Maths last 10 year papers

3 -3 +3-3 +9 -15 +3=0 6 -15 +6=0 Di ide each e ih2 2 -5 +2=0 2 -4 - +2=0 2 ( -2)-( -2)=0 ( -2)(2 -1)=0 -2 = 0 2 -1 =0 =2 = 1 2 A 29). Whe diffe e dice a e h ge he T a c e = 6 6 = 36 (i) F e e Fa ab e c e a e (1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6) N . f fa ab e c e = 18 P (e e )= T = 18 = 1 36 2 (ii) F e e d c Fa ab e c e a e (1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6). N . f fa ab e c e = 27 Downloaded from www.padhle.in

P (e e )= T = 27 = 3 36 4 A 30). ​A ea f haded egi = A ea f ec a gle - A ea f emi-ci cle = (21 14) 77 = 294 77 = 217 cm2 Pe ime e f haded egi = 21 + 14 + 21 + 7 = 56 + 22 = 78 cm A A ea f haded egi =​ 78 cm A 31). Gi e : Ba e ​ 2 m a d Heigh ​3 5 m. Downloaded from www.padhle.in

R​ ec a g a f : =22 ,b=20 C​ i d ica a : =1 ,h=3.5 ​The e f a = ​2​h = 22/7 1 1 3.5 = 11 ​3 A​ ea f f = b = 22 20 = 440 ​2 Rai fa = A 25 c Rai fa = 11 ​3​/440 3​ = 0.025 Downloaded from www.padhle.in

CBSE Ma he a ic 2016 GI : ()A . ( )T 30 A, B, C D. ( )S A 6 1 .S B 6 .S 2 ,S C 10 3 8 D 4 . ( )T .H , 34 3 .Y . ( )U . Downloaded from www.padhle.in

Qe i Sec i -A (1 Ma k Each) 1. I ABC, D a d E a e i AC a d BC e ec i el ch ha DE AB. If AD = 2 , BE = 2 1, CD = + 1 a d CE = 1, he fi d he al e f . 2. I A, B a d C a e i e i a gle f ​ A​ BC, he e ha : Sin (B+C) = C osA 2 2 3. If = 3 i a d = 4 c , fi d he al e f ​ ​(1​ 6 ​2​ + 9 ​2)​ 4. If e i ical ela i hi be ee ea , edia a d de i e e ed a ea = k(3 edia de), he fi d he al e f k. Sec i -B (2 Ma k Each) Downloaded from www.padhle.in

5. E e 23150 a d c f i i e fac . I i i e ? 6. S a e he he he eal be 52.0521 i a i al . If i i a i al e e i i he f / , he e , a e c - i e, i ege a d 0. Wha ca a ab i e fac i a i f ? 7. Gi e he li ea e a i 2 6 = 0, i e a he li ea e a i i he e a iable , ch ha he ge e ical e e e a i f he ai f ed i : (i) c i cide li e (ii) i e ec i li e 8. I a i cele ​ A​ BC igh a gled a B, e ha AC2​ ​= 2AB​2 ​ . 9. P e he f ll i g ide i : [ 1 tanA ] 2​ ​= ​ a ​2​A ∠A i ac e 1 cotA 10. Gi e bel i a c la i e f e e c di ib i able. C e di g i , ake a di a f e e c di ib i able M e ha e al 0 cf M e ha e al 10 45 M e ha e al 20 38 M e ha e al 30 29 M e ha e al 40 17 M e ha e al 50 11 6 Downloaded from www.padhle.in

