Set A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the eq

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1 Set - 0. A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation AD=C ln(bd) holds true. Then which of the combination is not a meaningful quantity? () A B C ( A C) D A B C C AD BD C. A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n R t where n is a constant. The power delivered to the particle by the force acting on it, is : () M n R t M n R t M n R t M n R t. A, B, C ÃÕÊ D øê U Á ÛÊ ÊòÊÊ Ò Á Ÿ Ë Áfl Ê Á ãÿ Ò Êappleß Ë ÊòÊÊ Áfl Ê- UÁ à ÊòÊÊ Ÿ Ë Ò, appleá Ÿ AD=C ln(bd) àÿ Ò Ã ÁŸêŸ apple apple ÊÒŸ Ê Êÿ- UÁ à ÊòÊÊ Ò? () A B C ( A C) D A B C C AD BD C. Œ ÿ ÊŸ M Ê áê ÁŸÁ øã ÁòÊíÿÊ R apple flîûêëÿ Õ U-ß Ê U ø U Ê Ò Á ÿ t U Á apple ãœ Ë àfl UáÊ n R t mê UÊ ÁŒÿÊ Ê ÃÊ Ò, ÿ Ê n ø U Ò Ã áê U ª U apple mê UÊ Êapple ŒË ªß ÊÁÄÃ Ò () M n R t M n R t M n R t M n R t. A, B, C A_ D A Qpf Sy>v$p-Sy>v$p `qfdpz ^fphsu Sy>v$u-Sy>v$u cp rsl$fpriap R>. s dp _u L$p C`Z `qfdpz frls _\u. Å AD=C ln(bd) kdul$fz kpqy lp e sp _uq Ap` g ` L$u L$ey k ep S>_ A A\ kcf (kpqu) fpri v$ip hsy _\u? () A B C ( A C) D A B C C AD BD C. M v$m ^fphsp L$Z R S> V$gu AQm róäep ^fphsp hsy mpl$pf dpn `f A hu fus Nrs L$f R> L $ t kde s _p L $ÞÖNpdu âh N n R t hx $ Ap`u il$pe; Äep n A AQmp L$ R>. sp L$Z `f gpnsp bm hx $ L$Z_ dmsp `phf (L$pe v$nsp) \i. () M n R t M n R t M n R t M n R t

2 Set - 0. Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute(rpm) to ensure proper mixing is close to : (Take the radius of the drum to be.5 m and its axle to be horizontal) : () Ë U Á Ä ø U ŸÊŸapple apple Á ÿapple Ë apple U, appleuã ÃÕÊ UÊapple«Ë Êapple ÉÊÍáÊË ÿ apple ŸÊ Ê U «U apple «UÊ Ê ÊÃÊ Ò ÿᜠ«U Ë ÉÊÍáÊ Ÿ-ªÁà Èà Ãapple Êapple ÃÊapple ÉÊ U «U Ë ŒËflÊ U apple Áø apple U Ãapple Ò ÊÒ U Á Ä ø U UË apple Ÿ Ë ŸÃÊ ÿᜠ«U Ë ÁòÊíÿÊ.5 m Ò ÊÒ U ß Ë œè UË ˇÊÒÁà Ò, à ë UË Ã U Á Ä ÊappleŸapple apple Á ÿapple M UË Áœ à ÉÊÍáÊË ÿ-ªáã rpm apple Ò () A L$ QpL$Nrs L$fsp _mpl$pfue X²$ddp rkd ÞV$, `Õ\f A_ f su_ c Np L$fu_ L$p q¾$v$ rdîz s epf L$fhpdp Aph R>. lh Å X²$d M b S> TX$`\u QpL$Nrs L$f sp rdîz L$f gp sòhp X²$d_u qv$hpg_ Qp V$u Åe R> A_ s d_y ep Áe rdîz b_phu il$psy _\u. sp `qfc dz ârs rd_uv$ (rpm) _p `v$dp, ep Áe rdîz b_hp dpv $_u X²$d_u dlñd L$p Zue TX$` u _ÆL$_u li. (X²$d_u róäep.5 m A_ s _u An kdrnrss> R> s d ^pfp ). ()

