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MATHEMATICS
糧ø ™èlÆý‡VýS† A…sôæ ѧéÅÆý‡$¦Ë$ ™èlÐ]l$ ^èl§ýl$Ð]l#Ë iÑ™èl…ÌZ ^ólÆý‡$MøÐéÍÞ¯]l ™öÍ VýSÐ]l$Å….
D VýSÐ]l*Å°² çœ$¯]lOÐðl$¯]l "{VóSyŠl'™ø §ésìæ™ól A™èl$ů]l²™èl MðSÈÆŠ‡ ¨Ô¶æV> Ayýl$VýS$Ë$ ç³yýl$™èl$¯]l²sôæÏ!
A…§ýl$MóS ™èlÓÆý‡ÌZ fÆý‡-VýS-»ZÄôæ$ 糧ø ™èlÆý‡-VýS† ç³È-„ýSÌZÏ Ð]l$…_ {VóSyŠl ´ëƇ¬…sŒæ HÐ]lÆó‡gŒæ (iï³H)
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C…§ýl$ÌZ ¿êVýS…V> D ÐéÆý‡… Ð]l*Å£ýlÐðl$sìæMŠSÞ ¼sŒæ »êÅ…MŠæ {ç³™ólÅMýS…...
¼sŒæ »êÅ…MŠæ
C…WÏ‹Ù Ò$yìlĶæ$…
òܵçÙÌŒæ
{ç³Ô¶æ²ç³{™èl… õ³ç³ÆŠ‡&1, õ³ç³ÆŠ‡&2ËMýS$ MýSÍí³
Ððl¬™èl¢… 100 Ð]l*Æý‡$PËMýS$ E…r$…¨.
JMøP õ³ç³ÆŠ‡ÌZ 1 Ð]l*Æý‡$P {ç³Ô¶æ²Ë$ ¯éË$VýS$…sêƇ¬.
15 Ð]l*Æý‡$PËMýS$ ¼r$Ï E…sêƇ¬. A…§ýl$Ð]lËÏ
GMýS$PÐ]l Ð]l*Æý‡$PË$ Ý뫨…_, 10 {VóSyŠl ´ëƇ¬…r$Ï
´÷…§éË…sôæ ÒsìæOò³ ™èlç³µ°çÜÇV> ç³r$t Ý뫨…^éÍÞ…§ól.
D {MýSÐ]l$…ÌZ ¼sŒæ »êÅ…MŠS òܵçÙÌŒæ Ò$ MøçÜ…..
th
Class
MýSÆð‡…sŒæ AOòœÆŠæÞ
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Bit Bank
Mathematics
"糨' {VóSyŠæ ´ëƇ¬…rÏ Ë„ýSÅ Ý뫧ýl¯]lMýS$..
Prepared by:
Y.Vanamraju,
Mathematics Faculty.
ZPHS, Nandikotkur.
™èlÓÆý‡ÌZ 糧ø ™èlÆý‡-VýS† ç³¼ÏMŠS
ç³È-„ýSË$ {´ëÆý‡…¿¶æ… M>¯]l$-¯é²Æ‡¬.
ÇÑ-f-¯ŒlMýS$ 15 ÆøkË$ MóSsê-Ƈ¬õÜ¢,
Ñ$W-ͯ]l çÜÐ]l$-Ķæ*°² çÜÐ]l$-Æý‡¦-Ð]l…™èl…V>
Eç³-Äñæ*-W…-^èl$-MýS$…sôæ A¯]l$-MýS$¯]l²
Ë„>Å°² ^ólÆý‡$-Mø-Ð]l^èl$a.
´ëuý‡Å-ç³#-çÜ¢MýS…, íÜË-º‹Ü Ð]l*Ç-¯]l-ç³µ-sìæMîS
´ëu>Å…-Ô>-ÌZÏ° ¿êÐ]l-¯]l-ËOò³ ç³r$t Ý뫨õÜ¢
H Ñ«§ýl…V> {ç³Ô¶æ² Ð]l_a¯é çÜÐ]l*-«§é¯]l…
Æ>Äñæ¬^èl$a. õ³ç³-ÆŠ‡-&1, õ³ç³-ÆŠ‡-&-2ÌZÏ
Ð]l¬QÅ A«§éÅ-Ķæ*Ë$, ™ólÍ-OMðS¯]l A…Ô>Ë$,
H A«§éÅĶæ$… ¯]l$…_ GÌê…sìæ {ç³Ô¶æ²Ë$
Ð]lÝë¢Æ‡¬? Ð]l…sìæÑ ™ðlË$-çÜ$-Mö°
{í³ç³-Æó‡-çÙ¯Œl Mö¯]l-Ýë-W…-^èlyýl… {糫§é¯]l….
ѧéÅ-Æý‡$¦Ë$ Ððl¬§ýlr Mö™èl¢V> Ñyýl$-§ýlË ^ólíܯ]l {ç³Ô¶æ²-ç³-{™é˯]l$ ç³Ç-Ö-Í…_, A«§éÅ-Ķæ*Ë ÐéÈV> ÐðlƇ¬-sôæ-i°
VýS$Ç¢…_ ç³sìæçÙt {ç³×ê-ã-MýS™ø {í³ç³-Æó‡-çÙ¯Œl Mö¯]l-Ýë-W…-^éÍ.
Ñ$W-ͯ]l çÜ»ñæj-MýS$t-Ë™ø ´ùÍõÜ¢ VýS×ìæ™èl… MýSçÙt-OÐðl$¯]l çÜ»ñæjMýS$t,
M>± A«¨MýS Ð]l*Æý‡$PË$ ´÷…§ól…-§ýl$MýS$ AÐ]l-M>-Ô¶æ-Ð]l¬¯]l²
çÜ»ñæjMýS$t M>ºsìæt ©°MìS ÆøkMýS$ MýS±çÜ… Æð‡…yýl$ VýS…rË$
MóSsê-Ƈ¬…-^éÍ.
{ç³çÜ$¢™èl ç³È„ýS Ñ«§é¯]l… (°-Æý‡…-™èlÆý‡, çÜÐ]l${VýS Ð]lÊÌêÅ…-MýS¯]l…-)ÌZ JMýS ¿êÐ]l-¯]lMýS$ çÜ…º…-«¨…-_¯]l {ç³Ô¶æ²Ë$ AyìlVóS
Ñ«§é-¯]l…Oò³ AÐ]l-V>-çßæ¯]l ò³…´÷…-¨…-^èl$-Mö°, A«§éÅPAPER - I
1. REAL NUMBERS
1. The prime factor of 2×7×11×17×23+23 is
____
2. A Physical Education Teacher wishes to
distribute 60 balls and 135 bats equally
among a number of boys. The greatest number receiving the gift in this way are___
3. The Values of X and Y in the given figure
are ____
ÐéÅçÜ-Æý‡*ç³ {ç³Ô¶æ²-ËMýS$ GMýS$PÐ]l Ð]l*Æý‡$PË$ E…sêƇ¬ M>ºsìæt
A«§éÅ-Ķæ*Ë ÐéÈV> D ™èlÆý‡à {ç³Ô¶æ²-˯]l$ VýS$Ç¢…_, Ðésìæ°
Ý뫨…-^éÍ. CÌê…sìæ {ç³Ô¶æ²Ë$ GMýS$P-Ð]lV> õ³ç³-ÆŠ‡-&-1-ÌZ°
ºçßæ$-ç³-§ýl$Ë$, °Æý‡*-ç³MýS Æó‡Rê-VýS-×ìæ™èl…, {ÔóæÉýl$Ë$; õ³ç³-ÆŠ‡-&-2ÌZ° çÜÆý‡*ç³ {†¿¶æ$-gê-ÌZÏ° íܧ鮅-™éË$, {†Mø-×æ-Ñ$† A¯]l$Ð]l-Æý‡¢-¯éË$, „óS{™èl-Ñ$† A«§éÅ-Ķæ*Ë ¯]l$…_ Ð]lÝë¢Æ‡¬. ÐéçÜ¢Ð]l
çÜ…QÅË$, çÜÑ$-™èl$Ë$, {†Mø-×æ-Ñ$†, Ýë…QÅ-MýS-Ô>ç܈…,
çÜ…¿ê-Ð]lÅ™èl A«§éÅ-Ķæ*-ÌZÏ° ÐéÅçÜ-Æý‡*ç³ {ç³Ô¶æ²Ë$ çÜ$Ë$-OÐðl¯]lÑ. ºçßæ$-ç³-§ýl$Ë$, Æð‡…yýl$ ^èlÆý‡-Æ>-Ô¶æ$ÌZÏ Æó‡TĶæ$ çÜÒ$-MýS-Æý‡×êË f™èl ¯]l$…_ C^óla {V>‹œ çÜÐ]l$-çÜÅË$, Æó‡Rê-VýS-×ìæ-™èl…-ÌZ°
°Æ>Ã-×êË$, Ýë…QÅMýS Ô>ç܈…-ÌZ° KiÐŒl Ð]l{MýS… {V>‹œ çÜÐ]l$çÜÅË$ MýS_a-™èl…V> Ð]l^óla {ç³Ô¶æ²Ë$. ™öË$™èl ÐéÅçÜ-Æý‡*ç³
{ç³Ô¶æ²Ë {í³ç³-Æó‡-çÙ-¯Œl¯]l$ ç³NÇ¢-^ól-Ķæ*Í.