Sec i -C (3 Ma k Each) 11. Fi d LCM a d HCF f 3930 a d 1800 b i e fac i a i e h d. 12. U i g di i i alg i h , fi d he ie a d e ai de di idi g f( ) b g( ) he e f( ) = 6 3 + 13 2 + 2 a d g( ) = 2 + 1. 13. If h ee e e f a l ial 4​ ​ 3​ ​ 3 2​ ​ +3 a e 0, 3 a d - 3 , he fi d he f h e . 14. S l e he f ll i g ai f e a i b ed ci g he a ai f li ea e a i : 1 - 4 =2 x 1 + 3 =​ 9 x 15. ABC i a igh a gled ia gle i hich ∠B = 90 . D a d E a e ai AB a d BC e ec i el . P e ha AE​2​ + CD2​ ​ = AC​2​ + DE​2​ . 16. I he gi e fig e, RQ a d TP a e e e dic la PQ, al TS ⊥ PR e ha ST.RQ = PS.PQ. Downloaded from www.padhle.in

17. If ec A = 2 , fi d he al e 3 f: tanA + 1+ sinA cosA tanA 18. P e ha : ec2​ ​ c ​2(​ 90 ) = c 2​ ​(90 ) + c ​2​ . 19. F he h f Feb a , a cla eache f Cla IX ha he f ll i g ab e ee ec d f 45 de . Fi d he ea be f da , a de a ab e . N be f da f ab e 04 48 8 12 12 16 16 20 20 24 N be f de 18 3 6 2 0 1 20. Fi d he i i g f e e c ( ) f he f ll i g di ib i , if de i 34.5 : C.I. F e e c Downloaded from www.padhle.in

0 10 4 10 20 8 = f0​ l = 20 30 10 = f​1 30 40 40 50 = f2​ 8 Sec i -C (4 Ma k Each) 21. P e ha 5 i a i a i al be . He ce h ha 3 + 2 5 i al a i a i al be . 22. Ob ai all he e e he l ial 4​ ​ + 6 ​3​ + ​2​ 24 20, if f i e e a e + 2 a d 5. 23. D a g a h f f ll i g ai f li ea e a i : = 2( 1) 4 + di a e f he i he e he e li e ee = 4 Al i e he c -a i a d -a i . 24. A b a g e 30 k ea a d 44 k d ea i 10 h . The a e b a g e 40 k ea a d 55 k d ea i 13 h . O hi i f a i e de g e ed he eed f he b a i ill a e a 8.5 k /h a d eed f he ea a 3.8 k /h. D ag ee i h hei g e ? E lai ha d e lea f he i cide ? 25. I a e ila e al ABC, E i a i BC ch ha BE = 1/4 BC. P e ha 16 AE​2​ = 13 AB​2​ . Downloaded from www.padhle.in

26. I he fig e, if ∠ABD = ∠XYD = ∠CDB = 90 . AB = a, XY = c a d CD = b, he e ha c (a + b) = ab. 27. I he ABC ( ee fig e), ∠A = igh a gle, AB = x a d BC = x + 5 E al a e i C. c C. a C + c ​2C​ . i A 28. If cosB = a d cosB = , he h ha ( 2​ ​ + ​2​ ) c ​2​A = 2​ ​ . SinA cosA 29. P e ha : secA 1 = ( 1 sinA )​2 secA + 1 + cosA 30. F ll i g able h a k ( f 100) f de i a cla e: Ma k N . f de M e ha e al 0 80 M e ha e al 10 77 M e ha e al 20 72 M e ha e al 30 65 M e ha e al 40 55 M e ha e al 50 43 M e ha e al 60 28 M e ha e al 70 16 M e ha e al 80 10 M e ha e al 90 8 Downloaded from www.padhle.in

M e ha e al 100 0 D a a ' e ha e' gi e. F he c e, fi d he edia . Al , check he al e f he edia b ac al calc la i . Ae A 1): Gi e : - 1. 1. DE BC 2. AD = 3. DB = - 2 4. AE = + 2 a d EC = T fi d: Val e f I​ ABC, e ha e DE BC , b Thale' he e AD = AE DB EC A​ D EC = AE DB ( -1) = ( -2)( +2) Downloaded from www.padhle.in