3 Set Velocity-time graph for a body of mass 0 kg is shown in figure. Work-done on the body in first two seconds of the motion is : 4. 0 kg Œ ÿ ÊŸ apple Á «U apple Á ÿapple flappleª- ÿ ª Ê» ÁøòÊ apple ÁŒÿÊ Ò Á «U U apple apple. apple Á ÿê ªÿÊ Êÿ Ò 4. 0 kg v$m ^fphsp `v$p\ dpv $_p h N-kde_p Apg M ApL $rñdp v$ip h g R>. `v$p\ `f â\d k L$ÞX$dp \su Nrs v$fçep_ \sy L$pe \i. () 000 J 000 J 4500 J 900 J () 000 J 000 J 4500 J 900 J () 000 J 000 J 4500 J 900 J 5. In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then BC is close to : AB () ÁŒÿapple ªÿapple ÁøòÊ apple ÃÊ U ABC ÊŸ Ò ÿᜠÁÃ- apple 㜠Á ŒÈ A apple äflê œ U ŸËøapple ÁSÕà Ò, à BC AB ª ª Ò () ApL $rñdp v$ip ìep dys>b ABC A kdp_ spf R>. Å spf_y Öìedp_ L $ÞÖ tbvy$ A _u bfp bf _uq Aphsy lp e sp BC _y d ëe u _ÆL$_y \i. AB ()

4 Set An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth s surface. The radius of the earth is R, while its mass is M. The gravitational pull F G on the astronaut is : () Zero since astronaut feels weightless GMm 0 < FG < R GMm GMm < F < ( ) G R+ h R GMm FG= ( R+ h) 6. ÎâflË Ë Ã apple h ŒÍ UË U ÁSÕà ª U m Œ ÿ ÊŸ Ê ÃÁ UˇÊ-ÿÊòÊË Ê U U Ê Ò ÎâflË Ê Œ ÿ ÊŸ M ÃÕÊ ÁòÊíÿÊ R Ò Ã ÿêòêë U ª U Ê ªÈL àflëÿ F G Ò () ÊÍãÿ, ÄÿÊapple Á fl ÿêòêë Ê U ËŸÃÊ Í UÃÊ Ò GMm 0 < FG < R GMm GMm < F < ( ) G R+ h R GMm FG= ( R+ h) 6. ` Õhu_u k`pv$u\u h KQpC A `qfc dz L$fsp k V gpcv$dp m v$m ^fphsp MNp mipõóu L$pe L$f R>. ` Õhu_u róäep R R> Äepf s _y v$m M R>. MNp mipõóu `f gpnsy NyfyÐhpL$j} M QpZ F G li. () i Þe, L$pfZ L $ MNp mipõóu hs>_frls [õ\rsdp R>. GMm 0 < FG < R GMm GMm < F < ( ) G R+ h R GMm FG= ( R+ h)

5 Set A bottle has an opening of radius a and length b. A cork of length b and radius (a+ a) where ( a<<a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is µ then the force needed to push the cork into the bottle is : 7. Êappleà apple È Ë ÁòÊíÿÊ a ÒÒ ÃÕÊ ê Êß b Ò b ê Êß ÊÒ U (a+ a) ÁòÊíÿÊ ( a<<a) flê apple Ê Êapple apple È apple Í UË Ã U Í U ÁŒÿÊ ªÿÊ Ò (ÁøòÊ ŒappleÁπÿapple) ÿáœ Ê Ê Êÿß àÿêsõãê ªÈáÊÊ B Ò ÃÕÊ Êappleà ÊÒ U Ê apple Ëø ÉÊ áê-ªèáêê µ Ò, Ã Ê Êapple È apple ÉÊÈ ÊŸapple apple Á ÿapple Êfl ÿ Ò 7. A L$ bp V$g_p Nmp_u róäep a A_ g bpc b R>. ApL $rñdp v$ip ìep dys>b, b g bpc_p A_ (a+ a) Äep ( a<<a) _u róäep ^fphsp b Q_ v$bpz` h L$ hx $ bp V$g_p Nmphpmp cpn_ k ` Z b ^ L$fhpdp Aph R>. Å b Q_p L$v$ [õ\rsõ\p`l$spa L$ B lp e A_ bp V$g A_ b Q hãq _p OjZp L$ µ lp e sp b Q_ bp V$gdp O kpx$hp S>ê$fu bm \i. () (πµb b) a (πµb b) a (πµb b) a (4πµB b) a () (πµb b) a (πµb b) a (πµb b) a (4πµB b) a () (πµb b) a (πµb b) a (πµb b) a (4πµB b) a

6 Set A Carnot freezer takes heat from water at 0 C inside it and rejects it to the room at a temperature of 7 C. The latent heat of ice is 6 0 J kg. If 5 kg of water at 0 C is converted into ice at 0 C by the freezer, then the energy consumed by the freezer is close to : () J J J J 8. ÊŸÊapple U» Ë U Ÿapple Œ U 0 C U Uπapple È apple c Ê apple U apple appleu apple ÃÊ ÊŸ 7 C U ÁŸc ÊÁ à UÃÊ Ò» Ë ªÈåà c Ê 6 0 J kg Ò ÿ᜻ Ë U apple UπÊ 0 C U 5 kg, 0 C U» apple Œ ÃÊ Ò Ã» Ë U mê UÊ π ÊßZ ªß Ê ª ª Ò () J J J J 8. A L$ L$p_p V$ f qäs>f V$f `pzudp \u 0 C sp`dp_ Dódp ip ju 7 C sp`dp_ fl gp hpsphfzdp a L $ R>. bfa_u g V $ÞV$ (Nyá) Dódp 6 0 J kg R>. Å f qäs>f V$fdp 0 C _y 5 kg `pzu 0 C bfadp ê$`p sfus L$fhy lp e sp f qäs>f V$f hp`f g EÅ u _ÆL$_y d ëe ^fphi. () J J J J

