÄß ¯ÉQ̸® À Ä G¥ÀAiÉÆÃV¸ÀĪÀ ¸À«ÄÃPÀgÀt: n
n
n
n
A. C1 = n B. C r = nPr /r! C. Cr = C n-r If nC8 = nC12 then n = 20. this can be calculated using the relation: A. nC1 = n B. nC r = nPr /r! C. nCr = nC n-r
D.
n
Cn = 1
D.
n
Cn = 1
nC15 = nC11 £À°è ‘n’ £À ¨É¯A É iÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄĪÀ ªÉÆzÀ® ºÀAvÀ nCr £ÀÄß nCn-r UÉ ¥ÀjªÀwð¸ÀĪÀÅzÀÄ JgÀq£ À ÃÉ ºÀAvÀ: A. n+15=n+11
B. 15=n+11
C. 15=n-11
D. 11= n-15
nC15 = nC11 to find the value of ‘n’ the first step is converting nCr into nCn-r. Second step is: A. n+15=n+11 B. 15=n+11 C. 15=n-11 D. 11= n-15
DgÀÄ d£ÀgÀ°è C±ÉÆÃPÀ£ÀÆ M§â. F UÀÄA¦¤AzÀ C±ÉÆÃPÀ££ À ÀÄß ¸ÉÃj¹zÀAvÉ 4 d£Àg£ À ÀÄß JµÀÄÖ «zsU À ¼ À ° À è Dj¸À§ºÀÄzÀÄ? 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
A
A
PÉÆnÖgÀĪÀ AiÀiÁªÀ ºÉýPÉUÀ¼ÀÄ nCr = nCn-r ¤§Azs£ À ÉAiÀÄ£ÀÄß C£ÀĸÀj¸ÀĪÀÅzÀÄ? A. 10C8 = 10C4
B. 10C8 = 10C2
C. 10C8 = 10C3
D. 10C5 = 10C2
Which of the following satisfy the relation nCr = nCn-r? A. 10C8 = 10C4
B. 10C8 = 10C2
C. 10C8 = 10C3
7 §tÚU½ À AzÀ ¥ÀæwzsÀédzÀ®Æè ¥ÀÄ£ÀgÁªÀwð¸ÀzÉ ªÀiÁqÀ§ºÀÄzÁzÀgÉ ¥Àæw zsÀédzÀ°è£À §tÚU¼ À À ¸ÀASÉå:
««zsÀ
¤¢üðµÀÖ
D. 10C5 =10C2
§tÚU¼ À £ À ÀÄß
¸ÀjºÉÆAzÀĪÀAvÉ
210
2
K
B
E
2
A
B
A
zsÀédUÀ¼£ À ÀÄß
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
tem No.
023
024
025
026
Questions nP2 = 2 ×
n-1
Ch.No
Obj
Key
Diff. Level
2
A
C
A
2
U
D
D
2
A
A
A
2
U
B
A
P3 , DzÀÝjAzÀ n(n-1) = 2 × -----------. E°è vÀ¦ À àºÉÆÃVgÀĪÀ ¥ÀzÀªÀÅ :
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) n-1 nP2 = 2 × P3 , 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) 5 ««zsÀ ¤WÀAlÄUÀ¼ÀÄ ªÀÄvÀÄÛ 4 ««zsÀ ªÁåPÀgt À ¥ÀĸÀÛPU À ¼ À £ À ÀÄß MAzÉà jÃwAiÀÄ ¥ÀĸÀÛPU À ¼ À ÀÄ MnÖUÉ EgÀĪÀAvÉ PÀ¥Án£À°è
eÉÆÃr¹zÁUÀ ¸ÁzsÀåªÁUÀĪÀ eÉÆÃqÀuU É ¼ À À «zsU À ¼ À À ¸ÀASÉå: 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! 5C2 ¨É¯A É iÀÄ£ÀÄß PÀAqÀÄ »rAiÀÄĪÁUÀ C£ÀĸÀj¹gÀĪÀ vÀ¥ÀÄà ºÀAvÀªÀ£ÀÄß UÀÄgÀÄw¹:
ºÀAvÀ 1 = 5! . 5-2! A. ºÀAvÀ 1
ºÀAvÀ 2 = 5! 3! B. ºÀAvÀ 2
ºÀAvÀ 3 = 5x4x3x2x1 3x2x1 C. ºÀAvÀ 3
ºÀAvÀ 4 = 10
D. ºÀAvÀ 4
Identify the wrong step while finding the value of 5C2 : 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
MAzÀÄ QæPÉmï ¸ÀAWÀz° À è 10 vÀAqÀU¼ À ÀÄ ¨sÁUÀª» À ¸ÀÄwÛª.É DrzÀ DlUÀ¼À ¸ÀASÉå
¥Àæw vÀAqÀªÀÅ JgÀqÉgÀqÀÄ ¨Áj EvÀgÉ vÀAqÀzÉÆqÀ£É DqÀ¨ÃÉ PÁzÀg,É
A. 2×10P2 B. 2×10C2 C. 2+10P2 D. 2+10C2 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. 2×10P2 B. 2×10C2 C. 2+10P2 D. 2+10C2
tem No.
027
028
M029
M030
M031
Questions ‘n’ ¨ÁºÀÄUÀ½gÀĪÀ §ºÀĨsÀÄdzÀ°è£À PÀtðUÀ¼À ¸ÀASÉå
Diff. Level
Ch.No
Obj
Key
2
U
A
A
2
S
C
A
2
A
B
A
3
K
A
E
3
K
B
E
[nc2 – n] PÀtðUÀ¼£ À ÀÄß M¼ÀUÉÆAqÀAvÉ 10 gÉÃSÁRAqÀU½ À zÀÝgÉ D
§ºÀĨsÀÄeÁPÀÈwAiÀÄÄ: A. ¥ÀAZÀ¨sÀÄd
B. µÀqÀÄâd
C. CµÀÖ¨sÀÄd
D. zÀ±¨ À sÀÄd
A polygon of ‘n’ sides has [nc2 – n] diagonals. If number of line segments including diagonals are 10, the polygon is: A. Pentagon B. Hexagon C. Octagon D. Decagon 5 ¸ÀªÀiÁAvÀgÀ gÉÃSÉU¼ À À UÀÄA¥À£ÀÄß 3 ¸ÀªÀiÁAvÀgÀ gÉÃSÉUÀ¼ÀÄ PÀvÀÛj¹zÁUÀ GAmÁUÀĪÀ ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðdUÀ¼À ¸ÀASÉå 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
À ¼ À £ À ÀÄß ªÀiÁqÀ¨ÃÉ PÁzÀgÉ PÉÊUÀ¼° À è £À «µÀÄ« Ú £À «UÀæºÀzÀ £Á®ÄÌ PÉÊUÀ¼° À è, zÀAqÀ, ZÀPÀæ, ±ÀAR ªÀÄvÀÄÛ ¥ÀzÀäU½ À ªÉ. EAvÀºÀ 12 «UÀæºU aºÉßUÀ¼£ À ÀÄß ¤ªÀð»¸À§ºÀÄzÁzÀ «zsU À ¼ À £ À ÀÄß »ÃUÉ ¥Àæw¤¢ü¸§ À ºÀÄzÀÄ: A. 4P1 B. 4P2 C. 4P3 D. 4P4 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. 4P1 B. 4P2 C. 4P3 D. 4P4 σ=
¥Àæ¸g À u À A É iÀÄ «ZÀ®£É, F ªÁPÀåªÀÅ ¸ÀÆa¸ÀĪÀÅzÀÄ:
A. ªÀiÁ£ÀPÀ«ZÀ®£É
B. ªÀiÁ¦ð£À UÀÄuÁAPÀ
C. ¸ÀgÁ¸Àj
The expression σ = variance, represents: A. Standard deviation B. Coefficient of variation
C. Mean
D. ¸ÀgÁ¸Àj «ZÀ®£É D. Mean deviation
ªÀUÁðAvÀgÀ 30-34 gÀ ªÀÄzsÀå©AzÀÄ: A. 30 +34 B. ½ ( 30 + 34) Mid point of the class interval 30 – 34 is: A. 30 +34 B. ½ ( 30 + 34)
C. ½ ( 34 -30)
D. 34 -30
C. ½ ( 34 -30)
D. 34 -30
em No.
032
033
034
035
036
Questions Ch.No
Obj
Key
Diff. Level
3
S
A
E
3
U
D
E
3
U
A
A
3
K
B
A
3
U
B
A
PÉÆnÖgÀĪÀ zÀvÁÛA±ÀU¼ À £ À ÀÄß G¥ÀAiÉÆÃV¹PÉÆAqÀÄ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉQ̸ÀÄ: N= 10, Σfx = 100 , Σfd2 = 210 A. 4.6 B. 5 C. 2.1 D. 21 Using the given data, calculate standard deviation N= 10, Σfx = 100 , Σfd2 = 210 A. 4.6 B. 5 C. 2.1 D. 21
F PɼV À £À ºÉýPÉU¼ À ° À è AiÀiÁªÀÅzÀÄ ªÀiÁ¦ð£À UÀÄuÁAPÀPÉÌ ¸ÀA¨sA À zÀ¥ÀnÖ®è? A. ¸ÁªÀiÁ£ÀåªÁV ±ÉÃPÀqÁ jÃwAiÀÄ°è ºÉüÀ®àqÀÄvÀÛz.É
B. ºÀg« À £À EAwµÀÄÖ ¸Á¥ÉÃPÀë C¼ÀvA É iÀÄ jÃwAiÀÄ°è
C. KPÀªÀiÁ£ÀU½ À ®èzÀ ¥ÀjªÀiÁtªÁV
D. PÉÃA¢æÃAiÀÄ ¥ÀæªÀèwÛAiÀÄ C¼ÀvÉ
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
MAzÀÄ ±Á¯ÉAiÀÄ 9£É vÀgÀUÀwAiÀÄ A ªÀÄvÀÄÛ B ¸ÉPÀë£ï UÀ¼ÀÄ UÀtv  Àz° À è UÀ½¹gÀĪÀ ¸ÀgÁ¸Àj CAPÀU¼ À ÀÄ PÀæªÀĪÁV 34.5 ªÀÄvÀÄÛ 28.5 DVzÀÄÝ, ªÀiÁ£ÀPÀ «ZÀ®£ÀªÀÅ 6.21 ªÀÄvÀÄÛ 4.56EzÀÝ°è, AiÀiÁªÀ ¸ÉPëÀ£ï ¤£À ¸Ázs£ À A É iÀÄ°è C¹Üvv À É ºÉZÀÄ,Ñ PÁgÀtàPÀj¹: A. ¸ÉPÀë£ï A
B. ¸ÉPÀë£ï B
C. ¸ÉPÀë£ï A ªÀÄvÀÄÛ B JgÀqÀÆ
D. ¸ÉPÀë£ï A ªÀÄvÀÄÛ B JgÀqg À ° À è
MAzÀÆ C®è
If the arithmatic mean in maths of a 9th 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 ‘n’ ªÀiË®åUÀ¼À ¸ÀgÁ¸Àj¬ÄAzÁzÀ «ZÀ®£ÉU¼ À À ªÉÆvÀÛªÀÅ, AiÀiÁªÁUÀ®Æ: A. -1
B. 0
C. +1
D. 1QÌAvÀ C¢üPÀ
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 A, B ªÀÄvÀÄÛ C vÀgÀUw À UÀ¼À CAPÀU¼ À £ À ÀÄß PÉÆqÀ¯ÁVzÉ. A. ªÀÄzsÀåPÀ «ZÀ®£É
B. ªÀiÁ¦ð£ÀÀ UÀÄuÁAPÀ
D vÀgÀUw À UÀ¼À «ZÀ® ªÉÊ«zÀåvÉAiÀÄ£ÀÄß w½AiÀÄ®Ä, G¥ÀAiÉÆÃV¸À§ºÀÄzÁzÀÄzÀÄ: C. ZÀvÀÄxÀðPÀ «ZÀ®£É
D. ZÀvÀÄxÀðPÀ «ZÀ®£ÉAiÀÄ UÀtPÀ
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
em No.