A«¨MýS Ð]l*Æý‡$PË Ý뫧ýl-¯]lÌZ ÐéÅçÜ-Æý‡*ç³ {ç³Ô¶æ²-Ë™ø ´ër$
çÜÓ˵ çÜÐ]l*-«§é¯]l (1 Ð]l*Æý‡$P, Æð‡…yýl$ Ð]l*Æý‡$P-Ë$)
{ç³Ô¶æ²Ë$ MîSËMýS…. Æð‡…yýl$ õ³ç³-Æý‡ÏÌZ CÌê…sìæ {ç³Ô¶æ²-ËMýS$ 28
Ð]l*Æý‡$PË$ E…sêƇ¬. A…§ýl$-Ð]lËÏ Òsìæ° »êV> {´ëMîSt‹Ü
^ólĶæ*Í.
¼sŒæÞ {í³ç³-Æó‡-çÙ¯Œl:
ѧéÅ-Æý‡$¦Ë$ 糨 {VóSyŠl ´ëƇ¬…r$Ï Ý뫨…-^èl-yýl…ÌZ ¼r$Ï
Ð]l¬QÅ-´ë{™èl ´ùíÙ-Ýë¢Æ‡¬. ¼sŒæÞ {í³ç³-Æó‡-çÙ¯Œl JMýS Ð]l*Æý‡$P
{ç³Ô¶æ²-ËMýS$ MýS*yé Eç³-Äñæ*-VýS-ç³-yýl$-™èl$…¨. Ððl¬™èl¢… Æð‡…yýl$ õ³ç³Æý‡ÏÌZ 30 Ð]l*Æý‡$P-ËMýS$ ¼r$Ï E…sêƇ¬. ´ëuý‡Å-ç³#-çÜ¢-MýS…-ÌZ°
A°² ¼rϯ]l$ {´ëMîSt‹Ü ^ólĶæ*Í. Cç³µsìæ ¯]l$…_ ¼rϯ]l$ »êV>
{´ëMîSt‹Ü ^ólõÜ¢ ç³¼ÏMŠS ç³È-„ýS-Ë™ø ´ër$ ´ëÍ-sñæ-MìS²MŠS, Hï³-B-ÆŠ‡gôæïÜ Ð]l…sìæ ç³È-„ýSÌZÏ Ð]l$…_ ÝùPÆŠ‡ Ý뫨…-^èl-Ð]l^èl$a.
terminate after ____
12. If a = 23×3, b = 2×3×5, c = 3n×5and LCM
(a, b, c) = 23×32×5, then n = ____
13. If n is any natural number, then 6n-5n
always ends with ____
14. If log216= x then x= ____
15. The standard base of a logarithm is ____
ç³È-„ýS-ËMýS$ 15 ÆøkË$ Ð]l¬…§ýl$-V>¯ól íÜË-º‹Ü ç³NÇ¢-^ólĶæ*Í. ÒOÌñæ-¯]l°² GMýS$P-Ð]l-ÝëÆý‡$Ï (MýS-±çÜ… 3Ìôæ§é 4 ÝëÆý‡$Ï)
ÇÑ-f¯Œl ^ólĶæ$yýl… Ð]lËÏ çÜ»ñæj-MýS$tOò³ ç³NÇ¢-Ýë¦Æ‡¬ ç³r$t
Ý뫨…-^èl-Ð]l^èl$a. ©°-Ð]lËÏ {ç³Ô¶æ²Ë$ G…™èl MìSÏçÙt…V> E¯]l²-ç³µsìæMîS ™ólÍV>Y çÜÐ]l$-çÜÅ-ËMýS$ çÜÐ]l*-«§é-¯éË$ CÐöÓ^èl$a.
¼sŒæÞ MøçÜ… 糧ø ™èlÆý‡-VýS† ´ëuý‡Å-ç³#-çÜ¢-M>-Ë™ø ´ër$, Hï³B-ÆŠ‡-gôæïÜ, ´ëÍ-sñæ-MìS²MŠS {ç³Ô¶æ²-ç³-{™é-ÌZÏ° ¼sŒæÞ¯]l$ MýS*yé
{´ëMîSt‹Ü ^ólĶæ*Í.
GÌê Æ>Ķæ*Í?
çÜ*{™é-˯]l$ VýS$Æý‡$¢…-^èl$-Mø-Ðé-Ë…sôæ..
VýS×ìæ™èl… A¯ól¨ çÜ*{™é-ËOò³ B«§é-Æý‡-ç³-yìl¯]l çÜ»ñæjMýS$t. çÜ*{™éË$
¯ólÆý‡$a-Mö°, VýS$Æý‡$¢…-^èl$-Mø-MýS$…sôæ çÜÐ]l$-çÜÅͲ Ý뫨…-^èlÌôæ….
M>ºsìæt A«§éÅ-Ķæ*Ë ÐéÈV> çÜ*{™é-˯]l$ JMýS-^ør Æ>çÜ$Mö°, ç³r$t-Ýë-«¨…-^éÍ. H çÜÐ]l$-çÜÅMýS$ H çÜ*{™èl… Eç³-Äñæ*W…-^éÌZ ™ðlË$-çÜ$-Mø-ÐéÍ.
Ý뫧é-Æý‡×æ ѧéÅ-Æý‡$¦Ë {í³ç³-Æó‡-çÙ¯Œl:
Ý뫧é-Æý‡×æ ѧéÅ-Æý‡$¦-ËMýS$ VýS×ìæ™èl… çÜ»ñæjMýS$t Ñ$W-ͯ]l çÜ»ñæj-MýS$tË™ø ´ùÍõÜ¢ MýSçÙt…V> E…r$…¨. ÒÆý‡$ Mö°² {ç³Ô¶æ²-˯]l$
MýS_a-™èl…V> {´ëMîSt‹Ü ^ólõÜ¢ ™ólÍV>Y E¡¢-Æý‡$~-Ë-Ð]l#-™éÆý‡$. ÒOÌñæ™ól 50
Ð]l*Æý‡$PË$ MýS*yé ™ðl^èl$a-Mø-Ð]l^èl$a. õ³ç³-ÆŠ‡-&-1ÌZ ºçßæ$-糧ýl$Ë$, Æð‡…yýl$ ^èlË-Æ>-Ô¶æ$ÌZÏ Æó‡TĶæ$ çÜÒ$-MýS-Æý‡-×êË f™èl
¯]l$…_ C^óla {V>‹œ çÜÐ]l$-çÜÅË$, çÜÆý‡*ç³ {†¿¶æ$-gêË$,
Ð]l–™é¢Ë çܵÆý‡Ø Æó‡QË$, Q…yýl¯]l Æó‡QË ¯]l$…_ C^óla °Æ>Ã×æ…
çÜÐ]l$çÜÅ, Ýë…QÅMýS Ô>ç܈… ¯]l$…_ C^óla {V>‹œ çÜÐ]l$çÜÅ (KiÐŒl Ð]l{MýS…) MýS_a-™èl…V> C^óla çÜÐ]l$-çÜÅË$, Òsìæ° çÜ$Ë$-Ð]l#V>
¯ólÆý‡$a-Mø-Ð]l^èl$a.
25.
26.
27.
28.
29.
as a = x5y2, b = x3y3 where x and y are
prime numbers then the HCF(a, b) = ____;
LCM (a,b) = ____
The product of two irrational numbers is
____
43.1234 is ____ number.
log ap.bq = ____
If 53 =125, then the logarithm form ____
log 7343 = ____
ANSWERS
3
X
7
4. If the LCM of 12 and 42 is 10m+4, then
the value of 'm' is ____
5. π is ____
6. log20152015 = ____
7. The reciprocal of two irrational numbers
is ____
8. The decimal expansion of 17/18 is ____
9. 2.547 is ____
27
10. Decimal expansion of number
2×5×7
has ____
11. The decimal expansion of 189/125 will
92-&-1-00 Ð]l*Æý‡$PË$ Ð]lõÜ¢ 糨 {VóSyŠl ´ëƇ¬…r$Ï Ý뫨…-_¯]lsôæÏ. M>ºsìæt Mö°² çÜÐ]l$-çÜÅͲ (8 Ð]l*Æý‡$PË Ð]lÆý‡-MýS$) Ý뫨…^èl-Ìôæ-MýS-´ù-Ƈ¬¯é 10 {VóSyŠl ´ëƇ¬…r$Ï ™ðl^èl$a-Mø-Ð]l^èl$a.
ÐéÅçÜ-Æý‡*ç³, çÜÓ˵ çÜÐ]l*-«§é¯]l {ç³Ô¶æ²Ë$:
4
Y
10 {VóSyŠl ´ëƇ¬…r$Ï Ý뫨…-^é-Ë…sôæ:
Ķæ*Ë ÐéÈV> íܧýl®-Ð]l$-ÐéÍ.