7 Set Which of the following shows the correct relationship between the pressure P and density ρ of an ideal gas at constant temperature? 9. Á Ë ÊŒ Ê ªÒ apple Á ÿapple ÁSÕ U ÃÊ ÊŸ U apple ŒÊ P ÃÕÊ ÉÊŸàfl ρ apple Ëø œ apple Á ÿapple ÁŸêŸ apple apple ÊÒŸ- Ê ÁøòÊ Ë Ò? 9. _uq Ap` g ApL $rsap ` L$u L$C ApL $rñ AQm sp`dp_ fl g Apv$i hpey dpv $ v$bpz P A_ O_sp ρ hãq _p kpqp k b ^ v$ip h R>. () () ()

8 Set In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to : () 0. Hz. Hz 0.7 Hz.9 Hz. A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 40 m/s, the frequency of the horn of the toy car is close to : () 680 Hz 50 Hz 40 Hz 70 Hz 0. ß Ÿ Ê Á S UŸ 7 cm ÊÿÊ Ë U - Êflà - ªÁà äflê œ U apple U U Ê Ò Á S UŸ apple U flê Ê U UπÊ Ò Êapple apple ÊÕ ø ÃÊ Ò Êapple U U Ë ªÁà œë appleu-œë appleu Êß ÊÃË Ò ÃÊapple Á S UŸ Ë ÊflÎÁûÊ Á U flê Ê U Á S UŸ Ê ÊÕ UÊapple«ŒappleÃÊ Ò, fl ª ª Ò () 0. Hz. Hz 0.7 Hz.9 Hz. Áπ ÊÒŸÊ Ê U ÊŸ ÊÃË Èß 5 m/s Ë ÁSÕ U ªÁà apple ŒËflÊ U apple ŒÍ U ÃÕÊ ÿáäã Ë Êapple U Ê U Ë Ò ÿáäã Êapple 5 Ë U/ apple. ÈŸÊß ŒappleÃË Ò ÿᜠflê apple äfláÿ Ë ªÁà 40 m/s Ò, à ʟ Ë ÊflÎÁûÊ ª ª Ò () 680 Hz 50 Hz 40 Hz 70 Hz 0. A L$ A [ÞS>_dp r`õv$_ DÝh qv$ipdp 7 cm _p L $`rhõspf kp\ SHM (k.ap.n) L$f R>. r`õv$ u D`f fl g hp if s _u kp\ S> Nrs L$f R>. r`õv$ Nrs L$fphsu dp V$f_u TX$` ^ud \u h^pfhpdp Aph R>. hp if r`õv$ u k`pv$u_ R>p X$u v$ s r`õv$ u S>ê$fu Aph rñ u _ÆL$_y d ëe li. () 0. Hz. Hz 0.7 Hz.9 Hz. A L$ lp _ hnpx$su fdl$x$p _u L$pf qv$hpg \u v $f sfa 5 m/s _u AQm TX$`\u Nrs L$f R>. A L$ Ahgp L$_L$pf, L $ S> _u sfa fdl$x$p _u L$pf Nrs L$f R>, A L$ k L$ÞX$dp 5 õ` v$ (beats) kp cm R>. Å lhpdp Ýhr p h N 40 m/s lp e sp L$pf_p lp _ _u Aph qñ u _ÆL$_u li. () 680 Hz 50 Hz 40 Hz 70 Hz

9 Set Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential V 0, V 0 + V, V 0 + V,... V 0 +N V ( V>0), are drawn and have increasing radii r 0, r, r,...r N, respectively. If the difference in the radii of the surfaces is constant for all values of V 0 and V then : () ρ (r) α r ρ (r) = constant ρ ( r) α r ρ ( r) α r. Êflapple Ê-ÉÊŸàfl ρ (r) apple Á Ë ªÊapple Ëÿ- Êflapple Ê-Áflà UáÊ, apple 㜠U N Áfl fl- Îc U, Á Ÿ Ë Áfl fl Ò V 0, V 0 + V, V 0 + V,... V 0 +N V ( V>0), Ê appleuáπã Á ÿapple ªÿapple Ò ÊÒ U Ÿ Ë ÁòÊíÿÊ apple Ê r 0, r, r,...r N Ò ÿᜠÁòÊíÿÊ Êapple Ê ãã UÊ, Ë V 0 ÃÕÊ V apple ÊŸÊapple apple Á ÿapple, ÁSÕ U Ò Ã () ρ (r) α r ρ (r)= ø U ρ ( r) α r ρ ( r) α r. ρ(r) S> V$gu Np gue rhûyscpf rhsfz dpv $, A_y¾$d r 0, r, r,...r N róäep ^fphsu A_ V 0, V 0 + V, V 0 + V,..., V 0 +N V ( V>0) S> V$gy [õ\rsdp_ ^fphsu N kd[õ\rsdp_ k`pv$u (` $) v$p fhpdp Aph R>. V 0 A_ V _p b^ps> d ëe dpv $ Å k`pv$uap _u róäep hãq _p saphs AQm fl sp lp e sp. () ρ (r) α r ρ (r) = AQm ρ ( r) α r ρ ( r) α r