037
038
039
040
Questions 1,2,3,4,5 ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄÄ 1.4 DzÀgÉ, 11, 12, 13, 14, 15 UÀ¼À ªÀiÁ£ÀPÀ
Ch.No
Obj
Key
Diff. Level
3
U
A
E
3
U
D
A
3
U
D
D
4
K
D
E
«ZÀ®£ÉAiÀÄÄ:
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 2
À ÀÄß PÀAqÀÄ»rAiÀÄÄvÁÛ£.É ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ MAzÀÄ DªÀvð À ¥ÀnÖ¬ÄAzÀ, M§â «zÁåyðAiÀÄÄ X, d ªÀÄvÀÄÛ d UÀ¼£ »rAiÀÄ®Ä £ÁªÀÅ ¯ÉQ̸À¨ÃÉ PÁzÀ ºÀAvÀªÀÅ C. √ Σfd2 D. fd2 B. Σfd2 N N 2 A student finds X, D and D of a given frequency distribution. The next step in finding the S.D is to calculate. A. Σfd2 B. Σfd2 C. √ Σfd2 D. fd2 N N
A. Σfd2
MAzÀÄ UÀÄA¦£À d£ÀgÀ ªÀAiÀĸÀì£ÀÄß DªÀvð À ¥ÀnÖAiÀÄ°è ¥ÀnÖ ªÀiÁqÀ¯ÁVzÉ. AiÀiÁªÀÅzÀÄ ºÉZÁÑUÀÄvÀÛzÉ?
EzÀgÀ ªÀUÁðAvÀgª À £ À ÀÄß ºÉa¹ Ñ zÁUÀ, F PɼV À £ÀªÀÅUÀ¼° À è
A. MlÄÖ ªÀUÁðAvÀgÀU¼ À À ¸ÀASÉå
B. d£ÀgÀ ªÀAiÀĸÀÄì
C. MlÄÖ DªÀvð À APÁ
D. ªÀUÁðAvÀgÀU¼ À À M¼ÀV£À DªÀÈwÛ
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
PɼV À £ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ ‘3P’ AiÀÄ£ÀÄß ¸ÁªÀiÁ£Àå C¥Àªv À ð À £ÀªÁV ºÉÆA¢gÀĪÀÅ¢®è? A. 3P3 B. 6P2 C. 9P1 D. 12P0 Which of the following cannot have ‘3P’ as a common factor? A. 3P3 B. 6P2 C. 9P1 D. 12P0
Item No.
Questions
M041
ax2-a3 ªÀÄvÀÄÛ
M042
x y z ªÀÄvÀÄÛ
4
B
E
2
4
K
C
E
4
K
C
E
4
S
B
E
4
S
D
A
4
S
C
A
D. x6y4z4 D. x6y4z4 3
2
5x -10 ªÀÄvÀÄÛ 5x -20 UÀ¼À ªÀÄ.¸Á.C.ªÀÅ : C. 5x
D. 5
C. 5x
D. 5
PɼV À £ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ, ab (a+b)+bc(b+c)+ca(c+a) UÉ ¸ÀªÀÄ£ÁVgÀĪÀÅ¢®è : A ∑ab (a+b) B. ∑c2 (a+b) C. ∑a2 (b+c) D. ∑b2 (a+b) Which of the following is not equal to ab (a+b)+bc(b+c)+ca(c+a)? A ∑ab (a+b) B. ∑c2 (a+b) C. ∑a2 (b+c) D. ∑b2 (a+b)
M046
K
ªÀÄ.¸Á.C ªÀ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä, 2x – x + 3x + 1 ©ÃdUÀÄZÀÒªÀ£ÀÄß §gÉzÀÄPÉƼÀÄîªÀ ¸ÀjAiÀiÁzÀ PÀæªÀÄ:
A. x-2 B. 5(x-2) HCF of 5x -10 and 5x2 -20 is A. x-2 B. 5(x-2) M045
4
x y z UÀ¼À ®.¸Á.C. ªÀÅ
A. 2x4+3x3–x2+1 B. 2x4-3x3–x2+1 C. 2x4+3x3–x2+0x+1 D. 2x4+3x3–x2+x+1 Correct arrangement of terms of the expression 2x4 – x2 + 3x3 + 1 to find HCF is: A. 2x4+3x3–x2+1 B. 2x4-3x3–x2+1 C. 2x4+3x3–x2+0x+1 D. 2x4+3x3–x2+x+1 M044
Key
6 2 4
A. x3y4z6 B. x3y2z4 C. x6y4z6 The L.C.M. of x3y4z6 and x6y2z4 is : A. x3y4z6 B. x3y2z4 C. x6y4z6 M043
Obj
bx-ab UÀ¼À ªÀĺÀvÀÛªÀÄ ¸ÁªÀiÁ£Àå C¥ÀªÀvð À £ÀªÀÅ:
A. (x+a) B. (x-a) C. (x2-a2) D. (x2+a2) 2 3 Highest common factor of ax -a and bx-ab is: A. (x+a) B. (x-a) C. (x2-a2) D. (x2+a2) 3 4 6
Ch.No
Diff. Level
∑a=0 DzÁUÀ, ∑a3
ªÀÅ :
A 0 B. abc 3 If ∑a=0, then ∑a will be: A 0 B. abc
C. 3abc
D. a3+b3+c3
C. 3abc
D. a3+b3+c3
Item No. M047
Questions 2
2
2
2
2
3
3
d) Σ b(a-b)
S
B
E
4
U
C
A
4
U
B
E
4
U
A
A
4
S
A
E
3
PɼV À £ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀ£ÀÄß a +b +c +3ab(a+b) UÉ PÀÆrzÁUÀ, CzÀÄ ZÀQæÃAiÀÄ ¸ÀªÀÄ«ÄwAiÀiÁUÀÄvÀÛz?É
ªÀÄÆgÀÄ ¸ÀASÉåUÀ¼À ªÉÆvÀÛ ‘0’ DVzÉ ªÀÄvÀÄÛ D ªÀÄÆgÀÄ ¸ÀASÉåUÀ¼À WÀ£U À ¼ À À ªÉÆvÀÛªÀÅ 36 DzÀgÉ, D ¸ÀASÉåUÀ¼À UÀÄt®§ÞªÀÅ:
(a-b)2=0 DzÁUÀ, F PɼV À £À AiÀiÁªÀ ¸ÀA§Azsª À ÀŤdªÁUÀÄvÀÛzÉ? A. 2(a2+b2) =(a+b) 2 B. 2(a2+b2) =(a-b) 2 C. 2(a2-b2) =(a+b) 2 When (a-b)2=0, which of the following relations become true? A. 2(a2+b2) =(a+b) 2 B. 2(a2+b2) =(a-b) 2 C. 2(a2-b2) =(a+b) 2
M051
4
d) Σ b(a-b)
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 M050
Key
ab –ac –a b +bc –cb +ca £ÀÄß Σ ¸ÀAPÉÃvÀª£ À ÀÄß G¥ÀAiÉÆÃV¹ §gɬÄj:
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 a3+b3+c3+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)] M049
Obj
2
a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) 2 2 2 2 2 2 Write ab –ac –a b +bc –cb +ca using Σ notation: a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) M048
Ch.No
Diff. Level
2
D. (a2-b2) =(a-b) 2 D. (a2-b2) =(a-b) 2
2
(x +4x+4) (x +6x+9) gÀ ªÀUð À ªÀÄÆ®UÀ¼À ¨É¯A É iÀÄ£ÀÄß PÀAqÀÄ»r¬Äj: A. x2+5x+6 B. x2+6x+5 C. x2-5x+6 Find the square root of (x2 +4x+4) (x2 +6x+9) : A. x2+5x+6 B. x2+6x+5 C. x2-5x+6
D. x2+5x-6 D. x2+5x-6
Item No.
