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

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1 ONLINE TEST PAPER JEE MAIN - 6 DATE : --6 ANSWER KEY WITH SOLUTION MATHEMATICS. C. A. A. A. D 6. A 7. D 8. A 9. C. D. D. A. C. C. D 6. D 7. A 8. A 9. A. D. B. A. D. A. B 6. B 7. C 8. D 9. D. B PHYSICS.... A , CHEMISTRY Rajeev Gandhi Nagar Kota, Ph. No , 7-967

2 MATHEMATICS. C. A y y(t) dt ( ) y y(t) dt A (,, ) y ( t) y(t)dt y dy d ( )y dy ( ) d d dy d logy y( ) log logc logy log logc log y C y C y e Ce. A Coplanar. A ( ) ( ), ± y / P P P y. D 6. A B D C,,,,, 7, AD AD ˆ i ˆ ( ) ĵ k î ĵ y dy d y sec tan y v y dy d dv d dv d i i v sec tan I.F. sec d e I.F. (sec tan) y 8 sec tan Z i i i.. ˆk 6 OA OB P P D A I A.(A A I) 9 - Rajeev Gandhi Nagar Kota, Ph. No , 7-967

3 8. A. A r r (r r)r r r r r (r ) r... 9 S S (, ) (, ) 9. C. D F G H a b c a b c 6 c a b c r (a b c / a) (a b c) r c D f() sin cos 8 f() sin cos f() (sin ) f () sin r 6 sin cos. C. C. D Eq n to hyperbola y a 9 a ( sin ) lim ( tan tan) sin lim. 8 6 /7 (, ) 7 y m / 7 7 m ()(7) 7 7m /7 ˆ ˆ 7 m 9 / 7 (a b) Equation ot incident ray y ( ) 8 8y 8 8y 8 6m 9 9 m 76m 8 m /8 9 - Rajeev Gandhi Nagar Kota, Ph. No , 7-967

4 6. D a d a 6d a d a d 7 (a 8d) 7 a 8d 8 S 7 7 (a 6d). D h S A A I 7A 7A I A A A A I A A 7A A A I A A I A I (A I) 8. A 9. A a 9 a ± a 6 6 a b b a b 6 b ()() b ± d ( ) d ( ) d ( ) tdt t t C. B. A h h 9) h () h ( ) 8 / I I [( ) ]d [ ] [ ] I 6 I d. D z l i a a ai z ( a ) i(a a ) pure real no a a z i a z (cos/ i sin/) S ( z ) z S i 9 i 9 - Rajeev Gandhi Nagar Kota, Ph. No , 7-967

5 . A y y /, y (, ). B y Eq n to tangent y / / y ( ) / / y y Sin ( tan ) cos ( ) sin cos tan 6. B () Coeff. of 8 r 6 r 8 r () Coeff. of ( ) r 8 r 6 r n 8 C r 7. C n n 6 n n (n ) (n ) (n) (n ).6... (n ) (n ) (n) (n )..9.8 n 9 8. D for min A B A B / tana tana tan / 9. D tan tan tan tan tan ( ) t t t t t t Am m t. B t t t t t. dy d 9 y P(, ) Eq n ot Normal y ( ) y 8 9 y 7 Normal passes through Pt (, 7). m n 8 8 C C ( / ) ( / ) Rajeev Gandhi Nagar Kota, Ph. No , 7-967

6 . Wrong question. Q remain 6 68 J.. B Q remain w T T T 68 7 w 7 w v frequency received directly from toy n v frequency received after reflection from wall v n v v v between n n v v n n n 7 PHYSICS 6. At least three reading are required 7. w B H B sin N S sin 9 E B H T P.D across wings B v l mv with left side at high voltage P.D between top & bottom B H v l hc K...() K hc K K hc hc f. A hc n n g a...() hc.8 a 7 n mv Energy.6 n ev 9. y (a b). c For y to be (a b) should be & c should be n ev 9 - Rajeev Gandhi Nagar Kota, Ph. No ,

