KISHORE VAIGYANIK PROTSAHAN YOJANA Date : Duration : 3 Hours Max. Marks : 160 STREAM - SB/SX

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1 KISHORE VAIGYANIK PROTSAHAN YOJANA - 04 Date : Duratio : Hours Max. Marks : 60 GENERAL INSTRUCTIONS STREAM - SB/SX The Test Booklet cosists of 0 questios. There are Two parts i the questio paper. The distributio of marks subjectwise i each part is as uder for each correct respose. MARKING SCHEME : PART-I : MATHEMATICS Questio No. to 0 cosist of ONE () mark for each correct respose. PHYSICS Questio No. to 40 cosist of ONE () mark for each correct respose. CHEMISTRY Questio No. 4 to 60 cosist of ONE () mark for each correct respose. BIOLOGY Questio No. 6 to 80 cosist of ONE () mark for each correct respose. PART-II : MATHEMATICS Questio No. 8 to 90 cosist of TWO () marks for each correct respose. PHYSICS Questio No. 9 to 00 cosist of TWO () marks for each correct respose. CHEMISTRY Questio No. 0 to 0 cosist of TWO () marks for each correct respose. BIOLOGY Questio No. to 0 cosist of TWO () marks for each correct respose.

2 PART-I Oe Mark Questios MATHEMATICS. Sol- Let a,a,a _ be the legth of side of square iscribed i circle c 0,c,c _ ad r, r, r, _ be radius of circle c, c, _ the, a πr r π a a πr π π r π i 0 ( ) Area Ci π.i 4 8 π π π+ + + π π π π (D). Sol.(A) [ x + y] [ x] + [ y] for 5 x, y false (B) [ xy] [ x][ y] 5 for x, y 5 6 false x (C)[ ] for x 7/ 7/ [7/] [ ] [7/] ( ) / 8 8 false x [ x] (D) y [ y] (A) true x R PAGE -

3 . Sol- Whe is eve A A C / C / the {,4,...,0} whe is odd A C A + / C / is true of or 9 As-(C) 4. As-(B) (0,), ( +,0) 5. Sol- As - (B) 6. Sol- AS SS SB e / a As - (D) PAGE -

4 7. Sol- ABBC Cosθ ad θ Si 6 α π θ θ cosα si 6 y cosα a 6 8. a y As- (C) 4 4 cos x + si x + cos x si x si x cos x 4 4 cos x si x cos (cos x si x) si x si x x cos x cosx 0 si x cos x cosx 0 x t, t [0,4 π ] si x cos x si x( si x) t( t) t t t t + D<0 0 O PAGE - 4

5 x + 5, x 9. Sol. f( x) x, x f(x) is discotiuous at x f(x) x + 5 x x + 5 x 4 x 9. As(B) 0. Sol- f(x) [x]siπx As - (D). Sol. six ta x si x six( si x) si x (si x + si ) 0 six 0 si x x 0, π si, π si As(B) PAGE - 5

6 . Sol- I f(x )dx Let x t 0 dx dt t dt I f(t) t 0 Q t dt dt f(t) f(t) t 5 I 0 0 As-(D). Sol.f'(x) +f(x) f(0) 0 f( x) + f( x ) l ( + f(x)) x the f(x + y) f(x) + f(y) f(x) f(y) As(C) 4. Sol. cos( π[ x]{ xy}) cos( π [ x ] dx ) dx As(C) 5. Sol- P(B) As -(B) yi 6. Sol. i µ ˆ µ σ ˆ Σy µ ˆ σˆ ( x + x) σˆ > σ. As() 7. Sol- Let side legth a GAGBa cosθ PAGE - 6

7 A a a G a D B E C As -(C) 8. As -(A) 9. As- (D) 0. Sol. 5 C C + 4 C [8 + 6] As - (C) PHYSICS. L, m J mv J.L V Cm (C) J/M J.L ω J ML ke M(L) ML ω ω J J + J /m m m PAGE - 7

8 . mgh mv + I ω mgh mv +. MR ω gh mv + 4 mv 4 v V 4gh V 4gh V gh Vp 4 VR (C) /. V (r) kr U (r) mkr ω k r F - du mk dr ω (A) k r T π r k 4. (D) 5. A V A V P + dv Cost. d desity P V P V (B) 6. (B) 7. (D) 8. PV C PV.V K RT.V K VT K V T V T V >V T <T PV PV V P V P K P. T C P k T P T T T PAGE - 8

9 P T T P (B) 9. v o v+ vs v v+ vs ' v v " v + v s s v+ v + " v vs (C) ' s (A). 0 cm + v u f f fm fl f 0 5 f -5 + v v v -6cm (B). (D) PAGE - 9

10 . Vx (A) v y ay.t v y ee. l m u v x u eel ta θ mu ta taθ θ ta θ 4 ta 4 θ 0. +q 4. +q -q -a/ a/ KQ W q R KQ kq W + ( q) R a W (C) kq a 5. Q C E Ceq C.KC CK CK C+ KC C(+ k) + K Q CK E + k Q Q (B) CK C E + k CK C E + k ck c(k ) (+ k) ck ck c ck c (+ k) (+ k) PAGE - 0