Questions
M052
1) √2
2) √12
3) √18
x √y = √80DzÀgÉ, DUÀ ‘y’£À
D. 1,3,4 3) √18 4) √200 D. 1,3,4
D
A
4
S
B
E
4
K
D
A
5
K
C
E
5
K
A
E
5
K
B
A
D. 10 D. 10
C. 2x - √ x
D. √ x
C. 2x - √ x
D. √ x
B. ¸Àg¼ À À §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ C.ªÀUð À §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ
A polynomial of degree two, in one variable is called: A. a binomial B. a linear polynomial C. a quadratic polynomial
D. §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ
D. polynomial
ªÀUð À ¸À«ÄÃPÀgÀtzÀ DzÀ±ð À gÀÆ¥ÀªÁzÀ ax2+bx+c=0 zÀ°è b=0 DzÀgÉ GAmÁUÀĪÀ ¸À«ÄÃPÀgt À ªÀÅ A. ±ÀÄzÀÞ ªÀUð À ¸À«ÄÃPÀgÀt
B. «Ä±Àæ ªÀUð À ¸À«ÄÃPÀgÀt
C. £ÉÃgÀ
D. ¸Àg¼ À À
In the standard form of the quadratic equation ax2+bx+c=0, if b=0 then the resulting equation is: A. Pure quadratic B. adfected quadratic C. linear D. simple M058
K
JgÀq£ À ÃÉ WÁvÀzÀ°ègÀĪÀ MAzÀÄ CªÀåPÀÛ¥z À ª À £ À ÉÆß¼ÀUÉÆAqÀ MAzÀÄ §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛAiÀÄ£ÀÄß »ÃUÉAzÀÄ PÀgA É iÀħºÀÄzÀÄ. A. ¢é¥ÀzÀ ©ÃeÉÆÃQÛ
M057
4
2x√ x £À CPÀgÀtàPÁgÀPÀ C¥ÀªÀvð À £ÀªÀÅ A. 2x√ x B. 2x + √ x Rationalizing factor of 2x√ x is A. 2x√ x B. 2x + √ x
M056
Key
¨É¯A É iÀÄÄ:
A. 4 B. 5 C. 8 If x √y = √80, then the value of ‘y’ will be: A. 4 B. 5 C. 8 M054
Obj
4) √200 F PÀgt À ÂU¼ À ° À è ¸ÀªÀÄgÀÆ¥À PÀgÀtÂU¼ À ÀÄ
A. 1,2,3 B. 2,3,4 C. 1,2,4 Like surds among the following are 1 ) √2 2) √12 A. 1,2,3 B. 2,3,4 C. 1,2,4 M053
Ch.No
Diff. level
2
ax +bx+c=0, ªÀUð À ¸À«ÆPÀgt À zÀ ±ÉÆÃzsPÀ À A. –b2-4ac B. b2-4ac C. b2+4ac The discriminant of the quadratic equation ax2+bx+c=0 is: A. –b2-4ac B. b2-4ac C. b2+4ac
D. –b2 ±√b2-4ac D. –b2 ±√b2-4ac
Item No. M059
Questions
B. 12 k 2-k-5=0
C. 12 k 2-4 k =5
D. 12 k 2-k =5 Standard
B. 12 k 2-k-5=0
C. 12 k 2-4 k =5
D. 12 k 2-k =5
B. ¸ÀªÀÄ
C. ¸ÀA«Ä±Àæ
K
A
A
5
K
A
E
5
U
B
A
5
U
A
A
5
S
B
D
D. ¨sÁUÀ®§Þ ¸ÀASÉå
PɼV À £À ¸À«ÄÃPÀgt À UÀ¼° À è ªÀÄÆ®UÀ¼ÀÄ ¸ÀªÀÄ£ÁVgÀĪÀ ªÀUÀð¸À«ÄÃPÀgt À ªÀÅ: A. x2-2x-1=0 B. x2-2x+1=0 C. 2x2-2x+1=0 D. x2-2x-3=0 Quadratic equation having equal roots among the following equation is : A. x2-2x-1=0 B. x2-2x+1=0 C. 2x2-2x+1=0 D. x2-2x-3=0 2
2
§ºÀÄ¥ÀzÀ x -9 £ÀPÉëAiÀÄ£ÀÄß J¼ÉzÁUÀ gÉÃSÉAiÀÄÄ x- CPÀ몣 À ÀÄß £ÀPÉëAiÀÄ£ÀÄß ¸ÀA¢ü¸ÀĪÀ ©AzÀÄUÀ¼ÀÄ A. (-3, 0) ªÀÄvÀÄÛ (3,0)
B. (-2, 0) ªÀÄvÀÄÛ (2,0)
C. (-2, -5) ªÀÄvÀÄÛ (2,-5)
D. (1,-8) ªÀÄvÀÄÛ (-1,-8)
When the graph of the polynomial x2-9 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) M063
5
¥ÀÆtðªÀUð À ªÀ®èzÀ MAzÀÄ ªÀUð À ¸À«ÄÃPÀg À Àt b -4ac>0 DzÀg,É CzÀgÀ ªÀÄÆ®UÀ¼ÀÄ In a quadratic equation if b2-4ac>0 and not a perfect square, then the roots are : A. Real B. Equal C. Imaginary D. Rational
M062
Key
2
A. ªÁ¸ÀÛªÀ
M061
Obj
4k (3 k -1) = 5 DzÀ±ð À gÀÆ¥ÀªÀÅ : A. 12 k 2-4k-5=0 from of 4k (3k -1) = 5 is: A. 12 k 2-4k-5=0
M060
Ch.No
Diff. Level
3x2-10x+3=0 ¸À«ÄÃPÀgÀtzÀ MAzÀÄ ªÀÄÆ®ªÀÅ 1/3 DVzÉ. E£ÀÆßAzÀÄ ªÀÄÆ®ªÀÅ : A. 1/3 B. 3 C. 3 1/3 D. 7 1/3 2 One of the roots of the equation 3x -10x+3=0 is 1/3. The other root is: A. 1/3 B. 3 C. 3 1/3 D. 7 1/3
Item No. M064
Questions
B. mn
5
S
C
E
5
U
C
A
6
K
A
E
6
K
D
A
6
K
C
E
C.
2
x -x-c=0 ¸À«ÆPÀgÀtzÀ°è ’c’ AiÀiÁªÀ ¨É¯A É iÀÄÄ, ¸À«ÆPÀgÀtzÀ ªÀÄÆ®UÀ¼ÀÄ ¸ÀA«Ä±Àæ ¸ÀASÉåUÀ¼ÁUÀĪÀŪÀÅ? A. 0 B. -1 C. +1 D. +2 2 In the equation x -x-c=0 what value of ’c’ makes the roots of the equation imaginary? A. 0 B. -1 C. +1 D. +2
FUÀ ªÉÃ¼É 3 UÀAmÉ DVzÀÝgÉ. 48 UÀAmÉU¼ À À »A¢£À ªÉüÉ: A. 3 UÀAmÉ
B. 6 UÀAmÉ
C. 9 UÀAmÉ
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 M067
Key
m ªÀÄvÀÄÛ n UÀ¼ÀÄ x -6x +2 =0 JA§ ªÀUð À ¸À«ÄÃPÀgÀtzÀ ªÀÄÆ®UÀ¼ÁzÀgÉ, PɼV À £ÀªÀÅUÀ¼° À è 3PÉÌ ¸ÀªÀÄ£ÁVgÀĪÀÅzÀÄ? m+n D. m2n2 mn If m and n are the roots of the quadratic equation x2 -6x +2 =0 then 3 is the value of D. m2n2 A. m+n B. mn C. m+n mn
M066
Obj
2
A. m+n
M065
Ch.No
Diff. Level
D. 12 UÀAmÉ D. 12’o’ clock
2005gÀ ªÀiÁZïð wAUÀ½£À 4 ªÀÄvÀÄÛ 11£Éà ¢£ÁAPÀU¼ À ÀÄ ±ÀÄPÀæªÁgÀU¼ À ÁUÀÄvÀÛª.É F ¸ÀA§Azsª À £ À ÀÄß »ÃUÉ
¥Àæw¤¢ü¸§ À ºÀÄzÀÄ: A. 4<11 (ªÉÆqï 7) th
th
B. 11-4 (ªÉÆqï 7)
C. 4>11 (ªÉÆqï 7)
D. 4 ≡ 11(ªÉÆqï 7)
March 4 and 11 of 2005 are Fridays. This relation can be expressed as: A. 4<11 (mod 7) M068
B. 11-4 (mod 7)
C. 4>11 (mod 7)
D. 4 ≡11(mod 7)
Y⊗4 Y = 1 DzÀg,É ‘Y’ £À ¸ÀjAiÀiÁzÀ ¨É¯É : 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
Item No. M069
Questions
Ch.No
Obj
Key
Diff. Level
6
S
D
E
6
S
D
E
6
S
B
E
7
K
A
E
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 M070
B. 2, 4
C. 3, 4
D. 4, 4
x+2≡4 (ªÉÆqï 5) DzÁUÀ, ‘x’ £À ¨É¯A É iÀÄÄ 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
M071
( 10⊕ 12 2 ) ⊕ 12 3 AiÀÄ ¨É¯É : A. 2
B. 3
C. 10
D. 15
C. 10
D. 15
The value of ( 10⊕ 12 2) ⊕ 12 3 is A. 2 M072
B. 3
Czsð À ªÀÈvÀÛz° À è£À JgÀqÀÄ eÁåUÀ¼À C£ÀÄ¥ÁvÀ 1:1EzÀÝgÉ CªÀÅUÀ¼ÀÄ GAlĪÀiÁqÀĪÀ ªÀÈvÀÛ RAqÀU¼ À À «¹ÛÃtðzÀ C£ÀÄ¥ÁvÀ: 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
Questions
Item No. M073
Ch.No
Obj
Key
Diff. level
7
U
A
E
7
K
D
E
avÀæz° À è CvÀåAvÀ aPÀÌ ®WÀÄ RAqÀª£ À ÀÄß ¥ÀqÉAiÀÄ®Ä AiÀiÁªÀ ªÀÈvÀÛ RAqÀPÉÌ §tÚ ºÀZÀÄ« Ñ j? F
A B
A. ABC C. ACDF
D
O
E
B. ABD D. ACDEF
C
In the given figure which segment would you shade to get the smallest minor segment? F E O
A
A. ABC C. ACDF
D B
M074
B. ABD D. ACDEF
C
¥Àg¸ À ÀàgÀ bÉâ¸ÀĪÀ AiÀiÁªÀÅzÉà JgÀqÀÄ ªÁå¸ÀU¼ À À vÀÄ¢©AzÀÄUÀ¼° À è J¼ÉAiÀÄ®àlÖ ¸Àà±ÀðPÀU¼ À ÀÄ GAlĪÀiÁqÀĪÀ DPÀÈwAiÀÄÄ MAzÀÄ: A. ZÀZËÑPÀ
B. DAiÀÄvÁPÁg
É
C. ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðd
D. ZÀvÀĨsÀÄðd
Tangents drawn at the end points of any two intersecting diameters always form a: A. Square B. Rectangle C. Parallelogram D. Quadrilateral
Questions
Item No. M075
Ch.No
Obj
Key
Diff. level
7
K
C
E
7
S
B
E
8
K
C
E
avÀæz° À è PABQ MAzÀÄ ¸ÀªÀÄ¢é¨ÁºÀÄ vÁæ¦dåªÁUÀ®Ä F ¸ÀA§Azs« À zÁÝUÀ ªÀiÁvÀæ A
C1
C2
P
D
C
B 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 P
C1
C2
B
D
C
Q
A. PA ≥ CQ M076
B. PB < CQ
C. PD=CQ
D. PB>CQ
12¸ÉA.«Ä GzÀÝzÀ JgÀqÀÄ ¸ÀªiÀ Á£ÁAvÀgÀ eÁåUÀ¼£ À ÀÄß‘x’¸ÉA.«Ä CAvÀgz À ° À è ªÀÈvÀÛPÃÉ AzÀæzÀ «gÀÄzÀÞ §¢UÀ¼À°è J¼É¢zÉ.
