NURTURE COURSE TARGET : JEE (MAIN) Test Type : ALL INDIA OPEN TEST TEST DATE : ANSWER KEY HINT SHEET. 1. Ans.

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1 Test Type : LL INDI OPEN TEST Paper Code : 0000CT CLSSROOM CONTCT PROGRMME (cadeic Sessio : 05-06) NURTURE COURSE TRGET : JEE (MIN) 07 TEST DTE : NSWER KEY HINT SHEET Corporate Office : CREER INSTITUTE, SNKLP, CP-6, Idra Vihar, Kota (Rajastha) ifo@alle.ac.i Test Patter : JEE-Mai Que s Que s. 4 4 Que s Que s Que s. 4. s. (4) V T f V T f T T T T T (.) T Mg 4.84 Mg S.G M SG g S.G S.G.84 S.G.6. s. (4) rea uder the velocity-tie graph is displaceet. If area X area Y the it iplies that agitudes of displaceets carrespodig to areas X ad Y are equal.. s. () KE 0, sice V costat KE v costat Mass is fallig dow so potetial eergy decreases at rate dx g gv [decreases] HS-/7

2 4. s. () HS-/7 T 0 0 t dq costat i (lets say) dt dt i i at, at i dt at 5. s. () Middle oe paper does ot fall. Hece there ust be a ode. 4x 4x 4x 6. s. (4) V R costat dv dr dr costat dv costat slope is costat v-t graph will be straight lie. 7. s. (4) Speed is axiu at the ea positio Distace betwee extree positio c 8. s. () V rs RT M give graph : RT RT LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/-0-06 : uber of oles V T : : V T 9. s. (4) cceleratio is axiu at extree positio. Velocity is axiu at ea positio. 0. s. (4) V R, R R the V 8V Work P (8V V) 7PV [isobaric process]. s. () s poit R, S ad T have zero itesity Destructive iterferece will occur at these poits..5 v f f 00 Hz. s. () Soap bubble has two surface Total legth (r) F T F 4r T 4r. s. () If ' represets the apparet frequecy ad the act ual oe, the use the relatio v w ' v w v where v is the velocity of s soud with respect to wid, w is the velocity of wid ad v s that of the source. Note that i this case the observer at rest. 4. s. () For particle y x dy dx vy v x & v B i ˆ & v x v B vx i ˆ v ˆ y j ˆ ˆ v i j v 5. s. (4) 6. s. () /s Note that the beat frequecy is ( ) ad the correspodig vibratig legths are (/ ) ad (/ + ). 0000CT00500

3 V Give : 0 V CT00500 /+ / V V V V Beat frequecy V V V V V V V V [(+x) +x] V V V V s. () New readig weigth of water (X ) + weight of water displaced by the object (Z) New readig X + Z 8. s. () Net force ad et torque should be zero. 9. s. () d d S dt d d LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/ s. (4) Note that pv costat ad that is iversely proportioal to V. diabatic process pv costat M p costat p M costat (M is costat) p costat. s. () Lets say the displaceet of cylider fro its equilibriu positio is 'x'. a gx a cylider g x g... (i) k sprig-block... (ii) cylider sprig-block... (iii) [give] K g [fro (i), (ii), (iii)]; K 7 N/. s. () F a Writtig torque equatio about a axis passig through, perpedicular to the plae of paper. F R a R R R 5... (i) 7 F a 0. s. () Durig SHM speed will be iiu i ad 5 regio. Hece probability of greatest uber of hit will icrease. HS-/7

