ANSWER KEY WITH SOLUTION PAPER - 2 MATHEMATICS SECTION A 1. B 2. B 3. D 4. C 5. B 6. C 7. C 8. B 9. B 10. D 11. C 12. C 13. A 14. B 15.

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1 TARGET IIT-JEE t [ACCELERATION] V0 to V BATCH ADVANCED TEST DATE : ANSWER KEY WITH SOLUTION PAPER - MATHEMATICS SECTION A. B. B. D. C 5. B 6. C 7. C 8. B 9. B 0. D. C. C. A. B 5. C 6. D 7. A 8. C 9. D 0. A PHYSICS SECTION - A. A. A. B. B 5. B 6. A 7. B 8. D 9. B 0. A. C. A. C. D 5. A 6. D 7. C 8. D 9. B 0. A CHEMISTRY SECTION - A. C. C. B. A 5. A 6. B 7. A 8. C 9. D 0. C. B. A. D. C 5. D 6. C 7. C 8. A 9. B 0. A 9 - Rajeev Gadi Nagar Kota, P. No ,

2 SOLUTIONS MATHEMATICS SECTION A Sigle correct. B. B Sice, period o si cos / it is possible we. D e e e e e e 0 6 ad e e...! > 0 e e 0 ece, () > 0 () is ito ad ' e 8 e '() 0 0 '() as real values o so uctio () is may oe. Hece, () is eiter oe - oe or oto. (say)y () or y (sg) y, y 0 y y, y 0 y, 0, 0, i 0, i 0, 0, 0. C () + + si '() () is icreasig uctio Rage [ (0), ()] [0,+] 5. B Divide above ad below by e /, te a 8e 0 b e / / b b b b / Te a R 6. C y () ad (a) 0 loge 6 a loge 6. a C a b( ) + c( ) 0...() a b c 0 Now, are te roots o a + b + c 0 Te, ad ad Hece,, are te roots o eq. (). 8. B Sice are te roots o ad r r Sr r r Rajeev Gadi Nagar Kota, P. No ,

3 B 0. D ta ta 8 (ta ) ta ta 8 or 0 I + + ' k (Eve iteger) + ' Now, (I + )' () (I + ) ( ) I or. C. C Sol. to () + ( ) g a () + g a ( ) a a a a a a a a a a a a (i) 995 Sol. r r times 995 r r Sol r r 0 (0) +. A a a iite iite r (rom eq. ()) r si ae be c l 0 iite at 0, Numerator a + b ad Deomiator 0 RHS is iite a + b 0 b a (i) si ae ae c l Now, 0 si a e e cl a 0 at 0, umerator + a + a + c ad Deomiator 0 RHS is iite, + a + c 0 c a 0 si ae ae a l 0 (by L' Hospital's rule) orm 0 0 cos ae ae a (by L' Hospital's rule) iite iite iite 0 orm Rajeev Gadi Nagar Kota, P. No ,

4 . B 5. C 0 si ae ae 6 Numerator must be a a + a a 0 From equatio (i), b a 6. D Sol. 5 to 6 I are te roots ad D be te discrimiat o te give quadratic equatio, we m m 8m, m...(i) ad D ( + m) ( + m)( + 8m) (m m) m( m ) I roots are real, te D 0 m,0 [, ) Sol.5. D < 0 m ( m ) < 0 0 < m < m, Sol.6. + > 0 ad > D 0 m 0 m 8m 0 m m m 0 m,,...(ii),, 8 m (,0] [, ) m, [, ) 7. A A P,S ; B Q, T ; C P, R (A) cos cos + cos cos or or cos Rage o () is, [0,] ( P,S) (B) () 6 () is deied or 0 ad 6 0 i.e, 6 Also, '() 6 or 6 5 () (5) (6) 0 6 Rage o () is,, Q, T (C) 0 + or, (R) 8. C A P,T ; B Q, S ; C R (A) Case I : I >, te + y 6, y we get, y Case II : I <, te (B) (C) y 6 y y, 0 Hece, te oly solutios are ( 0, ) ad (,) i.e. m Sice, y is positive or all values o y, te ( 8)( 0) sould be positve. Tereore > 0 or < 8 Sice, y is a power o, 0 ad 8 sould be bot powers o. ad 6 are oly values o tat it or tis coditio. Hece (, ) ad (6, ) are te oly solutios i.e, + y y + y y y( ) or y +, or, 0 te y, 0 y, 0 Hece,te oly solutios are (,) ad (0,0) i.e. p P m p m, Q p 9 - Rajeev Gadi Nagar Kota, P. No ,