11 6. V ed E 00 0um 7. V 00 5v 0 (A) dn λ dt dn λdt dt (D) 4 N 8. 4πR (C) N λ λ 5 λ λ 64 (B) Eergy required (A) CHEMISTRY 4. K SP Ag Br (Ag + ) (Br - ) (5 0-0 ) (0 - ) Cocetratio of Br - is 0 - M eq AgNO KpAgbr + [Ag ] (D) 5 0 (0 ) 5 0 m 4. Over bromiatio take place i activated Ailive (A) PAGE -

12 4. +6 is maximum oxidatio state of Cr (D) 44. (C) 45. Al O is amphoteic dxide (C) 46. L k L A (A) Ea R T 47. Ni(Co) 4 is tetrohedral with d 0 cofiguratio (C) 48. Ozelysis ad itromolecular aldol (B) 49. (B) 50. Eergy of t g < eg orbitats i octohedral complexes (A) 5. Whe Q C > K C Reactio move i backword directio (A) 5. SN- Reactio, morstable costocatio is formed (C) 5. KOH KCl + NaOH - KaCl (D) 54. Wolf kisher Reductio (B) 55. Compoud is AsCl (C) 56. Valecy factor of KMO 4 5 Se MO 4 + 8H + M + + 4H O (D) 57. (C) 58. S (A) H 6000J J/K.mol T k 59. Ullmaj reactio (A) 60. (C) PAGE -

13 BIOLOGY 6. (C) 6. (A) 6. (B) 64. (D) 65. (C) 66. (B) 67. (D) 68. (B) 69. (A) 70. (D) 7. (C) 7. (A) 7. (D) 74. (C) 75. (D) 76 (A) 77. (A) 78. (B) 79. (A) 80. (B) PART-II Two Mark Questios 8. As-(A) MATHEMATICS 8. w k k ( ) ( w ) R 0 + w e e e whe is multiplyig of, the Se, /e whe is ot multiple of three,the s / / e e As- (C) 8. Sol- y ax + bx + c a > 0, b < 0, c < 0 Also y() a + b + c < 0 As-(B) 84. r r Sol- Si θ AP AP AP AP+ r + r r r + r+ r r( ) r( + ) r + r As- (D) PAGE -

14 85. Sol- Let f(x) x - 5x f (x) 9x - 5 f (x) 0 ± 5 f(-5/) 50/9 ; 7.7 f(5/) -50/9 ; -7.7 ca take 55 values As-(C) 86. As-( ) 87. Sol- I π/ x cosxdx 0 π I +(-)I - I Also ( ) As- (A) 88. Sol- I ( ) I +!I +!!! [x][ x]dx dx +... {50 for 8 {66 for 9 As - (B) 89. As- (B), Check for,,,......() ( π ) π π! e 90. Sol- No correct Optio (,7), (,7),(,7),(4,7),(4,7),(6,7),(7,7) _ (6,7),(8,7) 7 poits Also (7,), (7,), _ (7,6), (7,8) 7 poits So there are more the 4 poits. As-() PAGE - 4

15 PHYSICS 9. Iitial w Fial VW'R A From cos. of aguler mometum about A v Rw 7 W w 7 (C) 9. (A) Tmi 9. T max - mg mv R from eergy cos. ki + ui kf + uf...(i) Tmax V mg mg mg cos O + mg (R-R cos θ ) mv +0 V gr (-cos θ ) Put i eq. (i) T max mg - mg cos θ T T max mi 4 θ 60 (B) 94. Heat cap. is defie as C Cv + R γ C R+ R + R (D) 95. (A) 96. (C) 97. At steady state capacitor will belave as ope circuit V 4V B 6V So charge store i µ F 4 4 µ C i µ F 4 8 µ C PAGE - 5

16 98. F P C.5 0 mg 8 0 m 0-6 kg (D) 99. E φ + ev E φ + e (.9).E φ + e(.9).e.e E ev put φ.4ev (B) 00. (ML o T - θ -4 ) (ML T - ) γ (ML T - θ - ) β (LT - ) γ Solvig we get (C) 0. (A) CHEMISTRY 0. d PM M drt RT P M acetic acid exiot as demie (B) 0. E H - (PV) H - grt (D) 04. (C) 05. N (g) + H (g) NH 4 (g) (BDE) Reacat (BDE) Products (B) 06. V k+ + V Cl- + 8 KCl form FCC Lattice (V K+ + V Cl- ) a edge legth of uit cell V a (C) 07. K Cr O 7 +6FeSO 4 + 7H SO 4 Cr (SO ) + Fe (SO ) + K SO + 7H O (B) 08. E o SRP cathode - SRP a mode Cell (-0.74) 0.V G - F E o ( 6 Cell ele- ) (C) 09. (A) 0. XeF 6 + H O XeO + 6HF XeO is SP hybrid ad pyramidal (C) PAGE - 6

17 BIOLOGY. (B). (D). (D) 4. (A) 5 (C) 6. (D) 7. (C) 8. (B) 9. (A) 0. (A) PAGE - 7

Narayana IIT Academy

Narayana IIT Academy INDIA XI STD IIT_LJ Jee-Advaced Date: 08-0-08 Time: HS 0_P MODEL Max.Marks:80 KEY SHEET PHYSICS b a b 4 d 5 b 6 c 7 c 8 c 9 d 0 b a,b,c a,c b,c 4 a,c 5 b,c,d 6 5 7 8 4 9 0 6 CHEMISTY c c b 4 a 5 c 6 b