DUÀ wædåªÀÅ: A. √ 144 – x2
4
B. √36 + x2
C. √36-x2
D. √144-x2
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 – x2 B. √36 + x2 C. √36-x2 D. √144-x2
4 M077
ABC ªÀÄvÀÄÛ
4 DEF ¸ÀªÀÄgÀÆ¥À wæ¨sÀÄdUÀ¼À C£ÀÄgÀÆ¥À ±ÀÈAUÀU¼ À ÀÄ A ªÀÄvÀÄÛ D, B ªÀÄvÀÄÛ E
ºÁUÀÆ C ªÀÄvÀÄÛ
F UÀ¼ÀÄ DVzÀÝgÉ, F PɼV À £ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À eÉÆvÉAiÀiÁVzÉ: A. AB ªÀÄvÀÄÛ DF
B. AC ªÀÄvÀÄÛ DE
C. BC ªÀÄvÀÄÛ EF
D. AC ªÀÄvÀÄÛ 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
Item No.
Questions
Obj
Key
8
K
C
E
8
U
B
E
8
U
C
E
0
M078
PQR wæ¨sÀÄdzÀ°è ∠PQR = 90 , DzÁUÀ, ¸ÀjAiÀiÁzÀ ¸ÀA§Azsª À ÀÅ AiÀiÁªÀÅzÀÄ? ¥ÀvÉÛ ªÀiÁrj: 2 2 2 2 2 2 B. PR = RP + QR A. PQ = PR + QR
M079
C. PR 2 = PQ 2 + QR 2 D. QR 2 = PR 2 + QP 2 For a triangle PQR where ∠PQR = 900, 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 MAzÀÄ ®A§PÉÆã wæ¨sÀÄdzÀ ¨ÁºÀÄUÀ¼À C£ÀÄ¥ÁvÀªÀÅ 3:4:5 F ¸ÀA§Azsª À £ À ÀÄß UÀªÀÄ£Àz° À èlÄÖPÉÆAqÀÄ, ©nÖgÀĪÀ ¥Àzª À £ À ÀÄß vÀÄA©¹ 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
M080
Ch.No
Diff. level
F avÀæz° À ègÀĪÀ ¥ÀgÁåAiÀÄ PÉÆãÀU¼ À À eÉÆvÉAiÀÄ£ÀÄß ¥ÀvÉÛ ªÀiÁrj: A. ∟PRQ & ∟MRN B. ∟QPR & ∟RMN C. ∟PQR & ∟NMR D. ∟RPQ & ∟RMN
M P N
R R
Q
Q In the given figure pair of alternate angles is A. ∟PRQ & ∟MRN B. ∟QPR & ∟RMN C. ∟PQR & ∟NMR D. ∟RPQ & ∟RMN
M P
R Q
Q
N
R
Questions
Item No. M081
Ch.No
Obj
Key
Diff. level
avÀæzÀ ¸ÀºÁAiÀÄ¢AzÀ ¥ÀÆtð ªÀiÁrj: AB : AQ : : BC : ______ A. AQ
B. AP C. PQ
D. AC
Complete the statement using the given figure AB : AQ : : BC : ______ A. AQ
M082
B. AP C. PQ
D. AC
avÀ檣 À ÀÄß £ÉÆÃr ¸ÀjAiÀiÁzÀ ¸ÀA§Azsª À À£ÀÄß ¥ÀvÉÛ ªÀiÁrj: A. B. C. D.
P
B
K
C
E
8
U
A
A
A
AP.AB = AQ.AC AP.AC = AQ.AB AP.AQ = AC.AB AP.PQ = BC.AC
Which is the correct relation among the following A. AP.AB = AQ.AC P P B. AP.AC = AQ.AB C. AP.AQ = AC.AB D. AP.PQ = BC.AC
8
A
P
Q
Q
C
B
C
Questions
Item No. M083
8
U
C
A
8
K
D
E
8
K
B
E
8
U
D
E
B. ªÀÈvÀÛzÀ CvÀåAvÀ zÉÆqÀØ eÁå
C. ªÀÈvÀÛª£ À ÀÄß JgÀqÀÄ Czsð À ªÀÈvÀÛU¼ À ÁV C¢üð¸ÀÄvÀÛzÉ
D. MAzÀÄ ¸Àg¼ À g À ÉÃSÉ
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
¨ÁºÀåªÁV ¸Àà²ð¸ÀĪÀ ªÀÈvÀÛUÀ½UÉ ¸ÀA§A¢ü¹zÀ ¸À«ÄÃPÀgÀtªÀ£ÀÄß ¥ÀvÉÛªÀiÁr: 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
M086
Key
MAzÀÄ ªÀÈvÀÛzÀ ªÁå¸ÀPÉÌ ¸ÀA§Azs« À ®èzA À vÀºÀ ºÉýPÉAiÀÄÄ: A. ªÀÈvÀÛzÀ wædåzÀ JgÀqg À µ À À ÄÖ
M085
Obj
JgÀqÀÄ ¸ÀªÀÄgÀÆ¥À wææ¨sÀÄdUÀ¼À «¹ÛÃtðªÀÅ 392 ZÀ.¸ÉA.«Ä ªÀÄvÀÄÛ 200ZÀ. ¸ÉA.«Ä CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À C£ÀÄ¥ÁvÀªÀÅ 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
M084
Ch.No
Diff. level
JgÀqÀÄ wæ¨sÀÄdUÀ¼ÀÄ ¸ÀªÀÄPÉÆäAiÀÄUÀ¼ÁVzÀÝgÉ, CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄ: A. ¸ÀªÀÄ B. ¸ÀªÀiÁ£ÁAvÀgÀ C. ®A§ D. If two triangles are equiangular, then their sides are: A. equal B. parallel C. perpendicular
¸ÀªÀiÁ£ÀÄ¥ÁvÀ D. proportional
Questions
Item No. M087
Key
8
U
B
A
9
K
D
E
9
U
C
E
MAzÀÄ ¥Áè¹ÖPï WÀ£À UÉÆüÀª£ À ÀÄß PÀgV À ¹, MAzÀÄ UÉÆA¨ÉAiÀÄ£ÀÄß ªÀiÁrzÁUÀ CzÀgÀ°è §zÀ¯ÁUÀzÉ EgÀĪÀÅzÀÄ A. DPÁgÀ B. GzÀÝ C. ªÉÄïÉäöÊ«¹ÛÃtð D. WÀ£¥ À s® À À 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
M089
Obj
JgÀqÀÄ ¸ÀªÀiÁAvÀgª À ÁVgÀĪÀ ¸Àà±ð À PÀU¼ À À £ÀqÀÄ«£À, MAzÀÄ ¸Àà±ð À PÀ bÉÃzÀPª À ÀÅ ªÀÈvÀÛ PÉÃAzÀæzÀ°è PÉÆãÀª£ À ÀäßAlĪÀiÁqÀÄvÀÛz.É D PÉÆãÀzÀ C¼ÀvA É iÀÄÄ: A. ®WÀÄ B. ®A§ C. C¢üPÀ D. ¸Àg¼ À À 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
M088
Ch.No
Diff. level
PÉÆnÖgÀĪÀ ¹°AqÀj£À°è, JgÀqÀÄ ©AzÀÄUÀ¼À £ÀqÀÄ«£À CvÀåAvÀ zÀÆgÀ : O
A
o
D
B
A. AB C. AC
B. AD D. OC
C
The farthest distance between the two points on the given cyclinder: O
A
B
o
D
C
A. AB C. AC
B. AD D. OC
Questions
Item No. M090
9
U
B
E
9
U
B
E
9
S
C
A
9
U
A
A
B
Key
B. §lÖ°£À NgÉ JvÀÛgÀ
C. §lÖ°£À D¼À
D. §lÖ°£À ªÁå¸À
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
MAzÀÄ ¹°AqÀgÁPÁgÀzÀ ¥É¤ß£À°è, MAzÀÄ ¨Áj ªÀĹ vÀÄA©zÁUÀ, 22 ¥ÀÄlUÀ¼µ À ÀÄÖ §gÉAiÀħºÀÄzÀÄ. 100 cc ªÀŬÄAzÀ 1600 ¥ÀÄlUÀ¼ÀÄ §gÉAiÀħºÀÄzÀÄ. ¥É¤ß£À AiÀiÁªÀ C¼ÀvA É iÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä F zÀvÁÛA±ÀªÀÅ ¸ÀºÁAiÀÄPÀªÁVzÉ? A. «¹ÛÃtð
B. ¥sÀ£¥ À ® sÀ
C. JvÀÛgÀ
D. wædå
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 M092
Ch.No
MAzÀÄ CzsÀðªÀÈvÁÛPÁgÀzÀ ¯ÉÆúÀzÀ ºÁ¼ÉAiÀÄ£ÀÄß, MAzÀÄ vÉgz À À ±ÀAPÀ«£À §lÖ® DPÁgÀzÀ°è §VιzÉ. DUÀ Czsð À ªÀÈvÀÛzÀ ªÁå¸ÀªÀÅ EzÀPÉÌ DUÀÄvÀÛz.É A. §lÖ°£À ¥Àj¢ü
M091
Diff. level
Obj
6¸ÉA.«Ä wædåªÀżÀî vÁªÀÄæzÀ UÉÆüÁPÁgÀzÀ UÀÄAqÀ£ÀÄß PÀgV À ¹zÉ ªÀÄvÀÄÛ CzÀ£ÀÄß 0.06 æ ¸ÉA.«Ä wæædå«gÀĪÀ
vÀAwAiÀÄ£ÁßV J¼É¢zÉ. vÀÀAwAiÀÄ GzÀݪÀÅ : A. 600 «Æ
B. 650 «Æ
C. 800 «Æ
D. 825 «Æ
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 M093