5 R P m 8 m, S T p p / + / + /8 + /. 9. D A P,Q,R,S,T ; B P,Q ; C P (A) a(b c) + b(c a) + c(a b) 0 is a root o a(b c) + b(c a) + c(a b) 0 Roots are equal te oter root is also. Product o roots c a b a b c ac b a c a,b,c are i HP. (S) Also, (d + a b) + (d + b c) 0 Wic is possible oly we d + a b 0, d + b c 0 a a + c a, b,c are i AP (Q) a,b,c are i AP ad HP te a b c(t) te a,b,c are also i GP(R) a b c a + b + c 0 (P) (B) ( b c) + (c a) + (a b) 0 is a root o (b c) + (c a) + (a b) 0 Roots are equal ote root is also. Te product o roots a b a c, b b c a,b,c are i AP. (Q) (C) Let be a commo positive root, te + p (i) + q (ii) ad + (p + q) (iii) Applyig equatio (i) + (ii) (iii), we get or 9 a ( is positive) let oter root o equatio (i) is a (give) te a a let oter root o equatio (ii) is b (give) te b 5 b 5 ad let oter root o equatio (iii) is c (give) te c 6 c a + b + c 0 (P) 0. A A Q,R ; B S,T ; C P,S,T ta + ta y + ta z y z yz ta y yz z y z yz 0 y yz z + y + z yz 0 or + y + z yz (R) Also, AM GM y z yz / yz yz / ( + y + z yz) (yz) / or yz Q (B) ta + ta y + ta z y z yz ta y yz z y z yz y yz z or y yz z 0 y + yz + z (T) Also, AM GM y yz z y.yz.z / ( y + yz + z ) y z / / yz, or (C) ta + ta y + ta z yz (s) Te y + yz + z (T)(rom above) ad + y + z ( + y + z) + y + z + (y + yz + z) + y + z + + y + z Hece, ( y) + ( y z) + (z ) ( + y + z y yz z) ( ) 0 y 0, y z 0 ad z 0 y z (P) AM GM y z yz / yz / yz S 9 - Rajeev Gadi Nagar Kota, P. No ,

6 SECTION - A. A Te distace travelled durig 0 to s 0 m + 0 m 0 m.. A. B Distace travelled is km.. B 5. B Time take Km Km 6Km /r 8Km /r 7 r r. 6 8 Average speed km 8 km / r 7r 7 7 km/r. a c MLT MLT MLT bt MLT 6. A At + Bt + Ct + D. Positio at t 0 is D 5m. Positio at t s is ( m/s ) (6s )+(m/s )(6s ) (m/s)(s)+5m ( ) m 5m. Tus, te displacemet durig 0 to s is 5 m 5 m 0 m. 7. B 8. D 9. B 0. A Average velocity 0m 0m / s s. C ;. A Displacemet 0 [() ()] [(0) (0)] m Now, velocity v d t dt i.e. v 0 at t sec or t < sec, V ve & or t > sec, v +ve Distace travelled Displacemet i ve directio + Displacemet i +ve directio or t 0 to t s + or t s to t s 0 + [() () (0)] + () + () + 5m PHYSICS. C ma (0)(000)kg 0000 N. D 5. A 6. D I 6 s it will reac to igest poit. Maimum eigt will be u g 80 m I et s it will all a distace 80m gt 0 m Average velocity displacemet time m/s 8 7. C A S ; B Q,R ; C Q,R ; D P,R t ucos y (u si ) t gt H gt Bullet will it te body, y > 0 u cos H gt g / / g g u ( H ) cos H H u 0 (give) Here H cos 0 m I u<u 0. bullet will it te groud beore ittig te body. I u > u 0, bullet will it te body. Sice, A > 0 ad i u > Au 0 ad u > A u 0, te u < u. Smaller te value o u, bullet will it te body but ot ear its iitial positio o rest (or u>au 0 ) Greater te value o u(e.g., A u 0 ) bullet will it te body ear its iitial positio o rest (or u>a u 0 ) 8. D (A) Q,S;(B) R; (C) P;(D) R Distace will be miimum because ma will reac rom A to B directly. B A 9 - Rajeev Gadi Nagar Kota, P. No ,