ïÜïÜD 糧ýl®-†Oò³ AÐ]l-V>-çßæ-¯]lMýS$ VýS™èl ïܽ-G-‹ÜD {ç³Ô¶æ²-ç³{™é-˯]l$, G‹Ü-ïÜ-D-B-ÆŠ‡sîæ Ñyýl$-§ýlË ^ólíܯ]l {ç³Ô¶æ²-ç³-{™é-˯]l$
ç³Ç-Ö-Í…-^éÍ.
{í³ç³-Æó‡-çÙ¯Œl ç³NÆý‡¢-Ƈ¬¯]l ™èlÆ>Ó™èl ÒOÌñæ-¯]l°² ¯]lÐ]lʯé {ç³Ô¶æ²ç³-{™é-˯]l$ {´ëMîSt‹Ü ^ólĶæ*Í.
If log102=0.3010, then log108 = ____
log10 0.01 = ____
The exponential form log4 64 = 3 is ____
log 15 = ____
The prime factorization of 216 is ____
HCF of 4 and 19 is ____
LCM of 10 and 3 is ____
If the HCF of two numbers is '1' , then the
two numbers are called ____
24. If the positive numbers a and b are written
16.
17.
18.
19.
20.
21.
22.
23.
1) 23; 2) 15; 3) X = 21, Y = 84; 4) 8;
5) An irrational number; 6) 1; 7) Always
an irrational number; 8) 2.125; 9) A
rational; 10) non-terminating but repeating; 11) 3 places of decimal; 12) 2; 13) 1;
14) 4; 15) 10; 16) 0.9030; 17) − 2; 18) 43
= 64; 19) log3 + log 5; 20) 23×33; 21) 1;
22) 30; 23) Co-Primes; 24) [x3y2; x5y3];
25) Sometimes rational, Some times irrational; 26) a rational number; 27) plog
a+q logb; 28) log5125 = 3; 29) 3.
2. SETS
1. The symbol for a Universal Set is____
2. If A = {a, b, c}, the number of subsets of
A is ____
Hyé¨ M>Ë…ÌZ ¯ólÆý‡$a-MýS$¯]l² ÑçÙ-Ķæ*Ë$ JMýS G™èl¢-Ƈ¬™ól, B
¯ólÆý‡$a-MýS$¯]l² A…Ô>Ë B«§é-Æý‡…V> {MýSÐ]l$-ç³-§ýl®-†ÌZ çÜÐ]l*-«§é¯éË$ CÐ]lÓyýl… Ð]l$Æø G™èl$¢. G…™èl {糆¿¶æ E¯]l² ѧéÅǦ
AƇ¬¯é çÜÐ]l*-«§é-¯éË$ çÜÇV> Æ>Ķæ$-MýS-´ù™ól Ð]l*Æý‡$PË$
MøÌZµÄôæ$ {ç³Ð]l*-§ýl-Ð]l¬…¨. ^èlMýSPsìæ §ýlçÜ*¢-Ç™ø Ayìl-W¯]l
Ðól$Æý‡MýS$ çÜÐ]l*-«§é¯]l… Æ>Ķæ*Í.
»êV> ™ðlÍ-íܯ]l {ç³Ô¶æ²-ËMýS$ Ð]l¬…§ýl$ çÜÐ]l*-«§é-¯éË$
Æ>Ķæ*Í. Mösìæt-Ðól-™èlË$ ÌôæMýS$…yé ^èl*yéÍ.
Ð]l¬QÅ-OÐðl$¯]l òßæyìlz…VŠSÞ, çÜ»Œæ òßæyìlz…-VŠSÞ¯]l$ A…yýl-ÆŠ‡-OÌñ毌l
^ólĶæ*Í. {ç³Ô¶æ²Ë çÜ…Qů]l$ çܵçÙt…V> Æ>Ķæ*Í. çÜÐ]l*«§é-¯é-°MìS, çÜÐ]l*-«§é-¯é-°MìS Ð]l$«§ýlÅ Mö…™èl gêV> Ð]l¨-ÌôæĶæ*Í.
Ððl¬§ýlr ÐéÅçÜ-Æý‡*ç³ {ç³Ô¶æ²Ë$, ™èlÆ>Ó™èl Æð‡…yýl$
Ð]l*Æý‡$PË$, B ™èlÆ>Ó™èl JMýS Ð]l*Æý‡$P {ç³Ô¶æ²-ËMýS$ çÜÐ]l*-«§é¯éË$ Æ>õÜ¢ Ð]l$…_¨. _Ð]lÆøÏ A§ýl-¯]lç³# {ç³Ô¶æ²-ËMýS$ çÜÐ]l*«§é-¯éË$ Æ>Äñæ¬^èl$a.
ç³sêË$, {V>‹œË$ ^èlMýSPV> ÐólĶæ*Í. _™èl$¢-ç³-°MìS Ð]l*Çj¯Œl¯]l$ Eç³-Äñæ*-W…-^èl$-Mø-ÐéÍ.
3. The set builder form of A∩B is ____
4. For every set A, A∩φ = ____
5. Two Sets A and B are said to be disjoint if
____
6. The Shaded region in the adjacent figure is
____
A
B
µ
7. A = {x: x is a circle in a give plane} is
____
8. n (A∪B) = ____
9. If A is subset of B, then A–B = ____
10. If A = {1, 2, 3, 4, 5} then the cardinal number of A is ____
A well defined collection of objects or
ideas is known as a SET.
Set Theory is a comparatively
new concept in Mathematics. It
was developed by Georg Cantor
(1845-1918). Cantor's
work between 1874
and 1884 is the origin of Set
Theory.
VýS$Æý‡$ÐéÆý‡… l
íœ{ºÐ]lÇ l 12 l 2015
11. A = {2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5} then
B–A = ____
12. If A⊂B then A∩B = ____
13. If A⊂B then A∪B = ____
14. The shaded region in the given figure represents ____
B
A
µ
15. The Symbol for null set is = ____
16. Roster form of { x: x∈N, 9≤ x≤ 16} is
_____
17. If A⊂B and B⊂A then ____
18. If A⊂B and B⊂C then ____
19. A∪φ = ____
20. The Set theory was developed by ____
21. If n(A) = 7, n(B) = 8, n(A∩B) = 5 then
n(A∪B) = ____
22. A set is a ____ collection of objects.
23. Every set is ____ of it self.
24. The number of elements in a set is called
the ____ of the set
25. A = { 2, 4, 6, ……}, B = {1, 3, 5, ……..}
then n(A∩Β)= ____
26. A and B are disjoint sets then A–B = ____
27. If A∪B = A∩Β then = ____
28. A = { x: x2 = 4 and 3x = 9 } is a ____ set
29. A = {2, 5, 6, 8} and B = {5, 7, 9, 1} then
A∪B = ____
30. If A⊂B, n(A) = 3, n(B) = 5, then n(A∩Β)
= ____
31. If A⊂B, n(A) = 3, n(B) = 5, then n (A∪B)
= ____
32. A, B are disjoint sets then (A–B)∩ (B–A)
= ____
33. A = {1, 2, 3, 4} and B = {2, 4, 6, 8} then
B – A = ____
34. Set builder form of A∪B is = ____
point (3, 2), then the value of p is ____
Y
−4
−2
o
2
4
Y1
4. The degree of the constant polynomial is
____
5. The zero of p(x) = ax–b is ____
6. If α and β are the zeroes of the polynomial 3x2+5x+2,then the value of α+β+αβ is
____
7. If the sum of the zeroes of the polynomial
p(x) = (k2−14) x2−2x−12 is 1, then k takes
the value (s) ____
8. If α and β are zeroes of p(x) = x2−5x+k
and α−β = 1 then the value of k is ____
9. If α, β, γ are the zeros of the polynomial
ax3+bx2+cx+d, then the value of
1/α+1/β+1/γ is ____
10. If the product of the two zeros of the polynomial x3−6x2+11x−6 is 2 then the third
zero is ____
11. The zeros of the polynomial of x3−x2 are
____
12. If the zeroes of the polynomial x3−3x2 + x
+ 1 are a/r, a and ar then the value of a is
____
13. If α and β are the zeroes of the quadratic
polynomial 9x2−1, the value of α2+β2 is
____
14. If α, β, γ are the zeroes of the polynomial
x3 + px2 + qx + r then 1/αβ + 1/βγ + 1/αγ
is ____
15. The number to be added to the polynomial x2–5x+4, so that 3 is the zero of the
polynomial is ____
16. If α, β are zeroes of p(x) = 2x2–x–6 then
the value of α–1+β–1 is ____
ANSWERS
1) µ; 2) 8; 3) {x:x∈A and x∈B}; 4) φ;
5) A∩Β = φ; 6) A∩B; 7) Infinite Set;
8) n(A)+ n(B)– n(A∩B); 9) φ; 10) 5;
11) {1, 3, 5}; 12) Α; 13) B; 14) Α–B;
15) φ; 16) {9, 10, 11, 12, 13, 14, 15, 16};
17) A = B; 18) A⊂C; 19) A; 20) George
Cantor ; 21) 10; 22) Well defined;
23) Subset; 24) cardinal number; 25) 0;
26) A; 27) A = B; 28) Null Set;
29) {1, 2, 5, 6, 7, 8, 9}; 30) 3; 31) 5;
32) φ; 33) {6, 8}; 34) {x: x∈A or x∈B}
3. POLYNOMIALS
1. The graph of the polynomial f(x) = 3x –7
is a straight line which intersects the xaxis at exactly one point namely ____
2. In the given figure , the number of zeros of
the polynomial f(x) are ____
Y
f(x)
X1
−3
o
1
3
X
Y1
3. The number of zeros lying between –2 and
2 of the polynomial f(x) whose graph in
given figure is ____
6. The value of
y = f(x)
X1
3
Bit Bank
Mathematics
26. The polynomial whose zeroes are –5 and 4
is ____
27. If –1 is a zero of the polynomial f(x) =
x2–7x–8 then other zero is ____
28. If the product of the zeroes of the polynomial ax3–6x2+11x–6 is 6, then the value of
a is ____
29. A cubic polynomial with the sum, sum of
the product of its zeroes taken two at a
time, and the product of its zeroes are 2,
–7 and –14 respectively, is ____
30. For the polynomial 2x3–5x2–14x+8, the
sum of the products of zeroes , taken two
at a time is ____
31. If the zeroes of the quadratic polynomial
ax2+bx+c are reciprocal to each other,
then the value of c is ____
32. ____ can be the degree of the remainder at
most when a biquadrate polynominal is
divided by a quadratic polynomial.