MAzÀÄ UÉÆüÀzÀ WÀ£À¥® sÀ ªÀÄvÀÄÛ ªÉÄïÉäöÊ «¹ÛÃtðUÀ¼ÀÄ ¯ÉPÁÌZÁgÀ ¥ÀæPÁgÀ MAzÉà DVzÁÝUÀ, CzÀgÀ ªÁå¸ÀªÀÅ: A. 3 KPÀªÀiÁ£ÀU¼ À ÀÄ
B. 6 KPÀªÀiÁ£ÀU¼ À ÀÄ
C. 8 KPÀªÀiÁ£ÀU¼ À ÀÄ
D. 9 KPÀªÀiÁ£ÀU¼ À ÀÄ
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
Item No. M094
Ch.No
Obj
Key
Diff. level
9
U
C
A
10
K
C
A
10
A
C
E
Questions 7 «Ælgï ªÁå¸À ªÀÄvÀÄÛ 5 «Ælgï GzÀݪÀżÀî MAzÀÄ gÉÆîgï ªÉÄÊzÁ£Àz° À è GgÀĽ¸À¯ÁVzÉ. gÉÆîgï
ªÀiÁrzÀ ¸ÀÄvÀÄÛU¼ À À ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä ¨ÉÃPÁzÀ zÀvÁÛA±ÀªÀÅ : A. gÉÆîgï£À MlÄÖ ªÉÄïÉäöÊ «¹ÛÃtð
B. CzÀgÀ ªÀPÀæ ªÉÄïÉäöÊ«¹ÛÃtð
C. gÉÆîgï£À ¸ÀªÀÄvÀlÄÖ ªÀiÁrzÀ GzÀÝ
D. gÉÆîgï£À
WÀ£¥ À s® À
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 M095
ªÉÄïÉäöÊUÀ¼À ¸ÀASÉå ªÀÄvÀÄÛ ±ÀÈAUÀU¼ À À ¸ÀASÉåUÀ¼ÀÄ AiÀiÁªÁUÀ®Æ MAzÉà ¸ÀªÀÄ£ÁVgÀĪÀ ¥s£ À ª À ÀÅ: A. µ ó t À ÄäRWÀ£À
B. ¥ÀlÖPÀ
C. UÉÆÃ¥ÀÄgÀ
D. ¥ÁèmÉÆäPï WÀ£À
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 M096
F PɼV À £ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ C¸ÁzÀå A. ªÀÄÆgÀÄ ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼À vÁgÀªÁºÀPÀ eÁ¯ÁPÀÈw gÀd£É eÁ¯ÁPÀÈw gÀZ£ À É C. MAzÀÄ ¨É¸À ¸ÀA¥ÁvÀ ©ªÀÄzÀÄ«gÀĪÀ eÁ¯ÁPÀÈw gÀZ£ À É gÀZ£ À É Which one of the following is impossible to do? A. drawing a traversable network of 3 nodes C. drawing a network of one odd node
B. JgÀqÀÄ ¨É¸À ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼À ¥ÁgÀªÁºÀPÀ D. JgÀqÀÄ ¨É¸À ¸ÀA¥ÁvÀ ©AzÀÄ«gÀĪÀ eÁ¯ÁPÀÈw
B. making a traversable network of 2 odd nodes D. drawing a network of two odd nodes
Questions
Item No. M097
Ch.No
Obj
Key
Diff. level
10
K
B
E
F eÁ¯ÁPÀÈwAiÀÄ ªÀiÁvÀÈPÉAiÀÄ°è JµÀÄÖ ¸ÀÄgÀĽUÀ½ªÉ: 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
M098
B. 2
C. 3
D. 4
F WÀ£ÁPÀÈwAiÀÄ£ÀÄß ºÉ¸j À ¹:
A. ªÀUð À ¥ÁzÀ UÉÆÃ¥ÀÄgÀ
B. ªÀUð À ¥ÁzÀ ¥ÀlÖPÀÉ
C. wæ¨sÀÄd¥ÁzÀ ¥ÀlÖPÀ
D. ¤AiÀÄ«ÄvÀ µÀtÄäR WÀ£À
Name the polyhedra
A. square based pyramid C. triangular prism
B. square based prism D. regular hexahedron
10
K
B
E
Item No.
Questions
M099
F eÁ¯ÁPÀÈwAiÀÄÄ ¥ÁgÀªÁºÀPÀ eÁ¯ÁPÀÈwAiÀÄ®è AiÀiÁPÉAzÀg:É
Ch.No B
Obj
Key
Diff. level
10
U
D
E
10
A
B
E
A. PÉêÀ® 4 ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ B. JgÀqÀÄ ¨É¸À ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ
AA
C
C. J¯Áè ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼ÀÄ ¸ÀªÀÄ ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼ÀÄ D. JgÀqÀQÌAvÀ ºÉZÀÄÑ ¨É¸À ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ
D
B
The given network is not a traversable network because: A. B. C. D. M100
there are 4 nodes there are two odd nodes all nodes are even nodes there are more than two odd nodes
AA
C
D
F PɼV À £À avÀ檣 À ÀÄß CzÀgÀ vÀÄ¢UÀ¼° À è ªÀÄrazÁUÀ GAmÁUÀĪÀ ¤AiÀÄ«ÄvÀ §ºÀÄ ¥À®PÀª£ À ÀÄß ºÉ¸j À ¹: A. ZÀvÀÄðªÀÄÄR WÀ£À C. CµÀÖªÀÄÄR WÀ£
B. µÀtÄäR WÀ£À D. zÁéz± À ª À ÀÄÄR
WÀ£À
Name the regular polyhedron can be formed by folding the given structure at its edges A. Tetrahedron C. Octahedron
B. Hexahedron D. Dodecahedron
D.S.E.R.T #4, 100 fT ring road, Banashankari III stage, Bangalore – 85
Subject : Mathematics
¨sÁUÀ II £ÀÄß GvÀjÛ ¸ÀĪÀÅzÀPÉÌ ¸ÀÆZÀ£É Instructions for answering Part II
PɼÀV£À ¥Àæ±ÉßUÀ¼À£ÀÄß, ¸ÀÆZÀ£ÉUÀ½UÉ vÀPÀÌAvÉ GvÀjÛ ¹:
Answer the following question as directed: Item Questions
Ch.No
Obj
Marks
Diff. Level
1
K,S
1+1
E
1
K,U
1+1
A
1
U,S
1+1
A
1
A,S
1+1
A
2
K,S
1+1
E
No.
M001
M002
M003
M004
M005
MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ªÉÆzÀ®£É ªÀÄvÀÄÛ 129£Éà ¥ÀzÀU¼ À ÀÄ PÀæªÀĪÁV 2 ªÀÄvÀÄÛ »r¬Äj.
258 DVªÉ.
65£Éà ¥Àzª À £ À ÀÄß PÀAqÀÄ
First and the 129th term of an A.P are respectively 2 and 258. Find the 65th term MAzÀÄ UÀÄuÉÆÃvÀÛgÀ ±ÉæÃrüAiÀÄ°è Tn-1 = 1 JAzÀÄ vÉÆÃj¹. In a G.P show that Tn-1 Tn+1
Tn+1 = 1 r2
r2
MAzÀÄ ZËPÀª£ À ÀÄß 16 aPÀÌ ZÀzg À U À ¼ À ÁV ¨sÁUÀªÀiÁrzÉ. M§â ºÀÄqÀÄUÀ£ÀÄ, ªÉÆzÀ®£É ZËPÀz° À è 2 UÉÆðUÀ¼£ À ÀÄß ªÀÄvÀÄÛ CzÀgÀ ªÀÄÄA¢£À ZËPÀzÀ°è 4 UÉÆðUÀ¼£ À ÀÄß EqÀÄvÁÛ£.É »ÃUÉAiÉÄà ¥Àæw ¸À®ªÀÅ 2 UÉÆðUÀ¼À£ÀÄß ºÉa¸ Ñ ÀÄvÁÛ ªÀÄÄAzÀĪÀj¸ÀĪÀ£ÀÄ. J¯Áè ZËPÀU¼ À £ À ÀÄß vÀÄA§®Ä CªÀ¤UÉ MlÄÖ JµÀÄÖ UÉÆðUÀ¼ÀÄ ¨ÉÃPÁUÀĪÀÅzÀÄ? 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?
ªÀÄÆgÀÄ KPÀPÃÉ A¢æAiÀÄ ªÀÈvÀÛU¼ À À wædåUÀ¼À C£ÀÄ¥ÁvÀªÀÅ MAzÉà ¸ÀªÀÄ¥ÁvÀzÀ°ègÀĪÀAvÉ J¼É¢zÉ. M¼ÀV£À ªÀÄvÀÄÛ CvÀåAvÀ ºÉÆgÀV£À ªÀÈvÀÛU¼ À À wædåUÀ¼ÀÄ PÀæªÀĪÁV 3 ¸ÉA.«Ä , 12 ¸ÉA.«Ä DVªÉ. ªÀÄzsÀåzÀ ªÀÈvÀÛzÀ wdåªÀ£ÀÄß PÀAqÀÄ»r¬Äj. 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.
Ñ ÀĪÀAvÉ JµÀÄÖ ¸ÀASÉåUÀ¼£ À ÀÄß 1, 2, 3, 4 ªÀÄvÀÄÛ 5 CAPÉU¼ À £ À ÀÄß G¥ÀAiÉÆÃV¹PÉÆAqÀÄ, ¥ÀÄ£ÀgÁªÀwð¸ÀzÉ, 2000PÀÆÌ ºÉag ªÀiÁqÀ§ºÀÄzÀÄ? How many numbers, more than 2000 can be formed using digits 1, 2, 3, 4 and 5 without repeating the digits?
Item No.