2​ -​ = 2​ ​ - 4 =4 A e : The al e f i 4. A 2): Gi e : A,B a d C a e i e i a gle f ABC ​N , ∠A+ ∠B+ ∠C = 180 f i e i a gle f ia gle ABC S , ∠B+∠C= 180 - ∠A. N​ , M l i l b h ide b 1 2 1 (∠​ B+∠C) = 1 (1​ 80 - ∠A) = ( 90 - A/2) [ e ed he b acke ] 2 2 N​ , ake i e f (∠B +∠C ) 2 Sin (∠B+∠C) Sin (90 A) ​[ Si ce, (∠B +∠C ) (90 A) 2 =2 2= 2] N , e k Si (​ 90- ) = C S, Sin (90 A) = Cos A 2 2 He ce, P ed. Downloaded from www.padhle.in

A 3) Gi e : =3 i a = 4c a T fi d, N , b i e 3 i a a he lace f a d 4c a a he lace f N , ek ha Si 2​ ​ + C ​2​ = 1 O a l i g hi i he l i ( i ce ​ i ​2​a + C 2​ ​a bec e 1) Downloaded from www.padhle.in

A 4). de) Gi e : ​ ea = k(3 edia We , e E ca f a M d =3M da -2M a S, ​2 Mea = 3 Med a - M de ​Mea = 3M edian M ode 2 We a e gi e , ea = k(3 edia de) S , b i i g he al e k(3 edia de) = 3M edian M ode ​k = 2 ​He ce, he al e f k i A 5). F da e al he e f a i h e ic a e ha he e a i f ie fac i a i f a be i i e. S , he e a i f i e fac i a i f 23150: 23150 = 2 5 5 463 Downloaded from www.padhle.in

A d 6). Ye , 5​ 2.0521 i a i al a i ca be e e ed i he / f 52.0521 = 520521 10000 A 7). ​The li e a1 + ​b1 + ​c1 a d ​a2 + b​ 2 + ​c2 = ​0​ a e c i cide if a1 = b1 = c1 a2 b2 c2 S , a he li e ca be ​2 -4 -12=0 C​ di i f li e be i e ec i g : a1 ​​ b1 a2 b2 S , a he li e ca be ​ -4 -6=0 A 8). ​Gi e : I ia gle ABC a gle B= 90 T P e: AC​2​ = 2AB​2 ​We k , B P hag a he e AB​2​ + BC2​ ​ = AC​2 A d, b i cele ia gle e, Downloaded from www.padhle.in

AB = BC S , AB​2​ + AB2​ =​ AC2​ ​ ( Si ce, AB =BC) The ef e, 2AB2​ ​ = AC​2 He ce, ed 2AB2​ ​ = AC​2 A 9).​ T e, [​ 1 tanA ] ​2 =​ ​ a 2​ ​A 1 cotA [ 1 tanA ] 2​ ​ ​(We k , C A = 1/Ta A) 1 cotA S , [​ 1 tanA ] ​2 1 1/tanA [ ] ​1 tanA 2 tanA 1 tanA [ tanA (1 tanA) ] 2​ tanA 1 F de i a , ake (-) [ tanA (1 tanA) ] ​2 (1 tanA) Red ce he i le f [ -​ a A ]​ 2​ =aA He ce, P ed! Downloaded from www.padhle.in

A 10). We f d e d a f e e c (f ) 45 38=7 38 29=9 TABLE 29 17=12 17 11=6 11 6=5 6=6 M e ha e al cf fi 0 45 7 38 9 M e ha e al 29 12 10 17 6 11 5 M e ha e al 6 6 20 M e ha e al 30 M e ha e al 40 M e ha e al Downloaded from www.padhle.in

50 A 11). ​HCf(3930,1800)= 30 LCM(3930,1800)=235800 S e -b - e e la a i : We ha e , 2 3930 ________ 3 1965 ________ 5 655 ________ * 131 2 1800 __________ 2 900 __________ 2 450 __________ 5 225 __________ 5 45 Downloaded from www.padhle.in