4 4. s. () x x path differece kx Hece destructive iterferece will occur at poit P. HS-4/7 resultat a a 4a a. It will reai costat with tie. 5. s. () h h h dh 4 c/hr give w F boyat (h)g (h ) g hg h g h h h h h dh dh dh dh 4 c/hr dh dh Therefore et fall of upper ed 4c/hr c/hr c/hr [rate of fall of upper ed of cadle] 6. s. () I0 0 0 log 0 I 0 0 I 0 0 log 0 T I 0 I I 7. s. () t 50 0 s t 8. s. () out of eergy itercepted [plitude] [surface area] LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/ s. () 0 0 P 0c g Mg p 0 Mg 0 g 0 M... () F b(/ ) g P 8 0 g p et 0 Mg Mg 0 g g M M0 M r r 6 0. s. () questio of uits ad diesios. Oly the diesio of optio () g atches the diesio of speed.. s.(4) 4ClO + 6N H 4 NO + 4Cl -factor 6 4. s.() M V 5 60 V 40 l. s.() s.() r l 9.97 Å 0000CT00500

5 5. s.() 6. s.() 7. s.() 8. s.() PM ZdRT PV ZRT V 4 litre 9. s.() 40. s.(4) NO (g) N O 4 at 00K P P P kp P... (i) P + P 0...(ii) P 8 at P at NO N O 4 ( + P) (4 P) P T (5 + P) (4 P) K p ( P) P 0.9 at P T 5.9 at 4. s.() X s.() 8 ole V V 500 l 4. s.() R R 9 9 H H CT00500 LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/ s.() 45. s. (4) 46. s. () 47. s. () 48. s. () 49. s. (4) 50. s. (4) 5. s. (4) 5. s. () 5. s. () 54. s. () 55. s. (4) 56. s. () 57. s. () 58. s. () 59. s. () 60. s. () 6. s. () Shift origi at (0, 4) 6. s. () Divide by x y y 0 x x + 0 Replace by y y 0 x x x xy y 0 6. s. () x + y 0 (R.) 64. s. () y (x ) x (y ) ƒ x x HS-5/7

6 65. s. () x + x + ; x x + x 0 (x + ) (x ) 0, (rejected) 66. s. (4) E + ( a ) + (b) +. a. b. E i p ; a b a b 0 HS-6/7 (0,0) x + y z 0 L 67. s. () > si > si95 > si6 68. s. () cosx + six > 0 & cosx six < 0, s. (4) ( ) 9 Relatio cotaiig (,), (,), (a,a) Relatio cotaiig (,), (,), (,), (,),(a,a) Relatio cotaiig (,), (,), (,), (,),(a,a) Relatio cotaiig (,), (,), (,), (,),(,), (,)(a,a) Total uber of relatio. 70. s. () B B B B B B 5 B B 0 5 B 8(B) 9() 8 B 9 8k; B 9k B 7k B 0k 0 k LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/ s. () si + cos < 0 si cos si / s. (4) x k x, 7 / k > 7. s. () Circucetre of BC Orthocetre of PQR 74. s. () 0 x x (M.GM) x Equality occurs of x ± But sec x takes axiu at x ƒ i (x) ƒ 75. s. () x < [x ] < x [x ] x x < x 0 < x < 0 < x < x / 76. s. (4) k B 8k D 8 k + 8k > ; 8k k > ; + k > 8k k 5 k Perieter < x < x su C < x < x / 0000CT00500

7 77. s. () s. () x si x si x x x 79. s. () / sec 0 Df,sec, 80. s. () x or x x x x x 0 x + x required su 5 8. s. () 8. s. () Graph is syetric about x 6 b 6 b LL INDI OPEN TEST/NURTURE COURSE/JEE (Mai)/ s. () 84. s. () 0 < LHS < {as it is absolute differece of distace of poit P(x,0) fro (,0) & B(,0)} 0 < a < < a < su 85. s. () Put x si si y cos 86. s. () coefficiet of x 00 o-egative itegral solutio of a + b + c 00 0 C 87. s. (4) 'ƒ' is odd ƒ is also odd su s. () (0,ƒ(0)) (,4) (6,ƒ(6)) ƒ(0) + ƒ(0) 8 siilarly every pair has su s. () 0 C 90. s. () 6, 7e, d, s, t,i uber of selectios CT00500 HS-7/7

Objective Mathematics

Objective Mathematics 6. If si () + cos () =, the is equal to :. If <