M006
Questions 10 d£ÀgÀ JvÀg Û À ªÀÄvÀÄÛ vÀÆPÀU¼ À ,À ¸ÀgÁ¸Àj ªÀÄvÀÄÛ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß PɼV À £À ¥ÀnÖAiÀÄ°è PÉÆqÀ¯ÁVzÉ. C¹Ügª À ÁVzÉ? UÀÄt®PÀt ë
X 174 ¸ÉA.«Ä
3.77
vÀÆPÀ
75 PÉ.f
1.05
Marks
Diff. Level
3
K,S
1+1
E
CªÀgÀ AiÀiÁªÀ ®PÀt ë ªÀÅ ºÉZÀÄÑ
The table below contains the mean and standard deviation of the heights and weights of 10 persons. characteristic do they vary more? X
Obj
൦
JvÀg Û À
Characteristic
Ch.No
In which
൦
Height
174 cms
3.77
Weight
75 Kg
1.05
M008
M009
Ch.No
Obj
Marks
Diff. Level
3
A
2
A
4
S
2
E
4
K,S
1+1
A
¨ÉÃgÉ ¨ÉÃgÉ PÀ¸ÀħÄUÀ¼° À è£À d£ÀgÀ UÀÄA¥ÀÄ, MAzÀÄ ¤UÀ¢üvÀ CªÀ¢A ü iÀÄ°è UÀ½¹zÀ ¢£ÀUÀÆ°AiÀÄ, ªÀiÁ£ÀPÀ«ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉPÁÌZÁgÀ ªÀiÁr, £ÀPÉëAiÀÄ°è vÉÆÃj¹zÉ. AiÀiÁªÀ UÀÄA¦£À d£ÀgÀ PÀÆ°AiÀÄÄ ¹Ügª À ÁVzÉ? 10 9 8 7 S.D's of wages
M007
Questions
6 5 4 3 2 1 0 Carpenter
Coolie
Driver
Painter
Plumber
Occupations
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? 10 9 8 7 S.D's of wages
Item No.
6 5 4 3 2 1 0 Carpenter
Coolie
Driver
Painter
Plumber
Occupations
a2-b2, (a-b)2 ªÀÄvÀÄÛ a3-b3 UÀ¼À ªÀÄ.¸Á.ªÀ £ÀÄß PÀAqÀÄ »r¬Äj: Find the H.C.F of a2-b2, (a-b)2 and a3-b3 3
3
3
x+y+z=9 ªÀÄvÀÄÛ xy+yz+zx=11 DzÁUÀ x +y +z -3xyz ¨É¯A É iÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. When x+y+z=9 and xy+yz+zx=11, find the value of x3+y3+z3-3xyz
Item No.
M010
M011
M012
M013
M014
M015
Questions
JgÀqÀÄ ©ÃeÉÆÃQÛU¼ À À ªÀÄ.¸Á.C ªÀÄvÀÄÛ ®.¸Á.C UÀ¼ÀÄ PÀæªÀĪÁV (x-3) ªÀÄvÀÄÛ (x3-5x2-2x+24)DVªÉ. ©ÃeÉÆÃQÛAiÀÄÄ (x2-7x+12) DzÀg,É ªÀÄvÉÆÛAzÀ£ÀÄß PÀAqÀÄ»r¬Äj.
Ch.No
Obj
Marks
Diff. Level
4
U,S
1+1
A
5
K
2
E
5
K,S
1+1
E
5
K,S
1+1
E
6
K.S
1+1
A
6
U
2
A
CªÀÅUÀ¼° À è MAzÀÄ
The H.C.F and L.C.M of two expressions are (x-3) and (x3-5x2-2x+24) respectively. If one of the expressions is (x27x+12), find the other 2
2x -3x+8=0 ¸À«ÆPÀgt À zÀ ªÀÄÆ®UÀ¼À §UÉÎ «ªÀIJð¹: Comment on the roots of the equation: 2x2-3x+8=0
MAzÀÄ ªÀUð À ¸À«ÆPÀgÀtzÀ ±ÉÆÃzsPÀ z À À ¨É¯É 16 DzÀg,É ªÀUð À ¸À«ÆPÀgÀtzÀ ªÀÄÆ®UÀ¼À ¸Àé¨sÁªÀªÃÉ £ÀÄ? If the value of the discriminant of a quadratic equation is 16. What is the nature of the roots of the equation?
ªÀÄÆ®UÀ¼ÀÄ (1-√5) ªÀÄvÀÄÛ (1+√5) EgÀĪÀAvÉ MAzÀÄ ªÀUð À ¸À«ÄÃPÀgt À ªÀ£ÀÄß §gÉ: Write the quadratic equation whose roots are (1-√5) and (1+√5) (6 87 ) 85 = 6 8 (7 85)JAzÀÄ vÉÆÃj¹: Show that (6 87 ) 85 = 6 8 (7 85) Z4 UÀÄuÁPÁgÀPÉÌ ¸ÀA§A¢ü¹zÀAvÉ PÉÆõÀ×PÀª£ À ÀÄß gÀa¸À®Ä ¸ÁzsÀåªÉÃ?
2
4
PÁgÀt w½¹ 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 Z4 under multiplication. State the reason 2 4 6 8 2 4 6 8
4 8 2 6
8 6 -
2 4 -
6 2 -
Item No.
Questions
Ch.No
Obj
Marks
Diff. Level
7
U
2
A
7
U
2
A
8
U,S
1+1
A
M016 4¸ÉA.«Ä wædå«gÀĪÀ £Á®ÄÌ ¸Àªð À ¸ÀªÀÄ ªÀÈvÀÛU¼ À À PÉÃAzÀæU¼ À ÀÄ A, B, C ªÀÄvÀÄÛ D DVªÉ.
F ªÀÈvÀÛU¼ À ÀÄ avÀæzÀ°è vÉÆÃj¹gÀĪÀAvÉ MAzÀ£ÉÆßAzÀÄ ¸Àà²ð¸ÀÄwÛª.É «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
ABCD ZËPÀzÀ
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
M017
M018
A ªÀÄvÀÄÛ B PÉÃAzÀæªÁUÀļÀî JgÀqÀÄ ¸Àªð À ¸ÀªÀÄ ªÀÈvÀÛU¼ À À wædå 2 ¸ÉA.«Ä DVzÉ. F
JgÀqÀÄ ªÀÈvÀÛU¼ À À, 4 ¸ÉA.«Ä wædå«gÀĪÀ C ªÀÄvÀÄÛ D PÉÃAzÀæU¼ À ÁVgÀĪÀ, JgÀqÀÄ ¸Àªð À ¸ÀªÀÄ ªÀÈvÀÛU¼ À £ À ÀÄß avÀæz° À è vÉÆÃj¹zÀAvÉ ¸Àà²ð¸ÀÄwÛª.É DAiÀÄvÀ ABCDAiÀÄ ¸ÀÄvÀÛ¼A É iÀÄ£ÀÄß ¯ÉQ̹.
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
avÀæz° À è AP ªÀÄvÀÄÛ BP UÀ¼ÀÄ ªÀÈvÀÛzÀ PÉÃAzÀæªÀÅ O ªÀÄvÀÄÛ ¨ÁºÀå ©AzÀÄ P ¤AzÀ J¼É¢gÀĪÀ ¸Àà±ð À PÀU¼ À ÀÄ, ∠APB=700 DzÀgÉ PÉÆãÀ ∠ACB AiÀÄ ¨É¯A É iÉÄãÀÄ?
In the adjoining figure AP and BP are tangents drawn to the circle with centre O from an external point P. If ∠APB=700, Find ∠ACB
Item No.
M019
M020
M021
M022
Questions
Ch.No
Obj
Marks
Diff. Level
8
U
2
A
8
U,A
1+1
A
8
K,A
1+1
A
9
U,A
1+1
A
F avÀæz° À è CAvÀ:¸ÀܪÁV ¸Àà²ð¸ÀĪÀ ªÀÈvÀÛU¼ À À eÉÆvÉ JµÀÄÖ?
In the adjoining figure how many pairs of internally touching circles are there?
APB ªÀÈvÀÛz° À è AB AiÀÄÄ ªÁå¸ÀªÁVzÉ.
AH ªÀÄvÀÄÛ BK UÀ¼ÀÄ PÀæªÀĪÁV A ªÀÄvÀÄÛ B ©AzÀÄUÀ½AzÀ, P ¬ÄAzÀ J¼ÉzÀ
¸Àà±ð À PÀPÉÌ ®A§UÀ¼ÁVªÉ. AH + BK = AB JAzÀÄ ¸Á¢ü¹. 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
avÀæz° À è AB || DC JAzÀÄ PÉÆnÖzÁÝUÀ, Δ DMU ||| Δ BMV JAzÀÄ ¸Á¢ü¹ In the figure, give that AB || DC, Prove that Δ DMU ||| Δ BMV
7«Æ. ªÁå¸À ªÀÄvÀÄÛ
20«Ælgï D¼À«gÀĪÀ MAzÀÄ ¨Á«AiÀÄ£ÀÄß CUÉ¢zÉ.
CzÀjAzÀ zÉÆgÉvÀ ªÀÄtÚ£ÀÄß ¸ÀªÀĪÁV ºÀgÀr 22«Æ x 14«Æ C¼ÀvA É iÀÄ MAzÀÄ dUÀÄ°AiÀÄ£ÀÄß ªÀiÁrzÉ. dUÀÄ°AiÀÄ JvÀÛgÀª£ À ÀÄß PÀAqÀÄ»r¬Äj. 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.
Item No.
M023
M024
M025
Questions 10¸ÉA.«Ä JvÀÛgÀ ªÀÄvÀÄÛ 6 ¸ÉA.«Ä ªÁå¸À«gÀĪÀ MAzÀÄ WÀ£À ¹°AqÀg£ À ÀÄß PÀgV À ¹, £ÁtåUÀ¼£ À ÀÄß ªÀiÁqÀ¨ÃÉ PÁVzÉ.
Ch.No
Obj
Marks
Diff. Level
9
K,A
1+1
A
9
A,S
1+1
D
10
K,S
1+1
A
¥Àæw
£ÁtåzÀ ªÁå¸ÀªÀÅ 1.5 ¸ÉA,«Ä ªÀÄvÀÄÛ 0.25 ¸ÉA.«Ä zÀ¥ À Àà«gÀĪÀAvÉ JµÀÄÖ £ÁtåUÀ¼£ À ÀÄß ªÀiÁqÀ§ºÀÄzÀÄ? 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?