ANSWERS
17. ____ is the coefficient of the first term of
the quotient when 3x3+x2+2x+5 is divided
by 1+2x+x2.
18. If the divisor is x2 and quotient is x while
the remainder is 1, then the dividend is___
19. The maximum number of zeroes that a
polynomial of degree 3 can have is ____
20. The number of zeroes that the polynomial
f(x) = (x–2)2 +4 can have is ____
21. The graph of the equation y = ax2+ bx+ c
is an upward parabola, if ____
22. If the graph of a polynomial does not
intersect the x – axis, then the number of
zeroes of the polynomial is ____
23. The degree of a biquadratic polynomial is
____
24. The degree of the polynomial
3
7u 6 − u 4 + 4u 2 + u − 8 is ____
2
25. The value of p(x) = x3−3x−4 at x = −1 is
____
1) (7/3, 0); 2) 3; 3) 2; 4) 0; 5) b/a; 6) –1;
7) ±4; 8) 6; 9) –c/d; 10) 3; 11) 0, 0, 1;
12) –1; 13) 2/9; 14) p/r; 15) 2; 16) –1/6;
17) 3; 18) x3+1; 19) 3; 20) 2; 21) a>0;
22) 0; 23) 4; 24) 6; 25) –2; 26) x2+x–20;
27) 8; 28) 1; 29) x3–2x2–7x+14; 30) –7;
31) a; 32) 1.
4. PAIR OF LINEAR
EQUATIONS IN TWO
VARIABLES
1. The point of intersection of the lines represented by 3x–2y = 6, the Y-axis is ____
2. If x = 2, y = 3 is a solution of a pair of lines
2x–3y+a = 0 and 2x+3y–b+2 = 0, then the
relationship between a and b is ____
3. If the units and ten's digit of a two digit
number are y and x respectively, then the
number will be in the form of ____
4. The age of a son is one third the age of his
mother. If the present age of mother is x
years, then the age of the son after 12
years is ____
5. If the line y = px–2 passes through the
2
x
+
3
y
when x = 4 and y
= 9 is ____
7. If ad≠bc, then the pair of linear equations
ax+by = p then and cx+dy = p has ____
solutions?
8. The pair of linear equations 3x+5y = 3,
6x+ky= 8 do not have solutions if k= ____
9. The point of the intersection of the lines x2 = 0 and y+6 = 0 is ____
10. ____ is the area of the triangle formed by
the coordinate axes and the line x+y = 6.
11. The sum of the two digits of a two digit
number is 12. The number obtained by
interchanging the two digits exceeds the
given number by 18. the number is ____
12. The point (–2, –2) lies in the ____
Quadrant.
13. If the difference between two numbers is
26. One number is three times the oth-er
number, then the two numbers are ____
14. If the system of equations 4x+y= 3 and
8x+2y= 5k has infinite solutions, then the
value of k is ____
15. The system of linear equations x+y= 14
and x–y= 4 are ____
16. If the system of linear equations (k–3)
x+3y = k, kx+ky = 12 has infinite number
of solutions then the value of k is ____
17. If the system of linear equations 3x–4y+7
= 0 and kx+3y–5 = 0 has no solutions then
value of k is ____
18. ____ is the condition if the pair of linear
equations, a1x+b1y+c1= 0, a2x+b2y+c2= 0,
has a unique solution?
19. The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes
1/2. then the fraction is ____
x+y
x−y
= 2&
= 6 , then value of y is
20. If
xy
xy
____
21. Two angles are complementary. The larger angle is 3 degrees less than twice the
measure of the smaller angle. The measure
of each angle is ____ and ____
22. The value of y when x = –1/2 that satisfies
2 3
the equation + = 5 is ____
x y
23. The length and breadth of a rectangle are
x, y respectively. The area of the rectangle
gets reduced by 9 square units, if its length
is reduced by 5 units and breadth is increased by 3 units. Then the equation we get
is ____
24. The larger of two supplementary angles
exceeds the smaller by 20 degrees. Then
the angles are ____ and ____
25. ____ is the value of 'a' so that the point (2,
a) lies on the line represented by 4x–y= 3?
Aryabhata
the famous Indian
mathematician gave formulas for the sum of squares and
cubes of natural numbers. His
work was "Arybhateeyam' (499
A.D.). He gave a formula for
finding the sum of "n
terms' of an Arithmetic
progression starting
with any term.
4
ANSWERS
1) (0, –3); 2) 3a = b; 3) 10x+y; 4)
x
+ 12 ;
3
5) 4/3; 6) 2 or –2; 7) unique solution;
8) k = 10; 9) (2, –6); 10) 18; 11) 57;
12) 3rd quadrant; 13) 39, 13; 14) 6/5;
15) consistent; 16) 6; 17) –9/4;
18)
Bit Bank
Mathematics
a1 b1
≠ ; 19) 5/7; 20) 1/4; 21) 31
a2 b2
degrees and 59 degrees; 22) 1/3;
23) (x–5) (y+3)=(xy–9); 24) 100 degrees,
80 degrees; 25) a = 5.
28. If the discriminant of the quadratic equation ax2 +bx +c = 0 is zero, then the roots
of the equation are ____
29. The product of the roots of the quadratic
equation √2x2–3x+5√2=0 is ____
30. The nature of the roots of a quadratic
equation 4x2–12x+9 = 0 is ____
31. If the equation x2–bx+1 = 0 does not possess real roots, then ____
32. If the sum of the roots of the equation
x2–(k+6)x+2 (2k–1) = 0 is equal to half of
their product, then k = ____
5. QUADRATIC EQUATIONS
1. The sum of a number and its reciprocal is
50/7, then the number is ____
2. The roots of the equation 3x2−2√6x+2 = 0
are ____
3. If x2–2x+1 = 0, then x +1/x = ____
4. If 3 is a solution of 3x2+(k–1)x+9=0, then
k = ____
5. The roots of x2–2x–(r2–1)= 0 are ____
6. The sum of the roots of the equation
3x2 –7x+11= 0 is ____
7. The roots of the equation
x2 − 8 1
=
x 2 + 20 2
are____
8. The roots of the quadratic equation
9
25
are ____
=
x 2 − 27 x2 − 11
9. The roots of the equation 2x 2 + 9 = 9 are
____
10. The two roots of a quadratic equation are
2 and –1. The equation is ____
11. If the sum of a quadratic equation 3x2 +
(2k+1)x–(k+5) = 0, is equal to the product
of the roots, then the value of k is ____
12. The value of k for which 3 is a root of the
equation kx2–7x+3 = 0 is ____
13. If the difference of the roots of the quadratic equation x2–ax+b is 1, then ____
14. The quadratic equation whose one root is
2–√3 is ____
15. ____ is the condition that one root of the
quadratic equation ax2 +bx+c is reciprocal
of the other.