__________ 39 __________ 3 N, 3930= 2 3 5 131 ad 1800= 2 2 2 3 3 5 5 =2 3 5 HCF(3930,1800)=2 3 5 = 30 P d c f he alle e f each c i e fac f he be LCM(3930,1800)= 2 3 5 131 = 235800 A 12). ​Di ide d = Di i = Di ide d = (Di i *Q ie ) + Re ai de 6 3​ +​ 13 2​ ​ + - 2 = (2 + 1 * 3 ​2​) + (10 ​2​ + - 2) 6 3​ ​+ 13 2​ ​ + - 2 = (2 + 1 * 3 ​2​ + 5 ) + (-4 - 2) 6 ​3 ​+ 13 2​ ​ + - 2 = (2 + 1 * 3 ​2​ + 5 -2) + 0 Downloaded from www.padhle.in

He ce, he e ai de c e be 0 a d ie i 3 ​2​ + 5 -2 A 13). ​ Gi e : P l ial: ​4​ 3​ ​ 3 ​2​ +3 R : 0, 3 a d - 3 T fi d: 4 h If ​0, 3 a d - 3 a e f he l ial, ​ ,( - 3) a d ( + 3) d be e fac . f ee a , c ea , ( -a) d be e fac ​Le a e f S, ​ ( - 3)( + 3)( -a) = 4​ ​ 3​ ​ 3 2​ ​ +3 ( -3)( -a) = ​4​ ​3​ 3 ​2​ +3 [​ (a+b)(a-b) = a2​ ​-b​2 ​] 4-a 3-3 2+3a = ​4​ ​3​ 3 ​2​ +3 O c a i g b h he ide , e ge a=1 He ce, he f h i a = 1. A 14). Downloaded from www.padhle.in

A 15). ​A ABE ,, ​ (AE)2​ ​ = (AB)​2 +​ (BE)2​ ​ ---------------> E ​ ​(1) S , DBC ,, ​ (CD)2​ ​ =(BD)​2​ + (BC)2​ ​ -----------------> E ​ (​ 2) O (1) (2), ​ (AE)​2​ + (CD)​2​ = (AB)2​ +​ (BE)2​ ​ + (BD)2​ ​ + (BC)2​ E ​ (​ 3) ​ (​ AE)2​ ​ + (CD)​2​ = (AB​2 +​ BC​2)​ + (BE​2​ + BD​2)​ -----------------> ​I ABC, AC2​ ​ =AB2​ ​ +BC​2 I​ DBE DE​2​ = BE​2​ + BD2​ ​ -----------------> ​E ​ (​ 4) Downloaded from www.padhle.in

O ​E ​ (​ 4) E ​ ​(3) P (AE)2​ ​ + (CD)2​ ​ = (AC2​ ​) + (DE​2)​ -------- H A 16). Gi e : RQ a d TP a e e e dic la PQ, al TS ⊥ PR T P e: ​ST.RQ = PS.PQ. S l​ ​:B a gle e R + P + Q = 180 1 + 2 + 3 = 180 Gi e ha , 3 = 90 . S , 1 + 2 + 90 = 180 1 + 2 = 90 .....(e 1) TS i a e e dic la d a li e PR ch ha TSP = 5 = 90 Al , TP i e e dic la li e PQ ch ha TPQ = 90 4 + 2 = 90 .....(e 2) O c a i g (e 1) a d (e 2) e ge , Downloaded from www.padhle.in

1+ 2= 4+ 2 1= 4 I RQP a d TSP 3 = 5 (each 90 ) 1 = 4 (f ab e) B AA RQP TSP The ef e, ST/PQ = PS/RQ C - l i l he ST.RQ = PS.PQ He ce, ed A 17). Gi e : SecA = 2 3 T fi d:​ tanA + 1+ sinA cosA tanA B​ ig e ide i : H=2a dB= 3 We k , H2​ =​ P​2​ + B2​ H​2 ​= P​2​ + B2​ 2​2 =​ P​2 ​+ ( 3 )2​ Downloaded from www.padhle.in