MAzÀÄ ±ÀAPÀÄDPÁgÀzÀ UÀÄqÁgÀzÀ°è 4 d£ÀjgÀ®Ä CªÀPÁ±À«zÉ. ¨ÉÃPÁUÀÄvÀÛz.É UÀÄqÁgÀzÀ JvÀÛgª À À£ÀÄß PÀAqÀÄ»r¬Äj.
¥ÀæwAiÉƧâ¤UÀÆ, £É®zÀ ªÉÄïÉ
4WÀ.«Æ £ÀµÀÄÖ UÁ½
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.
zÁézÀ±ª À ÀÄÄR WÀ£z À À ªÀÄÄRUÀ¼À ¸ÀASÉå, ±ÀÈAUÀ©AzÀÄUÀ¼À ¸ÀASÉå ªÀÄvÀÄÛ CAZÀÄUÀ¼À ¸ÀASÉåUÀ¼£ À ÀÄß Jt¹ §gɬÄj. EªÀÅUÀ¼£ À ÀÄß DAiÀÄè®gÀ£À . ¸ÀÆvÀæzÀ C£ÀéAiÀÄ vÁ¼É £ÉÆÃr.
Write the number of faces, vertices and edges of the given Dodecahedron . and verify Euler’s formula
Item No.
M026
M027
Questions
MAzÀÄ eÁ¯ÁPÀÈwAiÀÄ ªÀiÁUÀð ¸ÀASÁåAiÀÄvÀª£ À ÀÄß PÉÆnÖz.É PÀAqÀÄ»r¬Äj.
Ch.No
Obj
Marks
Diff. Level
10
K,U
1+1
A
10
U
2
A
À ègÀĪÀ PÀA¸ÀUÀ¼À ¸ÀASÉåAiÀÄ£ÀÄß eÁ¯ÁPÀÈwAiÀÄ£ÀÄß gÀa¸ÀzÉ CzÀg°
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
PɼV À £À avÀæPÉÌ DAiÀÄèg£ À À ¸ÀÆvÀæ C£Àé¬Ä¹ vÁ¼É£ÉÆÃqÀ®Ä ¸ÁzsÀå«®è, PÁgÀt w½¹: A E
B
D
C
It is not possible to verify Euler’s formula for the diagram given below. Give reason: A E
B
D
C
Item No.
M028
M029
M030
M031
M032
M033
M034
Questions
Ch.No
Obj
Marks
Diff. Level
1
K,S
1+2
E
2
U,S
2+1
E
3
U,A
1+2
A
4
K,S
1+2
A
4
U,S
2+1
A
5
U,S
1+2
E
7
A,S
1+2
A
MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ 4£Éà ªÀÄvÀÄÛ 7£Éà ¥ÀzU À ¼ À ÀÄ PÀæªÀĪÁV ªÀÄvÀÄÛ 23 DVªÉ. ‘d’ ªÀÄvÀÄÛ ‘a’.UÀ¼£ À ÀÄß PÀAqÀÄ»r¬Äj. In an A.P the fourth and the seventh terms are 17 and 23 respectively. Find ‘d’ and ‘a’. n=7 ªÀÄvÀÄÛ r=3 DzÀgÉ
nCr+nCr-1 =
n+1
Cr JAzÀÄ vÉÆÃj¹.
If n=7 and r=3 show that nCr+nCr-1 = n+1Cr A ªÀÄvÀÄÛ
B JA§ E§égÀÄ ¨ÁålìªÀÄ£ïUÀ¼ÀÄ DgÀÄ E¤ßAUïUÀ¼° À è UÀ½¹gÀĪÀ gÀ£ÀÄßUÀ¼À «ªÀgÀ »ÃVzÉ: A
48
50
54
46
48
54
B
46
44
43
46
45
46
EªÀg° À è: (a) GvÀÛªÀÄ g£Áß UÀ½¹zÀªÀ AiÀiÁgÀÄ (b) ºÉa£ Ñ À ¹Ügv À A É iÀÄļÀî DlUÁgÀ£ÁgÀÄ? 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
2
JgÀq£ À ÃÉ WÁvÀzÀ JgÀqÀÄ ©ÃeÉÆÃQÛU¼ À À ªÀÄ.¸Á.C ªÀÄvÀÄÛ ®.¸Á.C UÀ¼ÀÄ PÀæªÀĪÁV (p+2) ªÀÄvÀÄÛ p -2p -5p+6. 2 ©ÃeÉÆÃQÛ p +p-2 DzÀgÉ E£ÉÆßAzÀÄ ©ÃeÉÆÃQÛAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
MAzÀÄ
HCF and LCM of two expressions of second degree are (p+2) and p3-2p2-5p+6 respectively. If one of the expressions is p2+p-2. Find the other. 3
3
a +7b +6ab (a+2b) : ©ÃeÉÆÃQÛAiÀÄ£ÀÄß ¤ªÀÄUÉ w½¢gÀĪÀ MAzÀÄ ¸ÀÆvÀæ gÀÆ¥ÀPÉÌ vÀAzÀÄ, C¥ÀªÀwð¹. Factorise a3+7b3+6ab (a+2b) by reducing the expression to a known formula
UÀÄt®§Þ 224£ÀÄß PÉÆqÀĪÀ JgÀqÀÄ PÀæªÀiÁ£ÀÄUÀvÀ zs£ À ¥ À ÀÆtð ¸Àj¸ÀASÉåUÀ¼£ À ÀÄß PÀAqÀÄ»r¬Äj. Find two consecutive positive even integers whose product is 224
JgÀqÀÄ ¸ÀªÀÄ wædåUÀ½gÀĪÀ ªÀÈvÀÛU½ À UÉ £ÉÃgÀ¸ÁªÀiÁ£Àå ¸Àà±ÀðUÀ¼£ À É߼ɬÄj. Draw the direct common tangents to two equal circles
Item No.
M035
M036
M037
M038
Questions 2 ¸ÉA.«Ä wædå«gÀĪÀ MAzÀÄ ªÀÈvÀÛ J¼ÉzÀÄ, CzÀgÀ wædå OB AiÀÄ£ÀÄß
BX=2 ¸ÉA,«Ä EgÀĪÀAvÉ ªÀÈ¢Þ¹.
Ch.No
Obj
Marks
Diff. Level
7
A,S
2+1
D
8
U,S
1+2
A
8
U,A
1+2
A
8
U,S
1+2
A
AB AiÀÄ£ÀÄß ‘x’
©AzÀÄ«£À°è ¸Àà²ð¸ÀĪÀAvÉAiÀÄÆ ªÀÄvÀÄÛ (ªÉÆzÀ®Ä J¼Éz)À ªÀÈvÀÛª£ À ÀÄß ¨ÁºÀåªÁV ¸Àà²ð¸ÀĪÀAvÉ E£ÉÆßAzÀÄ ªÀÈvÀÛª£ À ÀÄß J¼É¬Äj. 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. ∆ABC zÀ° À è BDAiÀÄÄ
‘B’ ªÀÄÆ®PÀ J¼ÉzÀ JvÀÛgÀªÁVzÉ ªÀÄvÀÄÛ AD : CD = 1:2. DVzÉ. AC2=3 (BC2-AB2)
BD is the altitude through ‘B’ in the ∆ABC and AD : CD = 1:2. Prove that AC2=3 (BC2-AB2)
F avÀæzÀ°è AB \\ CD , AB = 9 ¸ÉA.«Ä, DE = 4¸ÉA,«Ä, CE = 5 ¸ÉA.«Ä ªÀÄvÀÄÛ CD = 6 ¸ÉA.«Ä DzÀgÉ BE AiÀÄ C¼ÀvA É iÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. 9 A
B 4 E
D
5 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 E 5 D C 6
JgÀqÀÄ ¸ÀªÀÄgÀÆ¥À wæ¨sÀÄdzÀ C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄÀ ®A§UÀ¼À C£ÀÄ¥ÁvÀª£ À ÀÄß PÀAqÀÄ »r¬Äj.
9 ¸ÉA.«Ä
ªÀÄvÀÄÛ
6¸ÉA.«Ä DVzÀÝg.É
F ¨ÁºÀÄUÀ½UÉ J¼ÉzÀ
Corresponding sides of two similar triangles are 9 cm and 6 cm. Find the ratio of their altitudes drawn to those two sides.
Item No.
M039
M040
M041
M042
M043
M044
M045
Questions
Ch.No
Obj
Marks
Diff. Level
8
U,S
1+2
A
9
K,S
1+2
A
10
K,S
1+2
A
1
A,S
2+2
A
5
K,S
2+2
E
7
A,S
2+2
A
8
K,S
2+2
E
44«ÄÃlgï JvÀÛg« À gÀĪÀ PÀlÖqª À ÀÅ 66 «ÄÃlgï GzÀÝzÀ £Ég¼ À £ À ÀÄß £É®zÀ ªÉÄÃ¯É ©Ã¼ÀĪÀAvÉ ªÀiÁrzÀgÉ CzÉà ¸ÀªÀÄAiÀÄzÀ°è 6
«ÄÃlgï JvÀÛgÀzÀ ªÀÄgÀªÀÅ GAlĪÀiÁqÀĪÀ £Ég½ À £À GzÀݪÃÉ µÀÄÖ? 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?
À UÉƼÀzÀ ªÉÄïÉ, MAzÀÄ ±ÀAPÀĪÀ£ÀÄß ¤°è¹zÀAwzÉ. CzsÀðUÉÆüÀ ªÀÄvÀÄÛ ±ÀAPÀÄ«£À wædåUÀ¼ÄÀ MAzÀÄ ªÀÄgÀzÀ DnPÉAiÀÄ DPÁgÀªÀÅ, Czsð vÀ¯Á 4.2 ¸ÉA.«Ä ªÀÄvÀÄÛ MlÄÖ DnPÉAiÀÄ JvÀÛgª À ÀÅ 4.2 ¸ÉA,«Ä DVzÉ. DnPÉUÉ ¨ÉÃPÁUÀĪÀ ªÀÄgÀzÀ UávÀæªÀ£ÀÄß ¯ÉQ̹. 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.