16. The roots of the quadratic equation x/p =
p/x are ____
17. If the roots of the equation 12x2+mx+5= 0
are real and equal then m is equal to ____
18. If the equation x2–4x+a has no real roots,
then ____
19. The discrimination of the quadratic equation 7√3x2+10x–√3=0 is ____
20. The value of
6 + 6 + 6 + ...... is ____
21. Standard form of a quadratic equation is
____
22. The sum of a number and its reciprocal is
5/2. This is represented as ____
23. “The sum of the squares of two consecutive natural numbers is 25”, is represented
as ____
24. If one root of a quadratic equation is 7–√3
then the other root is ____
25. The discriminant of 5x2–3x–2 = 0 is ____
26. The roots of the quadratic equation
x2–5x+6 = 0 are ____
27. If x = 1 is a common root of the equations
ax2 +ax+3 = 0 and x2+x+b = 0 then the
value of ab is ____
33. If one root of the equation 4x2–2x+(λ–4) =
0 be the reciprocal of the other, then λ =
____
34. If sinα and cosα are the roots of the equation ax2+bx+c = 0, then b2 = ____
35. If the roots of the equation (a2+b2)x2
–2b(a+c)x+(b2+c2) = 0 are equal, then b2 =
____
36. The quadratic equation whose roots are
–3, –4 is ____
37. If b2–4ac<0 then the roots of quadratic
equation ax2+bx+c = 0 are ____
11. Common difference in 1/2, 1, 3/2 ----- is
____
12. √3, 3, 3√3 is a ____
13. a=1/3, d= 4/3, the 8th term of an A.P is___
14. Arithmetic progression in which the common difference is 3. If 2 is added to every
term of the progression, then the common
difference of new A.P. is ____
15. In an A.P. first term is 8, common difference is 2, then ____ term becomes zero
16. 4, 8, 12, 16, ----- is ____ series.
17. Next 3 terms in series 3, 1, –1, –3 are ____
18. If x, x+2 & x+ 6 are the terms of G.P. then
x is ____
19. In G.P. ap+q= m, ap – q= n. Then ap = ____
20. In 3+6+12+24 -----. Progression, the
nthterm is ____
21. a12 = 37, d = 3, then S12 = ____
22. In the garden, there are 23 roses in the first
row, in the 2nd row there are 19. At the
last row there are 7 trees, ____ rows of
rose trees are there in the garden.
23. From 10 to 250, ____ multiples of 4 are
there.
24. The taxi takes Rs. 30 for 1 hour. After for
each hour Rs. 10, for each hour. how much
money can be paid & how it forms ____
progression
25. The sum of first 20 odd numbers is ____
26. 10, 7, 4, ----- a30 = ____
27. 1+ 2+3+4+ ----- +100 = ____
28. In the G.P 25, –5, 1, –1/5 ----- r = ____
29. The reciprocals of terms of G.P will form
____
ANSWERS
1) 1/7; 2) √2/3, √2/3; 3) 2; 4) –11;
5) 1–r, r +1; 6) 7/3; 7) ±6; 8) ±6; 9) x =
±6; 10) x2–x–2 = 0; 11) 4; 12) 2;
13) a2–4b = 1; 14) x2–4x+1 = 0 ; 15) a =
c; 16) ±p; 17) 4√15; 18) a>4; 19) 184;
20) 3; 21) ax2+bx+c = 0, a ≠ 0; 22) (x+1/x
= 5/2); 23) x2+(x–1)2 = 25; 24) 7+√3; 25)
49; 26) 2, 3; 27) 3; 28) real and equal; 29)
5; 30) real and equal; 31) b2–4<0 (or)
b2<4 (or) –2<b<2; 32) 7; 33) 8;
34) a2+2ac; 35) ac; 36) x2+7x+12 = 0;
37) Not real or imaginary.
6. PROGRESSIONS
1. The nth term of G.P is an= arn-1 where ‘r’
represents ____
2. The nth term of a G.P is 2 (0.5)n-1 then r
____
3. In the A.P 10, 7, 4 ---- –62, then 11th term
from the last is ____
4. ____ term of G.P 1/3, 1/9, 1/27 ---- is
1/2187
5. n–1, n –2, n –3, ---- an = ____
6. In an A.P a = –7, d = 5 then a18 = ____
7. 2 + 3 + 4 + ----- + 100 = ____
8. –1, 1/4, 3/2 ----- S81 = ____
9. In G.P, 1st term is 2, common ratio is –3
then 7th term is ____
10. 1, –2, 4, –8, ----- is a ____ Progression.
30.
31.
32.
33.
34.
35.
36.
If –2/7, x, –7/2 are in G.P. Then x = ____
1 + 2 + 3 + ----- + 10 = ____
If a, b, c are in G.P, then b/a = ____
x, 4x/3, 5x/3, ..a6 = .____
In a G.P a4 = ____
1/1000, 1/100, 1/10, 1 ----- are in ____
The 10th term from the end of the A.P;
4, 9, 14 ----- 254 is ____
37. In a G.P. an–1 = ____
38. In a A.P. Sn–Sn–1 = ____
39. 1.2 + 2.3 + 3.4 + ------ 5 terms = ____
40. In a series a n =
n(n + 3)
,a17 = ____
n+2
41. In –3, –1/2, 2 -----. A.P. then nth term ____
42. a3 = 5 & a7 = 9, then the A.P. is ____
43. The nth term of the G.P. 2(0.5)n-1, then the
common ratio = ____
44. In 4, –8, 16, –32 then the common ratio is
____
45. The nth term t n =
n
then t4 = ____
n +1
46. In an A.P, l = 28, Sn = 144 & total terms
are 9, then the first term is ____
47. In an A.P 11th term is 38 and 16th term is
73, then common difference of A.P is ____
48. In a garden there are 32 rose flowers in
first row and 29 flowers in 2nd row and 26
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flowers in 3rd row, then ____ rose trees
are there in the 6th row.
49. In –5, –1, 3, 7 ------. Progression, then 6th
term is ____
50. In Arithmetic progression, the sum of nth
terms is 4n–n2, then first term is ____
ANSWERS
1) Common ratio; 2) 0.5; 3) –32; 4) 7;
5) 0; 6) 78; 7) 5049; 8) 3969; 9) 1458;
10) GP; 11) 1/2; 12) GP; 13) 29/3; 14) 3;
15) 5th term; 16) Arithmetic; 17) –5, –7,
–9; 18) 2; 19) mn ; 20) 3.2n–1; 21) 246;
22) 9; 23) 60; 24) Arithmetic progression;
25) 400; 26) –77; 27) 5050; 28) –1/5 ;
29) Geometric Progression; 30) ±1;
31) 55; 32) c/b ; 33) 8x/3; 34) ar3;
35) G.P.; 36) 209; 37) arn-2; 38)an; 39) 70;
40) 340/19; 41) 1/2(5n–11); 42) 3, 4, 5, 6,
7; 43) 0.5; 44) –2; 45) 4/5; 46) 4;
47) 7; 48) 17; 49) 15; 50) 3.
7.COORDINATE GEOMETRY
1. For each point on X-axis, Y-coordinate is
equal to ____
2. The distance of the point (3, 4) from Xaxis is ____
3. The distance of the point (5, −2) from origin is ____
4. The point equidistant from the points (0,
0), (2, 0) and (0, 2) is ____
5. If the distance between the points (3, a)
and(4,1) is √10, then the value of a is___
6. If the point (x, y) is equidistant from the
points (2, 1) and (1, −2) then ____
7. The closed figure with vertices (−2, 0), (2,
0), (2, 2), (0, 4) and (−2, 2) is a ____
8. If the coordinates of P and Q are (acosθ,
bsinθ) and (−asinθ, bcosθ) then OP2 +
OQ2 = ____
9. In ____ quadrant does the point (−3, −3)
lie?
10. If the distance between (k, 3) and (2, 3) is
5 then the value of k is ____
11. ____ is the condition that A, B, C are the
successive points of a line.
12. The coordinates of the point, dividing the
join of the point (5, 0) and (0, 4) in the
ratio 2:3 internally are ____
13. If the point (0, 0), (a, 0) and (0, b) are colinear then ____
14. The coordinates of the centroid of the triangle whose vertices are (8, −5), (−4, 7)
and (11, 13) are ____
15. The coordinates of vertices A, B and C of
the triangle ABC are (0, −1), (2, 1) and (0,
3). the length of the median through B is
____
Carl Friedrich
Gauss (1777-1855) the
great German mathematician, proposed a formula to
find the Sum of first "n' terms in
Arithmetic Progression. He contributed significantly to
many fields like number theory, algebra,
geophysics,
optics etc.
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16. The vertices of a triangle are (4, y), (6, 9)
and (x, 4). The coordinates of its centroid
are (3, 6). The values of x and y are ____
17. If a vertex of a parallelogram is (2, 3) and
the diagonals cut at (3, −2). ____ is the
opposite vertex.