7 v w si ad V m V vmw Hece i b., d Time take is miimum i w V mw is perpedicular to V w. Hece II, c., iv. c. I Vmw V w, te drit or distace is sortest i v mw si. Hece (iii) a. v 9. B A P ; B Q ; C R ; D S (A) a. Rage is maimum, we te agle o projectio is 5. v v H si 5 g g (i) Velocity, at al o te maimum eigt is v. H v v v v v si 5 g v r (B) b. Velocity at te maimum eigt v v cos 5 v v [Because vertical compoet o velocity is zero at te igest poit] (C) c. Projectio velocity At projectio poit, vv cos 5 î + v si 5 ĵ At te poit, we te body strikes te groud V v cos 5 î v si 5 ĵ v V ( V t) v si 5( j) V v si 5 v (D) d. Average velocity Total displacemet Total time V av R/ R/ H Displacemet V av R H v si g V v g g v g H R R H v si g H v g v 5 v 5 v v g 0. A A P,R ; B Q,S ; C P,R ; D P,Q,R,S i. I uiorm circular motio, acceleratio ad velocity are perpedicular to eac oter, but i o uiorm circular motio, agle betwee velocity ad acceleratio lies betwee zero ad /. ii. I straigt lie motio, acceleratio vector ad velocity vector are colliear to eac oter, i.e., agle betwee tem is eiter zero or 80. iii. I projectile motio, agle betwee velocity ad acceleratio ca vary rom 0 < <. iv. I space agle betwee velocity ad acceleratio may be Rajeev Gadi Nagar Kota, P. No ,

8 CHEMISTRY. (C) E Z system SECTION - A. C H C O. H O ad. B. [A] 6 Equivalet wt. W Y Z Boat (cis) cair (tras) X Boat (cis) W 0.6 g 5. A Equivalet o K Cr O 7 equivalet o N H also equivalet o KMO equivalet o N H So, equivalet o K Cr O 7 equivalet o KMO 0. 6 V 0. 5 V so V /5 V 6. B 7. A 8. C milli equivalet o H PO milli equivalet o Ba(OH).5 V So, V 0 ml 9. [D] Cl Cl Cl Same groups. 0. C 0 Eq. o Hg 5 (IO 6 ) Eq. o I Eq. o Na S O (moles o Hg 5 (IO 6 ) ) moles o Hg 5 (IO 6 ) B. A M + O M+ + O Case-I M + X M + + X m O m 0. 6 M 60 M D Sum o proto are 6. C bod order O + /(8 ) 5/.5 5. D 6. C 7. C A R; B S; C P, D Q (A) OA MO C O MO CO RA O.A R.A (B) ClO + F + Cl + FeO OA RA O.A RA (C) HO +Cr + CrO + HO OA RA O.A RA (D) N H + 6Cu + N O + Cu OA 6 RA R.A O.A 8. A a s ; b rp ; c qps ; d qs 9. B A Q, B S, C R, D P 0. A A Q, B S, C P, D R 9 - Rajeev Gadi Nagar Kota, P. No ,

SAFE HANDS & IIT-ian's PACE EDT-10 (JEE) SOLUTIONS

SAFE HANDS & IIT-ian's PACE EDT-10 (JEE) SOLUTIONS . If their mea positios coicide with each other, maimum separatio will be A. Now from phasor diagram, we ca clearly see the phase differece. SAFE HANDS & IIT-ia's PACE ad Aswer : Optio (4) 5. Aswer : Optio