O l i g, P=1 We al ead ha e, H=2, B= 3 We al k , Si A= P H S , Si A= 1 2 C A= B H C A= 3 2 Ta A= P B Ta A = 1 3 O b i i g he e al e i tanA + 1+ sinA cosA tanA We ge , 4+9 3 6 S, tanA + 1+ sinA = 4+9 3 cosA tanA 6 [I e a , i e d he l i al ] A 18). T e: ec​2​ c 2​ ​(90 ) = c 2​ ​(90 ) + c 2​ ​ . Downloaded from www.padhle.in

​LHS = ​ ec2​ ​ c 2​ (​ 90 ) = ec​2​ - a 2​ ​ = 1/C ​2​ - i 2​ ​ /c ​2​ = (1 - i 2​ ​ )/ c ​2​ = C 2​ ​ /c ​2​ = 1 RHS = c 2​ (​ 90- ) + c ​2​ Si 2​ ​ + c 2​ ​ = 1 LHS = RHS, He ce P ed A 19). Downloaded from www.padhle.in

A 20). Gi e : M de ---> 34.5 , l = 20 T fi d: S , acc di g he f la f de M de = l + ​ ( f1 f0 )h​ 2f 1 f 0 f 2 34.5 = 20 + (​ 10 8 8 x )1​ 0 20 34.5 = 20 + ​( 2 x )​10 12 34.5 - 20 = ​( 2 x )​10 12 14.5 = (​ 20 x ) 12 14.5 (12- ) = 20 20 = 12 - 14.5 O i lif i g ---> 40 = 12 - 29 = 12 - 40 29 = 348 40 29 = 308 29 = 10.62 Downloaded from www.padhle.in

A 21). 5 ha c fac Le a e ha 5 i a i al a d / ha c fac c adic i 5= / S a i g b h ide ( 5 ) =( / ) 5= / 5= 5 i a fac f al 5 i a fac f le = 5 5 =(5 ) 5 =25 =5 S 5 i a fac f al 5 i a fac f He ce e aid ha 5 i a i al b acc di g 5 i i a i al. 3+ 5 =k 5 =k-3 LHS i i a i al i ce 5 i i a i al a ed He ce, RHS i i a i al . Downloaded from www.padhle.in

A 22). P​ l ial ( ) = ​4​ + 6 3​ ​ + 2​ ​ 24 20 The gi e e e a e: ​2 a d (-5) ​Acc di g Fac The e ( -2) a d ( +5) a e fac a e ( ) ​Al , ( -2) ( +5) = ​ 2​ ​+ 5 - 2 - 10 2​ +​ 3 - 10 +3 -10 i al a fac f ( ) N​ , 20​ ​ b +3 -10 Di i g ( ) ​ ​4​ + 6 ​3​ + 2​ ​ 24 We ge Q( ) = + 3 +2 ( )=0 ( ) = ( 2​ ​ + 3 - 10)( ​2​ + 3 + 2) = ( -2)( +5)( ​2​ + + 2 + 2) = ( -2)( +5)( +1)( +2) S , he e e f ( ) a e: Downloaded from www.padhle.in

-2 = 0 , = 2 + 5 = 0 , = -5 + 1 = 0 , = -1 + 2 = 0 , = -2 A 23). *GRAPH* A 24). ​=x​ ​ \\ T ​= ​ ​ \\ L​ S (​ x​ +​ ​ ​)​km/​ h​ r S (​ x​ ​ ​ )​ ​km/​ ​hr i e= distance speed Downloaded from www.padhle.in