18. Three consecutive vertices of a parallelogram are (−2, 1), (1, 0) and (4, 3). The
fourth vertex is ____
19. If the points (1, 2), (−1, x) and (2, 3) are
collinear then the value of x is ____
20. If the points (a, 0), (0, b) and (1, 1) are
collinear the 1/a+1/b ____
21. The coordinates of the point of intersection of X-axis and Y-axis are ____
22. For each point on Y-axis, X-coordinate is
equal to ____
23. The distance of the point (3, 4) from Yaxis is ____
24. The distance between the points (0, 3) and
(−2, 0) is ____
25. The opposite vertices of a square are (5,−
4) and (−3, 2). The length of its diagonal is
____
26. The distance between the points (acosθ +
bsinθ, 0) and (0, asinθ − bcosθ) is ____
27. The coordinates of the centroid of the triangle with vertices (0, 0), (3a, 0) and (0,
3b) are ____
28. If OPQR is a rectangle where O is the origin and P(3, 0) and R (0, 4), then the coordinates of Q are ____
29. If the centroid of the triangle (a, b), (b, c)
and (c, a) is 0 (0, 0) then the value of a3 +
b3 + c3 is ____
30. If (−2, −1), (a, 0), (4, b) and (1, 2) are the
vertices of a parallelogram then the value
of a and b are ____
31. The area of the triangle whose vertices are
(0, 0), (a, 0) and (0, b) is ____
32. One end of a line is (4, 0) and its middle
point is (4, 1), then the coordinates of the
other end ____
33. The distance of the mid point of the line
segment joining the points (6, 8) and (2, 4)
from the point (1, 2) is ____
34. The area of the triangle formed by the
points (0, 0), (3, 0) and (0, 4) is ____
35. The coordinates of the mid point of the
line segment joining the points (x1, y1)
and (x2, y2) are ____
36. The distance between the points
(acos250, 0) and (0, acos650) is ____
37. The line segment joining points (−3, −4)
and (1, −2) is divided by Y-axis in the ratio
____
38. If A (5, 3), B (11, −5) and P (12, y) are the
vertices of a right angled triangle if right
angled at p, then y is ____
39. The perimeter of the triangle formed by
the points (0, 0), (1, 0) and (0, 1) is ____
40. The coordinates of the circumcentre of the
triangle formed by the points 0(0, 0), A(a,
0) and B (0, b) is ____
ANSWERS
1) 0; 2) 4; 3) √29; 4) (1, 1); 5) 4, −2;
6) x+3y = 0; 7) pentagon; 8) a2+b2; 9) 3;
10) 7; 11) AB + BC = AC; 12) (3, 8/5);
13) ab = 0; 14) (5, 5); 15) 2; 16) −1, −5;
17) (4, −7); 18) (1, 4); 19) 0; 20) 1;
21) (0, 0); 22) 0; 23) 3; 24) √13; 25) 10;
26) a 2 + b2 ; 27) (a, b); 28) (3, 4);
29) 3abc; 30) a=1, b=3; 31) 1/2ab;
x +x y +y
32) (4, 2); 33) 5; 34) 6; 35) 1 2 , 1 2
2
2
36) a; 37) 3:1; 38) 2 or − 4; 39) 2+√2;
40) (a/2, b/2).
above the ground. Then the length of the
ladder is ____
19. ∆ABC ∼∆PQR, if m∠A = 500 and m∠B =
600 then m∠R = ____
20. In the given figure, AC = 13 cm, then the
length of the Median BD = ____
A
PAPER - II
D
8. SIMILAR TRIANGLES
1. The ratio of the corresponding sides of the
two similar triangles is 1:3, then the ratio
of their areas is ____
2. ∆PQR is formed by joining the mid points
of the sides of ∆ABC, then the ratio of the
areas of the ∆PQR and ∆ABC is ____
3. D, E are the mid-points of the sides AB
and AC of the ∆ABC. If DE measures 4
cm, then the side BC measures ____
4. If the side of an equilateral triangle is 8
cm, then its area is ____
5. In the given figure DE//BC, AD = 6 cm,
DB=8 cm and AE=9 cm, then EC = ____
21. The areas of two similar triangles are 16
cm2 and 25 cm2 respectively. Then the
ratio of their corresponding sides is ____
22. In ∆ABC, DE//BC and DE = 1/2BC, then
AD:DB = ____
23. In the given figure ∆ACB ∼∆APQ. If AB
= 6 cm, BC = 8 cm and PQ = 4 cm, then
AQ = ____
B
C
6. In ∆ABC ∠Β=900 then b2 = ____
A
b
B
C
a
7. Two congruent polygons are ____
8. In the given figure AD ⊥ BC, then AB2 +
CD2 = ____
C
D
A
A
9. The length of the diagonal of the square is
5√2 cm, then the area of the square in cm2
is ____
10. The symbol for 'is similar to' is ____
11. ∆ABC ∼∆PQR, if AB = 3.6, PQ = 2.4 and
PR = 5.4, then AC = ____
12. In the given figure, ∠Q = 900 and ∠S =
900; QS = t, PQ = r QR = P and PR = q
then 1/t2 = ____
q
t
R
p
r
Q
13. ∆ABC ∼∆PQR, if AB = 6, BC = 4, AC =
8 and PR = 6 then PQ+QR = ____
14. A man goes 7 metres due east and then 24
metres due north, then his distance from
starting point is ____
15. If ∆ABC ∼∆DEF, ∠A=500 then ∠E+∠F =
____
16. The side of a rhombus with diagonals 16
cm & 30 cm is ____
17. Basic Proportionality Theorem is also
known as ____
18. A ladder is placed in such a way that its
foot is at a distance of 15 metres from the
wall and its top reaches a window 8 m
9. If a circle touches all the four sides of an
quadrilateral ABCD at points P, Q, R, S
then AB + CD = ____
10. If AP and AQ are the two tangents a circle
with centre O so that ∠POQ =1100 then
∠PAQ is equal to ____
11. If two concentric circles of radii 5 cm and
3 cm are drawn, then the length of the
chord of the larger circle which touches
the smaller circle is ____
12. If the semi perimeter of given ∆ΑΒC = 28
cm then AF+BD+CE is ____
C
E
A
Q
24. The relation between a diagonal of a
Square and its side is ____
25. In ∆ABC, ∠B=900 and BM is an altitude.
then ∆AMB is similar to ____
26. In the rhombus ABCD, AB = 6cm, then
AC2 + BD2 = ____
27. The area of an equilateral triangle whose
height 'h' is ____
28. If the ratio of the medians of two similar
triangles is 1:2, then the ratio of their areas
is ____
29. In an equilateral triangle ABC, if AD ⊥
ΒC then, 3AB2 = ____
30. The length of the diagonal of a Square is
5√2 cm, then the area of the square is ____
1) 1:9; 2) 1:4; 3) 8 cm; 4) 16 √3cm2; 5) 12
cm; 6) b2 = a2+c2; 7) similar;
8) BD2+AC2; 9) 25; 10) ∼; 11) 1.8;
12)
1
1
+ 2 ; 13) 10; 14) 25m; 15) 1300;
2
p
r
16) 17 cm; 17) Thales Theorem; 18) 17
m; 19) 700; 20) 6.5 cm; 21) 4:5; 22) 1:1;
23) 3 cm; 24) diagonal = √2 . Side; 25)
∆ABC; 26) 144; 27) h2/√3; 28) 1:4; 29)
4ΑD2; 30) 25 cm2
P
s
•
P
ANSWERS
B
O
F
B
C
E
c
C
B
A
D
5
Bit Bank
Mathematics
9. TANGENTS & SECANTS
TO A CIRCLE
A
O
600
C
B
16. If the sector of the circle made at the centre is x0 and radius of the circle is r, then
the area of sector is ____
17. If the length of the minute hand of a clock
is 14 cm, then the area swept by the
minute hand in 10 minutes ____
18. If the angle between two radii of a circle is
1300, the angle between the tangents at the
ends of the radii is ____
19. If PT is tangent drawn from a point P to a
circle touching it at T and O is the centre
of the circle, then ∠OPT+∠POT is ____
20. Two parallel lines touch the circle at
points A and B. If area of the circle is
25πcm2, then AB is equal to ____
21. A circle have ____ tangents.
22. A quadrilateral PQRS is drawn to circumscribe a circle. If PQ, QR, RS (in cm) are
5, 9, 8 respectively, then PS (in cms) equal
to ____
23. From the figure ∠ACB = ____
A
•
1. The length of the tangents from a point A
to a circle of radius 3 cm is 4 cm, then the
distance between A and the centre of the
circle is ____
2. ____ tangents lines can be drawn to a circle from a point outside the circle.
3. Angle between the tangent and radius
drawn through the point of contact is ____
4. A circle may have ____parallel tangents.
5. The common point to a tangent and a circle is called ____
6. A line which intersects the given circle at
two distinct points is called a ____ line.
7. Sum of the central angles in a circle is___
8. The shaded portion represents ____
B
D
13. The area of a square inscribed in a circle
of radius 8 cm is ____ cm2.
14. Number of circles passing through 3
collinear points in a plane is ____
15. In the figure ∠BAC ____
D
B
C
•
In a right angled
triangle the square of
the hypotenuse is equal to
the sum of the squares of the
other two sides. Pythagoras (570
BC-495 BC), the great Greek
mathematician
announced it. More
than 50 proofs are
available for this
theorem.
6
24. PA and PB are tangents to the circle with
centre O touching it at A and B respectively. If ∠APO = 300, then ∠POB ____
25. Two concentric circles of radii a and b
where a>b are given. The length of the
chord of the larger circle which touches
the smaller circle is ____
26. From the figure, the length of the chord
AB If PA = 6 cm and ∠POB = 600 ____
A
6c
m
600
P
15.
