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1 NARAYANA IIT ACADEMY INDIA Sec: XI-IC SPARK CPT-5 Date: TIME: 3 HOURS MAX MARKS:86 JEE-ADVANCED-06-P-Model KEY SHEET PHYSICS d d b b d a, c d c, d b, d a,b,c,d a c a, c CHEMISTRY d b a d d b a c a,b,c,d a,c,d a, c a, c a, b, c MATHEMATICS a a c b a a b a, d a,b,c,d a,b,c a,b,c,d a c,d Page
2 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 Physics.. 0 m R m R e 0 L L m R m R i f 0 3 c o s y c o s, s i y 3. R y M R M R I, I y 4 M R c o s L I i I j i s i j & c o s i s i j A s, L I ˆ ˆ ˆ ˆ ˆ ˆ y y R l / y I m / F o r R 0 y m / m / y 6 F 0 i h e r p p e i y v N N m u m v m /...( I) e / / 6 V...( II) (0 u ) 4. for traslatio 0 a b o u t B, F k f R c o s f s i m g R m g ta k k R R ta m a s s / le g th 5 About hige mg = m m F C B A F k g & fo r is m a im u m d 0 d JEE-Advace Solutios Page No :
3 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT F d F d F d 0 3 F F F 3 F F m a 5 F F 3 N Net torque actig about poit = 0 F c m Legth of rod= m 8. All poits i the body i plae perpedicular to the ais of rotatio revolves i cocetric circles. All poits layig o the circle of same radius have same speed (ad also same magitude of acceleratio) but differet directio of velocity (also differet directio of acceleratio) Hece there caot be two poits is the give plae with same velocity or with same acceleratio. At metioed above poits lyig a circle of same radius have same speed. Agular speed of body at ay istat w.r.t. ay poit o the body is same by defiitio. 9. F o r p e cm 5u R V u R 0 f is i rt L e t u p to fi a l ro lli g a b o u t 0; fo r v 5 u 7 0 m R m u R m v R 5 R 5 k v, fric tio w ill b e k i e tic 0. For give coditio rollig is satisfied for ay her F eve F & for ay ever 0. Coceptual. Coceptual 3. i pure traslatio T e = 0 about ay pt. & f k = Mgsi about c.m. N = f K ta N fk O P V /R V f k 4. mg si mg cos JEE-Advace Solutios Page No :3
4 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 M g T M a... i cm l m l T... ii a cm L... iii From equatio (i), (ii) ad (iii) T Mg 5 N 4 5. The applied few pulls the cm of the disc with us acceleratio a ad rotates the disc with a agular acceleratio r R From torque equatio r F I R 4 Fr I R 4 r a d s 6. About c.m. e = 0 f / f / m g F F f F N 7. mg F c o s m g s i F M g / s N F cos F & a b o u t c.m. F R M R 5 m g M R g 4 ra d / s e c 5 5 R 8. about O; T t ~ 0 L L e i f Mg si Mg cos Fsi V o 7 m v si R m R m V R o si 3 0 V 5 R 5 N f V/R O V Vo Chemistry JEE-Advace Solutios Page No :4
5 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 9. For buffer capacity of 0. we should have c 0. 0 c 0. Where c is cocetratio of weak acid or salt i the buffer solutio So, c 0. 0 c S o 9 c. o r. c 9 So, moles required for 90ml solutio 0..4 g N H g g N H R N H a q. V o lu m e o f s o lu tio moles = m moles. 9 is e g lig ib le w.r.t. s o. p O H [ p K lo g C ] b H H A H A H A D u e to c o m m o io e ffe c t e g le c t w.r.t K a A 0 H A A F C H C O O H a q. F C H C O O a q. H a q. a t e q m. c c c K a H F C H C O O F C H C O O H F C H C O O H a t e q m. F C H C O O H T o ta l c o c e tra tio is egligible w.r.t. H maily from first step 3 JEE-Advace Solutios Page No :5
6 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT H K C a H A 0 A 3 K 0 a 3 H A H A 3 A 0 X 0 ; HA p X 0 p K p K. 8 p H a a is e g lig ib le w.r.t. fo r b o th a c id s o H K C K C a a H H A 0 M ( e g lig ib e l w.r.t. ) H M, H 0 M So we shold cosider [H + ] from H O [H + ] total = 0 7 without cosiderig commo io effect ph = 6.7, so poh = 7.3 but due to C.I. effect H + from H O will be less So ph > After dilutio [H + ] = 0 ph = Let V litre solutio of ph = is added i origial solutio so that ph remais fied V 0 H 0 0 V This result is idepedet of volume take. 5 3 H M to which the solutio i ( A, C & D) are ISOHYDRIC. 9. (ph) =pk a + log(y/) (ph) = pk a +log (/y) y p H p H lo g lo g lo g y y So y y y 9.5 p H p H p K lo g lo g p K 9.5 so, p K y a a a JEE-Advace Solutios Page No :6
7 Narayaa IIT Academy 30. A t e q u a tio H A H H A ; C X y y , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 a a A t e q u a tio H A H A p K p K 5 7 y y y y is v e ry le s s s o y 3. K a a a y K y 0 ; p K c p H p K lo g c a 3 p K p K 5 a a 5 p H 8 lo g 8 lo g p H 8 lo g 8 lo g 3 5 C h a g e i p H lo g 3 lo g lo g 3 3 H S O, H P O, H C O, H S O, H S O, H C ro Because 8 9 H s H O Which is very small ad egliable if ioizatio of is ot eglected, the H O H O H K H O H w % e r r o r 0 0 % Mathematic 37. Greatest biomial coeff. I the epasio of is c. As per the requiremet ( + ) th term of the epasio must be the greatest terms. c c c F ro m c c, w e g e t F ro m, c c, w e g e t JEE-Advace Solutios Page No :7
8 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 r r 38. r r 0 c a.b. c o s rb r A r r R e c a.b.e r r 0 ib ia i rb r A r ib R e c r a.e. b.e R e a e b.e ia r R e a c o s B ia s i B b c o s A ib s i A 39. R e a c o s B b c o s A c JEE-Advace Solutios Page No :8
9 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT JEE-Advace Solutios Page No :9
10 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT JEE-Advace Solutios Page No :0
11 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT JEE-Advace Solutios Page No :
12 Narayaa IIT Academy , IIT XI-IC Spark_JEE-ADV(06_P Model) CPT-6 JEE-Advace Solutios Page No :
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