PÀæªÀĪÁV 3 ,4 ªÀÄvÀÄÛ 3 ªÀUð«gÀĪÀ A, B ªÀÄvÀÄÛ C ¸ÀA¥ÁvÀ ©ªÀÄzÀÄUÀ½gÀĪÀ eÁ¯ÁPÀÈwAiÀÄ£ÀÄß gÀa¹. Construct a network of 3 nodes A, B,C which are of the order 3 ,4 and 3 respectively
MAzÀÄ PÀAvÀÄ ªÁå¥ÁgÀzÀ AiÉÆÃd£ÉAiÀÄ°è PÁgÀ£ÀÄß PÉƼÀÀÄzÁVzÉ. ¥ÁægA À ¨sz À ° À è 5gÀÆ dªÉÄ ªÀiÁr, D wAUÀ¼À PÉÆ£ÉAiÀÄ°è 10gÀÆ £ÀÄß C£AvÀgz À À ¥Àæw wAUÀ¼À PÉÆ£ÉAiÀÄ°è »A¢£À wAUÀ¼À PÀAw£À ªÉƧ®V£À JgÀqgÀµÀÖgÀAvÉ ºÀt PÀlÖ¨ÃÉ PÀÄ. ºÁUÉ M§â£ÄÀ 17£É PÀAw£À°è gÀÆ. 3,27,680 PÀnÖzÀg,É CªÀ£ÀÄ PÀnÖzÀ MlÄÖ ªÉÆvÀÛª£ À ÀÄß AiÀiÁªÀÅzÁzÀgÀÆ ±ÉæÃrüAiÀÄ vÀvÀ骣 À ÀÄß G¥ÀAiÉÆÃV¹ PÀAqÀÄ»r¬Äj. 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 17th instalment paid is Rs. 3,27,680. Find total amount paid using principles of progressions.
MAzÀÄ ªÁºÀ£z À À ¸ÁªÀiÁ£ÀåªÉÃUÀª£ À ÀÄß WÀAmÉUÉ 5 Q.«Ä £ÀµÀÄÖ vÀVιzÀgÉ, ªÁºÀ£ÀªÀÅ 300 Q.«Ä zÀÆgÀª£ À ÀÄß PÀæ«Ä¸À®Ä 2WÀAmÉ ºÉZÀÄÑ vÉUz É ÀÄPÉƼÀÄîvÀÛz.É ºÁUÁzÀgÉ CzÀgÀ ¸ÁªÀiÁ£ÀåªÉÃUÀª£ À ÀÄß PÀAqÀÄ»r¬Äj? 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. 2.5 ¸ÉA.«Ä wædåªÀżÀîÀ ªÀÈvÀÛPÉÌ ‘P’ ©AzÀÄ«£À°è MAzÀÄ QPR ¸Àà±ð À PÀª£ À ÀÄß gÀa¹j. ªÀÈvÀÛzÀ ºÉÆgÀUÉ ¸Àà±ð À PÀzÀ ªÉÄð®èzÀ MAzÀÄ
©AzÀÄ ‘S’ ªÀ£ÀÄß UÀÄgÀÄw¹. ¥ÁæAiÉÆÃVPÀªz À sÁ£À¢AzÀ JgÀq£ À ÃÉ ¸Àà±ð À PÀ SPT ªÀ£ÀÄß gÀa¸À®Ä ¸ÁzsÀå«®è JAzÀÄ vÉÆÃj¹. 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.
JgÀqÀÄ wæ¨sÀÄdUÀ¼ÀÄ ¸ÀªÀÄ PÉÆãÀU¼ À ÁVzÀÝg,É CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄ ¸ÀªÀiÁ£ÀÄ¥ÁvÀzÀ°ègÀÄvÀÛªÉ, ¸Á¢ü¹. Prove that if two triangles are equiangular, then their corresponding sides are proportional.
gÀZÀ£Á vÀAqÀ Kannada Sri.B.S.Gundu Rao, Deputy Director , Gandhi Centre for Peace and Human Values Bangalore Sri.C.S. Banashankariah, Bangalore Sri. P.Dharukaradhya, Basaveshwara Girls High School, B’lore Sri.N.Gopal Krishna Udupa, Bangalore Smt. Prema H.Tahsildar, Bharati Vidyalaya, Khasbag, Belgaum Smt.Bhuvaneshwari.G.S, Women’s Peace league, Bangalore Smt. Bhagirathi Bhat, GHS, Ketamaranahalli, Bangalore Smt. Vasundhara M.G, Bharatamata Vidyamandir, Bangalore Sri. V. Krishnaiah, Sir M.V. Comp. PU College, Bangalore Smt. S. Padmavathi, Vidya Vardhaka Sangha, Bangalore Sri.Nagaraj.S, Vivekananda Vidya Kendra, Bangalore Smt. Kannika, Sri Aravind Vidya Mandira, Bangalore Smt. Srilata G.S, MES Kishore Kendra, Bangalore English Prof. G.S. Mudambadithaya, Bangalore Sri.A.P. Gundappa, Attibele Smt. Umadevi, R.V.Girls High School, Bangalore Smt. Maya Ramchand, Bangalore Smt. Shobha Kulkarni, Govt. Sardar HS, Belgaum Sri.Sathya Prakash, Vidya Vardhaka Sangha HS, Bangalore Smt. Asha, Saraswathi Vidya Mandir, Bangalore Smt. Prameetha Adoni, HM, GHS, KR Puram, Bangalore Sri.G.N. Deshpande, HM, BN Darbar GHS, Bijapur Sri. Shankaranarayana Rao.P , SS High School, Kadandale, DK
Hindi Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum Dr. Ispak Ali, Lalbahudar Sastry B.Ed College, Bangalore Sri. Abdul Nazir, Q.Islam HS, Bangalore Sri. G.H. Balakrishna, Bangalore Smt. Shyalaja H.Naidu, DPH HS, Bangalore Smt. Urmilla Nahar, DPH HS, Bangalore Sri. Anand.S. Kalasad, KC PU College, Hirebagewadi, Belgaum Sri. Ashok.H.Balunnavar, MM Comp. PU College, Belgaum Smt. Geetanjali.P.Yogi, Benson’s HS, Belgaum Dr.Bharati T.Savadattu, Govt. Saraswathi PU College, Belgaum Dr. K.L.Sattigeri, Principal, Dr. B.D. Jatti COE, Belgaum Urdu Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum Smt. Shaheda Perveen, BRP, Shankarapura, Bangalore Sri. Bahadur Khan, MO Girls HS, Bangalore Sri.S.G. Deshnoor, Al-Ameen HS, Belgaum Sri. F.A. Yallur, Islamai Girls High School, Belgaum Sri.D.M. Momin, Bashiban High School, Belgaum Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum Smt.Shaila.V.M, Mahila Vidyalaya HS, Belgaum Smt. Sunitha.D. Mathad, Ushatai Gogate Girls HS, Belgaum Sri. P.T. Malege, MM Comp. PU College, Belgaum Sri. C.Y. Patil, Talakwadi HS, Belgaum Sri. A.L. Patil, MM Central HS, Belgaum
Smt. Lata Rao, HM, SJR High School, Bangalore
Smt. Sheela Deshpande, LBS B.Ed College, Bangalore
Marati
Sanskrit Dr. Satish Hegde, R.V. Girls High School, Bangalore Sri. Shridhar Hegde, National High School, Bangalore Sri. Narayan Ananth Bhat,Govt PU College, Chamarajpet, B’lore Sri.Venkataramana D.Bhat, Govt Jr. College, Vartur, B’lore Sri.Narasimha Bhagavat, Janaseva Vidya Kendra, Chennenahalli Smt. Shylaja.V, Chamarajpet Jr. College, Bangalore Sri. Krishna V. Bhat, Vasavi Vidyaniketan, Bangalore Sri. Mahesh Bhat, PTA High School, Bangalore Sri. Balasubramanian, Methodist HS, Kolar Smt. Geeta B.S, Seshadripuram GHS, Bangalore Telugu Dr. T.K. Jayalakshmi, Director, RVEC, Bangalore Sri. Nagesam.C, RBANM High School, Bangalore Sri. G. Venkata Rama Reddy, Telugu Pandit, Bangalore Sri. P.Hema Chendra Babu, Telugu Pandit, Bangalore Tamil Prof. Susheela Sheshadri, Principal, Amrita Shikshana M.Vidyala,Mysore Sri. Pulavar V. Vishwanathan, Bangalore Sri.S.Ramalingam, Seva Ashram High School, Bangalore Sri.G. Sampath, Bangalore
Mathematics Dr. D.S. Shivananda, Bangalore Sri. Kailash Nekraj, HM, Jnanamitra HS, Bangalore Sri.N.C. Satyaji Rao, Bangalore Smt. K.S. Susheela, 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
Science Dr. Sameera Simha, Vijaya Teachers College, Bangalore Dr. S. Srikanta Swamy, R.V. Teachers College, Bangalore Sri.P.G.Dwarakanath, Vidya Vardhaka Sangha, Bangalore Dr.R.Mythili, Associate Director, RVEC, Bangalore Smt. Shantha Kumari.B.S., Bangalore Smt. Vasanthi Rao, Bangalore Smt. Rekha Hegde, Vani High School, Bangalore Smt. K.S. Shyamala, HM, Vasavi High School, Bangalore Smt. R. Geetha, Vasavi High School, Bangalore Smt. S.K. Prabha, Retd. Lecturer, DIET, Bangalore Smt. Bhagyalakshmi, Stella Mari’s School, Bangalore Smt. V. Padma, Vidya Vardhaka Sangha HS, Bangalore Social Studies Prof. G.P. Basavaraj, Retd Director, NCERT Sri. P.A. Kumar, HM, Vijaya High School, Bangalore Prof. B.R. Gopal, MES Teachers College, Bangalore Smt. Lorna Pinto, SAM High School, Bangalore Smt. Radhika.S, Hymamshu Jyothi Kala Kendra, Bangalore Smt. T.R. Sandhyavalli, Basaveshwara Jr. College, Bangalore Smt. R. Vijayavalli, Nirmala Rani GHS, Bangalore Smt. Shamala Prasad, MES Kishore Kendra, Bangalore Smt. Sukanya.N.R, Sardar Patil HS, Bangalore Smt. Meera, Vidya Vardhaka Sangha HS, Bangalore Smt. N.S. Vyjayanthi, Vidya Bharathi Eng. School, Bangalore Smt. Lakshamma, Bangalore