7 . The V-I graph of i/p characterstic is I V This means that increasing the voltage decreases the resistance almost to zero. This means that increases /r to Hence. correct graph is. Redistribution will stop when qvb qe E vb E vb 6 vb vb vb. B FV AV F F F BAV V B(b) (a G) a )b a b abb(a a aa a ) abb.a a a F (bba) F req. R F (bba) ( bb) G a V. Rg G...() G...() 9 Rg 9 Rg Rg 9 Rg 8 Rg Rg from eqn. () G G G. G ua/div ful scape deflection current is A/div AP ma Hence, is incorrect Hence, correct option is only is correct. Image due to reflection Uf U f. V cm Image due to refraction d app dreal n n I cm. R. The ratio of r to r i is very high for transistors almost in the range of to 9 - Rajeev Gandhi Nagar Kota, Ph. No ,

8 6. y 8. 9., Dimensionally B D & AD C (,) co-ordinal of AB / l l X co-ordinal of BC Centre of mass should below A 8 cm let lines mass density so m AB m l l t l l l l l l n n ()( ) n Amplitude modulated O/P is given by C(m) V C cos (W e t) mv c cos (wc w ) t mv c cos (wc W ) t comparing with the given equation mv c m w c f c f c Hz w c w w fm fm Hz. (i) D A D C D A D AD D A A (meaningful) C AD C AD C (ii) D BD C BD AD BD C (iii) A (BC) D (iv) B A C BD C d S S a (meaningful) C D C (meaningful) d a...() A sin....() A _~... 6 A (meaningful) A S d m _~ 8 km. In case of EM wave, the direction of oscillation of electric field and magnetic field i s perpendi cular to t he directi on of propagation. Options A and B are incorrect. Also E B gives the direction of propogation ( ĵ kˆ) ( ĵ kˆ ) î î î ( ĵ kˆ) (j ˆ k) ˆ î i Hence correct option is S 9 - Rajeev Gandhi Nagar Kota, Ph. No ,

9 .. v n Rt r v nrt dv nr dt F t mnr P FV (MnR) nrt mn R t v rg rw rg w n g r g r. Wrong question. Induced current R A r Be R t / T B T TR db r dt r r e t/t d de dv a m/s dt F ma Newton distance travelled in two seconds is s Ut at s 9 w F.d Ma.d 9 J f RT M w 8 8 C 9 C eq. 8 8 C 9 C 9C C 9C C C Heat generated r B TR r B e TR r B TR 6. t T I Rdt e t/t Rdt r B TR [e e ] v The given situation tells that is constant r which means that electric field inside the sphere is constant. This is possible only when is function of r. R F t mdv dt v R t dv R m v f m ln v t R ln v f v dt 9 - Rajeev Gandhi Nagar Kota, Ph. No ,

10 . (). () Rate constant does not depned on concentration of reactans. (). () Rhumann's purple is a confirmatory test of protein. Its also know as ninhydrin test. () 6. () 7. () 8. () 9. (). (). () MX eq. n M aq aq (n ) ( ) y /. Ans. CHEMISTRY 9. (). (). (). (). () LiH B H 6 Li[BH ]. () N N Taken rms rms (New) RT 8 R T Cl. (). (). (). () lone pair of nitrogen at ninth position's involved in resonance i.e. not available for donation 6. () 7. () 8. () XY (s) y a ( bar) q ( bar) k p Ans Work P ekt (V V ) P et. V o nort bar bar 8.. Ans.. () 6. () it is a free radical r H A OH ().N.. v. V ml 7. () 8. () 9. () (CH ) (CO H ) () OOC CH CH (). () CH CH (g) CO (q) e (). mol. 6.7 lit. 9 - Rajeev Gandhi Nagar Kota, Ph. No , 7-967