16.
17.
18.
19.
20.
21.
22.
23.
B
27. Two circles of radii 5 cm and 3cm touch
each other internally. The distance
between their centres is ____
28. The lengths of tangents drawn from an
external point to a circle are ____
ANSWERS
1) 5 cm; 2) 2; 3) 90°; 4) 2; 5) Point of
contact; 6) Secant line; 7) 360°; 8) Minor
segment; 9) BC + AD; 10) 70°; 11) 8 cm;
12) 28cm; 13) 128;14) 1; 15) 30°;
16)
Bit Bank
Mathematics
x
2
× πr 2 17) 102 sq.cm; 18) 50°;
360
;
3
19) 90°; 20) 10cm; 21) Infinitely many;
22) 4cm; 23) 90°; 24) 65°; 25) 2 a 2 − b2 ;
26) 6cm; 27) 2cm; 28) equal.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
10. MENSURATION
1. Area of circle with d as diameter is ____
sq.units
2. Number of diameters of a circle is ____
3. The ratio between the volume of a cone
and a cylinder is ____
4. Heap of stones is example of ____
5. Volume of a cylinder =88cm3, r = 2cm
then h = ____ cm
6. Area of Ring = ____
7. Book is an example of ____
8. The edge of a pencil gives an idea about
____
9. In a cylinder d = 40cm, h = 56cm then
CSA = ____ cm2
37.
38.
39.
40.
= ____ cm2
The base of a cylinder is ____
In a cylinder r = 10cm, h = 280cm then
volume = ____ cm3.
Volume of cube is 1728 cm then its edge is
____ cm
If d is the diameter of a sphere then its volume is ____ cubic units
Volume of cylinder is ____
Circumference of semi circle is ____ units
The area of the base of a cylinder is 616
sq.cm then its radius is ____
Volume of hemisphere is ____
T.S.A of a cube is 216cm2 then volume is
____ cm3
In a square the diagonal is ____ times of
its side.
Volume of sphere with radius r units is
____ cubic units
In the cone l2 = ____
Number of radii of a circle is ____
Number of edges of a cuboid is ____
Diagonal of a cuboid is ____
In a hemisphere r = 3.5cm, then L.S.A =
____ cm2
L.S.A of cone is ____
Rocket is a combination of ____ and ____
Volume of cone is ____ (or) ____
The surface area of sphere of radius 2.1
cm is ____ cm2
In a cone r = 7cm, h = 21cm Then l = ___
cm
The base area of a cylinder is 200 cm2 and
its height is 4cm then its volume is ____
cm3.
The diagonal of a square is 7√2cm. Then
its area is ____ cm2
The ratio of volume of a cone and cylinder
of equal diameter and height is ____
In a cylinder r = 1.75cm, h = 10cm, then
CSA = ____ cm2
T.S.A of cylinder is ____ sq.units.
ANSWERS
1) πd2/4; 2) infinite; 3) 1:3; 4) cone; 5) 7;
6) π(R2–r2); 7) cuboid; 8) cone; 9) 7040;
10) 8; 11) 38.808; 12) 264; 13) spherical;
14) 50.28; 15) circle; 16) 88000; 17) 12;
18) 1/6πd3; 19) πr2h ; 20) 36/7r. 21)
14cm; 22) 2/3 πr3; 23) 216; 24) √2; 25)
4/3 πr3; 26) r2 + h2; 27) infinite; 28) 12;
29) 12 + b 2 + h 2 ; 30)77; 31) πrl; 32) cone,
cylinder; 33) 1/3×volume of cylinder (or)
1/3×πr2h; 34) 55.44; 35) √490; 36) 800;
37) 49; 38) 1:3; 39) 110; 40) 2πr (h+r).
32. Sec2θ−1 = ____
33. If secθ + tanθ = p, then the value of secθ
− tanθ = _____
34. The value of sinA or cosA never exceeds
_____
35. sec (900− A) = _____
ANSWERS
4. The maximum value of sinθ is ____
5. If A is an acute angle of a ∆ABC, right
angled at B, then the value of sin A+cos A
is ____
6. The value of
2 tan 30 0
is _____
1 + tan 2 300
7. If sinθ = 1/2, then the value of (tanθ +
cotθ)2 is ____
8. If sinθ−cosθ = 0 then the value of sin4θ +
cos4θ is ____
9. If θ = 450 then the value of
1 − cos 2θ
is _____
sin 2 θ
10. If tanθ = cotθ, then the value of Secθ is
____
11. If A+B = 900, cotB = 3/4, then tan A is
equal to _____
12. If sin (x−200) = cos (3x−10)0. Then x is
____
13. The value of 1+tan50cot850 is equal to___
14. If any triangle ABC, the value of sin is
B+C
2 ____
15. If cosθ = a/b, then cosecθ is equal to ____
16. The value of cos200cos700− sin200sin700
is equal to ____
17. The value of tan50tan 250tan450tan650tan
850 is ____
18. If tanθ + cotθ = 5 then the value of
tan2θ + cot2θ is ____
19. If cosecθ = 2 and cotθ = √3p where θ is an
acute angle, then the value of P is ____
20.
1 + sin A
is equal to ____
1 − sin A
21. If cosecθ−cotθ = 1/4 then the value of
cosecθ + cotθ is ____
22. sin 450+ cos 450 = ____
23. 2tan2450+ cos2300−sin2 600 = ____
24. sin (900−A) = _____
25. If sinA=cosB then, the value of A +B =
26. If sec θ =
11. TRIGONOMETRY
m+n
then sinθ =
2 mn
27. In the figure, the value of secA is ____
C
1. In the following figure, the value of cot A
is ____
C
10. If each side of a cube is doubled then its
volume becomes ____ times
11. r=2.1cm then volume of the sphere is ____
cm3
12. The volume of right circular cone with
radius 6cm and height 7cm is ____ cm3
13. Laddu is in ____ shape
14. In a cylinder r = 1cm, h = 7cm, then TSA
A
5
B
13
2. If in ∆ABC, ∠B =
AB = 12 cm and
BC= 5cm then the value of cosc is ____
900,
b
then the value of
a
cos θ + sin θ
is _____
cos θ − sin θ
3. If cot θ =
12
12
5
VýS$Æý‡$ÐéÆý‡… l
íœ{ºÐ]lÇ l 12 l 2015
A
B
13
28. If sin2A=1/2, tan2450, where A is an acute
angle then the value of A is _____
29. The maximum value of 1/secθ, 00 <θ<900
is _____
30.
sin 2 θ
is equal to _____
1 − cos 2 θ
31. If cotθ=1 then
1 + sin θ
= _____
cos θ
1) 5/12; 2) 5/13; 3) b+a/b−a; 4) 1;
5) greater than one; 6) sin 600; 7) 16/3;
8) 1/2; 9) 1; 10) √2; 11) 3/4 ; 12) 300;
13) sec250; 14) cosA/2; 15) b2 − a 2 / b ;
16) 1; 17) 1; 18) 23; 19) 1; 20) secA +
tanA; 21) 4; 22) √2; 23) 2; 24) cos A;
25) 900; 26) m−n/m+n ; 27) 13/5;
28) 150; 29) 1; 30) 1; 31) √2 + 1;
32) tan2θ; 33)1/p; 34) 1; 35) cosecA.
12. APPLICATIONS OF
TRIGONOMETRY
1. If the angle of elevation of the top of a
tower at a distance of 500 m from the foot
is 300. Then the height of the tower is
____
2. A pole 6m high casts a shadow 2√3m long
on the ground, then sun’s elevation is ____
3. The height of the tower is 100m. When the
angle of elevation of sun is 300, then shadow of the tower is ____
4. If the height and length of the shadow of a
man are the same, then the angle of elevation of the sun is ____
5. The angle of elevation of the top of a
tower, whose height is 100m, at a point
whose distance from the base of the tower
is 100m is ____
6. The angle of elevation of the top of a tree
height 200√3 m at a point at distance of
200m from the base of the tree is ____
7. A lamp post 5√3 m high casts a shadow
5m long on the ground. The sun’s elevation at this moment is ____
8. The length of shadow of 10m high tree if
the angle of elevation of the sun is 300
____
9. If the angle if elevation of a bird sitting on
the top of a tree as seen from the point at a
distance of 20m from the base of the tree
is 600. Then the height of the tree is ____
10. The tops of two poles of height 20m and
14m are connected by a wire. If the wire
makes an angle of 300 with horizontal,
then the length of the wire is ____
11. The ratio of the length of a tree and its
shadow is 1:1/√3. The angle of the sun’s
elevation is ____ degrees.
12. If two towers of height h1 and h2 subtend
angles of 600 and 300 respectively at the
The
definition of probability was given by Pierre
Simon Laplace in 1795.
Probability theory had its origin in
the 16th century when an Italian
physician and mathematician J.Cardan
wrote the first book on the subject, The
Book on Games of Chance.