T​ i e ake c e 30 k ea = 30 x ​Ti e ake c e 44 k d ea = 44 x+ S , acc di g he ei : 30 + 44 ​= 10 x x+ T​ i e ake c e 40 k ea = 40 ​Ti e ake c e 55 k d x ea = 55 x+ S , acc di g he e i : 40 + 55 = 13 x x+ Le 1 = a d​ 1 = x x+ ⇒ 30​u​+44​v=​ 10 ------> e​ qn​ ​1 ⇒ 40u​ +​ 55​v​=13 ------> ​eq​n2​ ⇒ (150u​ ​+220​v=​ 50) (160​u​+220v​ =​ 52) [ M l iplied b 5 and b ac ed bo h he e n​ ]​ S , =⅕a d = N ,a ek 1 = a d​ 1 = x x+ Downloaded from www.padhle.in

S , 1 = =⅕, - =5 x A d, ​ 1 = , + =11 x+ O b ac i g he e 2 e a i =8a d =3 H, =​ 8​ \\ T ​=3​ \\ (Sh he l i al i e a ) A 25). J i A id i f BC a D. S ,ED = BE = ( 1 )BC -----> e ​ ​1 4 I ia gle AED, AE = AD + ED -----> e ​ 2​ I ia gle ABD, AD = AB - BD -----> e ​ ​3 P i g al e f AD f (3) i (2), AE = AB - BD + ED = AB -( BC ) +( BC ) 2 4 a BD = (1/2)BC a d ED = (1/4)BC f (1)....,,, Downloaded from www.padhle.in

S e ge ....16AE = 13AB A 26). Gi e : ∠ABD = ∠XYD = ∠CDB = 90 . AB = a, XY = c a d CD = b, A ABD = XYD = CDB = 90 ⇒ AB XY CD I ABD AS AB XY S , DY = c BD a ⇒ DY = c (BD) .-----> e ​ (​ 1) a I BDC A CD XY S, Downloaded from www.padhle.in

BY = c BD b BY = c (BD) ......(2) b Addi g (1) a d (2), e ge DY + BY = c (BD) + c (BD) a b BD = c( 1 + 1 )BD a b 1 = 1 + 1 c a b 1 =​ a+b c ab c(a+b) = ab He ce ed. A 27). I ABC, i g he hag a he e , Downloaded from www.padhle.in

A =1 Downloaded from www.padhle.in

A 28). c ​2​B(Si 2​ A​ + c 2​ A​ )/ i 2​ ​A c 2​ ​B/ Si 2​ ​A = 2​ ​ = RHS A 29). ec A - 1 \\ ec A + 1 M l i l i g a d di idi g b SecA - 1 ( ec A - 1) / ( ec A - 1) Downloaded from www.padhle.in

1 ( ec A + 1 - 2 ecA) [ ec A - 1 = a A] Di ide he e a i b Ta 2​ ​A c A ( a A + 2 - 2 ecA) [ 1 =c A] tanA 1 + 2c A - 2 1 C osA C osA [ l i l i g] cosA SinA SinA [ C osA =c A 1 = ecA] SinA C osA (1 + c A) + c A -2c Ac ecA c ec A + c A - 2c ec Ac A = c ec A (c A - c ecA) He ce P ed! ​ Downloaded from www.padhle.in

CBSE Maths 2015 1. All questions are compulsor . A, B, C and 2. The question paper consists of 31 questions divided into four sections D. 3. Section A contains 4 questions of 1 mark each. 4. Section B contains 6 questions of 2 marks each. 5. Section C contains 10 questions of 3 marks each 6. Section D contains 11 questions of 4 marks each. Questions - EC I N A 1. If the quadratic equation px2 2 5px + 15 = 0 has two equal roots then find the value of p. 2. In the following figure, a tower AB is 20 m high and BC, its shadow on the ground, is 20 3 m long. Find the Sun s altitude. 3. Two different dice are tossed together. Find the probabilit that the product of the two numbers on the top of the dice is 6. 4. In the following figure, PQ is a chord of a circle with center O and PT is a tangent. If ∠QPT = 60 , find ∠PRQ. Downloaded from www.padhle.in