James Bernoulli, A.DeMoivre,
and Pierre Simon Laplace
are among those who
made significant contributions to this
field.
VýS$Æý‡$ÐéÆý‡… l
íœ{ºÐ]lÇ l 12 l 2015
13.
14.
15.
16.
17.
18.
19.
20.
mid-point of the line joining their feet,
then h1: h2 is ____
The line drawn the eye of an observer to
the object viewed is called ____
If the angle of elevation of the sun is 300,
then the ratio of the height of a tree with
its shadow is ____
From the figure θ = ____
The angle of elevation of the sun is 450.
Then the length of the shadow of a 12m
high tree is ____
When the object is below the horizontal
level, the angle formed by the line of sight
with the horizontal is called ____
When the object is above the horizontal
level, the angle formed by the line of sight
with the horizontal is called ____
The angle of depression of a boat is 60m
high bridge is 600. Then the horzontal distance of the boat from the bridge is ____
The height or length of an object can be
determined with help of ____
ANSWERS
11. P(E)=1/2 then P (not E) = ____
12. If two dice are rolled at a time then the
probability that the two faces show same
number is ____
13. If three coins are tossed simultaneously
then the probability of getting at least two
heads is ____
14. ____ is probability that a leap year has 53
mondays.
15. A number is selected from numbers 1
to 25. The probability that it is prime is
16. R = Red, Y = yellow, from the figure, the
probability to get yellow colour ball is
____
R
R
1) 500√3; 2) 600; 3) 100√3m; 4) 450;
5) 450; 6) 600; 7) 600; 8) 10√3m;
9) 20√3m; 10) 12m; 11) 600; 12) 3:1;
13) Line of sight; 14)1: √3; 15) 600;
16) 12m; 17) Angle of depression;
18) Angle of elevation; 19) 20√3m;
20) Trigonometric Ratios.
13. PROBABILITY
1. The probability of getting king or queen
card from the play cards (1 deck) ____
2. Among the numbers 1, 2, 3….15 the probability of choosing a number which is a
multiple of 4 is ____
3. Gita said that the probability of impossible
events is 1, Pravallika said that probability of sure events is 0 and Gowthami said
that the probability of any event lies in
between 0 & 1. In above with whom you
will agree ____
4. The probability of a sure event is ____
5. If a die is rolled then the probability of
getting an even number is ____
6. P(E) = 0.2 then P( E ) ____
7. No of playing cards in a deck of cards is
____
8. In a single throw of two dice the probability of getting distinct number is ____
9. A card is pulled from a desk of 52 cards,
the probability of obtaining a club is ____
10. P(x) + P(x) = _____
2m
R
17. A game of chance consists of spinning an
arrow which comes to rest at one of the
number 1, 2, 3, 4, 5, 6, 7, 8 and these are
equally likely outcomes the possibilities
that the arrow will point at a number
greater than 2 is ____
8
1
7
2
6
3
x
f
ANSWERS
below 10
3
1) 1/13; 2) 1/5; 3) Gowthami; 4) 1; 5) 1/2;
6) 0.8; 7) 52; 8) 5/6; 9) 1/4; 10) 1;
11) 1/2; 12) 1/6; 13) 1/2; 14) 2/7; 15)
9/25; 16) 2/5; 17) 3/4; 18) 6; 19) 0, 1; 20)
equally likely events; 21) 62 = 36; 22)
2/3; 23) J.Cardon; 24) impossible; 25)
1/2; 26) sure; 27) 1/13; 28) 0; 29) false;
30) 1/3; 31) 3/10; 32) 5/6; 33)1/13; 34)
11/84.
below 20
12
below 30
27
below 40
57
below 50
75
below 60
80
14. STATISTICS
1. The 'h' indicates in mode
 f − f0 
Mode = l + 
 × h is ____
 2 f1 − f0 − f1 
2. Mid values are used in calculating ____
3. Mean of 23, 24, 24, 22 and 20 is ____
4.
5
26. Class mark of the class 'x-y' is ____
27. L. C. F curve is drawn by using ____and
the corresponding cumulative frequency.
28. The modal class for the following distribution is ____
3m
Y
Y
∑ fi xi = 1390, ∑ f i = 35 then mean x
____
4
18. When a die is thrown once, the possible
number of outcomes is ____
19. The probability of an event lies between
____ and ____
20. If two events have same chances to happen then they are called ____
21. In a single throw of two dice, the probability of getting distance, numbers is ____
1
3
22. P(E) = then P(E) = ____
23. “The book on games of chance” was written by ____
24. Getting “7” when a single die is throw is
an example of ____
25. The probability of a baby born either boy
(or) girl is ____
26. When a die is thrown the event of getting
numbers less than or equal to 6 is an
example ____ event
27. If a card is drawn from a pack the probability that it is a king is ____
28. The probability of an event that cannot
happen is ____
29. The probability of an event is 1.5. Is it true
(or) false ____
30. If a two digit number is chosen at random
that the probability that the number chosen is a multiple of 3 is ____
31. A number is selected at random from the
numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9. Then the
probability that the selected number is
their average is ____
32. If a number X is chosen from the number
1, 2, 3 and a number Y is selected from the
numbers 1, 4, 9 then p(xy<9) is ____
33. A card is drawn dropped from a pack of 52
playing cards the probability that it is an
ace is ____
34. Suppose you drop a die at random on the
rectangular region shown in the figure
what is the probability that it will land
inside the circle with diameter m ____
7
Bit Bank
Mathematics
5. ____ is based on all observations?
6. If the mode of the following data is 7, then
the value of 'k' in 6, 3, 5, 6, 7, 5, 8, 7, 6,
2k+1, 9, 7, 13 is ____
7. The data arranged in descending order has
25 observations. ____ observation represents the median.
2 1 −7
8. A. M. of 6, −4, ,1 ,
is ____
3 4 6
9. Median of 17, 31, 12, 27, 15, 19 and 23 is
____
10. A. M. of 1, 2, 3, ......., 10 is ____
11. Range of 1, 2, 3, 4, ......., n is ____
12. For the given data with 50 observations
'the less than ogive' and 'the more than
'ogive' intersect at (15.5, 20). The Median
of the data is ____
13. The Mean of first 'n' odd natural numbers
n2
is
. then n = ____
81
14. A. M of 1, 2, 3, ........, n is ____
15. If the mean of 6, 7, x, 8, y, 14 is 9, then x
= ____
16. The A.M. of 30 students is 42. Among
them, two students got zero marks. Then
A.M. of the remaining students is ____
17. Marks
10
number of students 5
18.
19.
20.
21.
22.
23.
24.
25.
20
30
9
3
From the above data the value of median
is ____
Data having one Mode is called ____
A.M. of 1, 2, 3, ........, n is ____
Sum of all deviations taken from A.M. is
____
Mode of A, B, C, D, ......., Z is ____
Mean of first 5 Prime numbers is ____
The observation of an ungrouped data in
their ascending order are 12, 15, x, 19, 25.
If the Median of the data is 18, then x =
____
A.M. of a-2, a, a+2 is ____
Median of 1, 2, 4, 5 is ____
29. If the A. M of x, x+3, x+6, x+9 and x+12
is 10, then x = ____
30. If 35 is removed from the data 30, 34, 35,
36, 37, 38, 39, 40. then the Median
increases by ____
31. Range of first 10 Whole numbers is ____
32. Construction of Cumulative frequency
table is useful in determining the ____
33. Exactly middle value of data is called ___
34. In the formula of Mode
 f1 − f0 
=l+
 × h, f 0
represents
 2 f − f 0 − f2 
____
35. Median
36.
37.
38.
39.
n

 2 − cf 
M =l+
 × n ; 'l' represents ____
 f 


The term ''ogive'' is derived from ____
Range of the data 15, 26, 39, 41, 11, 18, 7,
9 is ____
The Mean of first 'n' natural number is
____
Median of first 'n' natural number is ____
ANSWERS
1) Length of the Class Interval;
2) Arithmetic Mean; 3) 22.6; 4) 39.71;
5) Mean; 6) 3; 7) 13th; 8) 0.55; 9) 19;
10) 5.5; 11) n-1; 12) 15.5; 13) 81;
n +1
14)
15) x + y = 19; 16) 45; 17) 9;
2
n +1
18) unimodal data; 19)
; 20) 0;
2
21) no mode; 22) 5.6; 23) 18; 24) a;
x+ y
25) 3; 26)
; 27) upper boundary;
2
28) 30 - 40; 29) 4; 30) 0.5; 31) 9;
32) Median; 33) Median; 34) frequency
of preceding modal class; 35) lower limit
of Median class; 36) ogee; 37) 34;
n +1
n +1
38)
; 39)
.
2
2
Hipparchus, a
Greek mathematician
established the relationships
between the sides and angles
of a triangle. The first trigonometric table was apparently compiled by Hipparchus, who
is now consequently
known as "the
father of
trigonometry'.
8
Competitive Guidance
Current Affairs
VýS$Æý‡$ÐéÆý‡… l
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