EC I N B 5. In the following figure, two tangents RQ and RP are drawn from an external point R to the circle with centerO, If ∠PRQ = 120 , then prove that OR = PR + RQ. 6. In the following figure, a ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectivel of lengths 6 cm and9 cm. If the area of ABC is 54 cm2 , then find the lengths of sides AB and AC. 7. Solve the following quadratic equation for x: 4x2 + 4bx (a2 b2 ) = 0. Downloaded from www.padhle.in

8. In an AP, if S5 + S7 = 167 and S10 = 235, then find the A. P., where Sn denotes the sum of its first n terms. 9. The points A (4, 7), B (P, 3) and C (7, 3) are the vertices of a right triangle, right-angled at B, Find the values of P. 10. Find the relation between x and if the points A(x, ), B ( 5, 7) and C( 4, 5) are collinear. EC I N C 11. The 14 th term of an A. P. is twice its 8 th term. If its 6 th term is 8, then find the sum of its first 20 terms. 12. Solve for x: 3x2 2 2x 2 3 = 0. 13. The angle of elevation of an aeroplane from point A on the ground is 60 . After flight of 15 seconds, the angle of elevation changes to 30 . If the aeroplane is fl ing at a constant height of 1500 3m, find the speed of the plane in km/hr. 14. If the coordinates of points A and B are ( 2, 2) and (2, 4) respectivel , find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB. 15. The probabilit of selecting a red ball at random from a jar that contains onl red, blue and orange balls is 1/4 . The probabilit of selecting a blue ball at random from the same jar 1/3 . If the jar contains 10 orange balls, find the total number of balls in the jar. 16. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60 . Also find the area of the corresponding major segment. [ Use = 22/7 ]. Downloaded from www.padhle.in

17. Due to sudden floods, some welfare associations jointl requested the government to get 100 tents fixed immediatel and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a c linder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but height 2.8 m, and the canvas to be used costs Rs. 100 per sq. m, find the amount, the associations will have to pa . What values are shown b these associations? [ Use = 22/7 ]. 18. A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 c lindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer. 19. A cubical block of side 10 cm is surmounted b a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs. 5 per sq. cm. [ Use = 22/7 ]. 20. 504 Cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere, Find the diameter of the sphere and hence find its surface area. [ Use = 22/7 ]. EC I N D 21. The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field. 22. Find the 60 th term of the AP 8, 10, 12, ., if it has a total of 60 terms and hence find the sum of its last 10 terms. 23. A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journe , what is its first speed? Downloaded from www.padhle.in

24. Prove that the lengths of the tangents drawn from an external point to a circle are equal. 25. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc. 26. Construct a ABC in which AB = 6 cm,∠A = 30 and ∠B = 60 , Construct another AB C similar to ABC with base AB = 8 cm. 27. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30 . The angle of depression of the reflection of the cloud in the lake, at A is 60 . Find the distance of the cloud from A. 28. A card is drawn at random from a well-shuffled deck of pla ing cards. Find the probabilit that the card drawn is i. a card of spade or an ace. j. a black king. k. neither a jack nor a king l. either a king or a queen. 29. Find the values of k so that the area of the triangle with vertices (1, 1), ( 4, 2k) and ( k, 5) is 24 sq. units. 30. In the following figure, PQRS is square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersections of its diagonals. Find the total area of the two flower beds (shaded parts). Downloaded from www.padhle.in

31. From each end of a solid metal c linder, metal was scooped out in hemispherical form of the same diameter. The height of the c linder is 10 cm and its base is of radius 4.2 cm. The rest of the c linder is melted and converted into a c lindrical wire of 1.4 cm thickness. Find the length of the wire. [ Use = 22/7 ] Downloaded from www.padhle.in

CBSE Maths 2015 Sol ions : 1. We ha e one form la if a q adratic eq ation of the form ������ 2 + ������ + ������ = 0 ha e eq al roots then ������2 4������������ = 0. In the gi en eq ation ������ = , ������ = 2 5 and ������ = 15, ( 2 5p)2 4 p 15 = 0 20 2 60 = 0 = 0 or = 30 = 0 is not possible so p = 30 2. From trigonometric e pressions clearl ������ =������B/������������ ������ = 20/20 3 ������ = 1/ 3 = 30o 3. When t o dice are tossed together there ill be 36 possibilities. Possibilities for prod ct of the n mbers is (1,6), (2,3), (3,2) and (6,1). Req ired probabilit is= 4/36 . 4. ∠������������������ = 90o From the fig re ∠������������������ = ∠OPT ∠QPT = 90o 60o = 300 From the fig re ∠POQ = 2∠QPT = 2 60o = 120o Refle angle of ∠POQ = 360o 120o = 240o ∠PRQ = 1/2 refle angle ∠POQ = 1/2 240o = 120o 5. ∠������������������ = 900 Downloaded from www.padhle.in

Gi en that ∠������������������ = 120 From the propert of the circle one can get ∠������������������ = ∠������������������ = 120/2 = 600 We kno that lengths of tangents from an e ternal points are eq al. Th s, from diagram ������������ = ������������. After ������������ and ������������. Both are the radii from the center ������, ������������ is perpendic lar to ������������ and ������������ is perpendic lar to ������������. Th s, ������������������ and ������������������ are right angled congr ent triangles. Hence, ∠������������������ = 900 ∠������������������ = 900 600 = 300 . ∠������������������ = 900 ∠������������������ = 900 600 = 30o ������ ∠������������������ = ������ 300 = From the diagram ������ 300 = ������������/������������ implies ������������/������������ = 1/2 ������������ = 2������������ ������������ = ������������ + ������������ ������������ = ������������ + ������������. Downloaded from www.padhle.in

6. Let the gi en circle to ch the sides ������������ and ������������ of the triangle at points ������ and ������ respecti el and let the length of line segment AR be . No , it can be obser ed that: ������������ = ������������ = 6 ������ (tangents from point B) ������������ = ������������ = 9 ������ (tangents from point C) ������������ = ������������ = (tangents from point A) ������������ = ������������ + ������������ = + 6 ������������ = ������������ + ������������ = 6 + 9 = 15 ������������ = ������������ + ������������ = 9 + 2 = ������������ + ������������ + ������������ = + 6 + 15 + 9 + = 30 + 2 = 15 + ������ = 15 + 15 = ������ = 15 + ( + 9) = 6 ������ = 15 + (6 + ) = 9 Area of the triangle ������������������ = [ ( ������)( ������)( ������)] 54 = [(15 + ) (6)(9)] 18 = [(15 + 2)(6) 2 + 15 54 = 0 ( + 18)( 3) = 0 Distance can t be negati e then = 3 ������������ = 3 + 9 = 12 ������������ = ������������ + ������������ = 6 + = 6 + 3 = 9 7. Downloaded from www.padhle.in

8. S10=10/2 (2a+9d)=235 5(2a+9d)=235 10a+45d=235 Di iding hole b 5 2a+9d=47 M ltipl ing b 6 12a+54d=282 1 S5+S7=5/2 [2a+(5-1)d]+ 7/2 [2a+(7-1)d] 5/2 (2a+4d)+ 7/2 (2a+6d) 5 (a+2d)+ 7 (a+3d)=167 5a+10d+7a+21d=167 Downloaded from www.padhle.in

12a+31d=167 2 S btracting 2 from 1 , e get, 23d=115 D=115/23 D=5 2a +9d = 47 2a+ 9*5=47 2a=49-47 2a=2 A=1 A.P., is 1,6,11,16 Downloaded from www.padhle.in

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10. 11. ' '' , Downloaded from www.padhle.in ------- (1) , (1) +13 = 2( +7 ) +13 =2 +14 -2 =14 -13 - =1 = - ------------ (2)

. , +5 = -8 ------- (3) (2) = - (3) - + 5 = -8 4 = -8 = -8/4 = -2 , = -(-2) . =2 = -2 20 . =20 , , S 1 20 -340 12. Downloaded from www.padhle.in