10 Set Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be µf is :. ÁøòÊ œêá UòÊÊapple Ê ÁŸ Êÿ Œ ÊÊ ÃÊ Ò, Ê µf apple œêá UÃÊ Œ ÊÊ Ãapple Ò A fl B apple Ëø ÊflË œêá UÃÊ µf ÊappleŸapple apple Á ÿapple C Ë œêá UÃÊ ÊappleŸË øêá ÿapple. ApL $rñdp k OpfL$p _p b_ gy _ V$hL $ v$ip h R> Äep L $` kuv$f_u bpsy>dp gm g _ bf s L $` kuv$f_y dpc¾$p a fpx$dp d ëe v$ip h R>. Å A A_ B hãq _y `qfzpdu L $` kuv$þk (k OpfL$sp) µf Å Csy lp e sp k OpfL$ C _y d ëe Å Ci. () µf µf µf 4 µf () µf µf µf 4 µf () µf µf µf 4 µf

11 Set The resistance of an electrical toaster has a temperature dependence given by R(T)=R 0 [+α(t T 0 )] in its range of operation. At T 0 =00 K, R=00 Ω and at T=500 K, R=0 Ω. The toaster is connected to a voltage source at 00 V and its temperature is raised at a constant rate from 00 to 500 K in 0 s. The total work done in raising the temperature is : () 00 J ln J. 00 ln J ln J 6 4. Á Ë apple ø Ÿapple flê apple UÊappleS U U apple Áà UÊappleœ Ê ÃÊ ÊŸ apple Œ Êfl R(T)=R 0 [+α(t T 0 )] mê UÊ ÁŒÿÊ ªÿÊ Ò T 0 =00 K U R=00 Ω Ò ÃÕÊ T=500 K U R=0 Ω Ò UÊappleS U U 00 VU apple dêappleã apple È«Ê Ò, ÃÕÊ Ê ÃÊ ÊŸ 00 K apple ÊŸ Œ U U U 0 s apple 500 K Êapple ÊÃÊ Ò Ã ß apple Á ÿê ªÿÊ È Êÿ Ò () 00 J ln J. 00 ln J ln J 6 4. A L$ Cg ¼V²$uL$ V$p õv$f_p s _p D`ep N v$fçep_, sp`dp_ kp\ _p k b ^ R(T)=R 0 [+α(t T 0 )] hx $ Ap`hpdp Aph R>. T 0 =00 K dpv $ R=00 Ω A_ T=500 K dpv $ R=0 Ω R>. V$p õv$f_ A L$ 00 V _p hp ëv $S> Dv¹$Nd kp\ Å X$u s _y sp`dp_ AQm v$f 00 \u 500 K ky^u gc S>hpdp Aph R>. s dpv $ gpnsp kdenpmp 0 s R>. sp sp`dp p h^pfp L$fhp dpv $ S>ê$fu Ly$g L$pe. () 00 J ln J. 00 ln J ln J 6

12 Set Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed v in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities σ and σ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) : 5. Ã Ë œêãè ÊË U Îc U apple ê flã UπË Ò ÊÒ U ÁøòÊ apple ÁŒπÊß ÁŒ ÊÊ apple flappleª v apple ÊŸ øèê Ëÿ- ˇÊappleòÊ B apple ø U Ë Ò øèê Ëÿ-ˇÊappleòÊ ß Ã Îc U apple flapple Ê U U Ê Ò ÿáœ ß ÊË U Ë ÊßZ ÊÒ U ŒÊßZ à Êappleapple U Ê Îc U- Êflapple Ê-ÉÊŸàfl σ ÃÕÊ σ appleá Uà ÊappleÃapple Ò, Ã Ê Ã- Êfl Êapple Ÿªáÿ ÊŸÃapple È σ ÃÕÊ σ apple ÊŸ Êapple ªapple 5. kdp Nu Qy bl$ue n Ó B dp, `yõsl$_p ` S>_ g b A_ v S> V$gu AQm TX$`\u ` S>_u A v$f v$pmg \su ^psy_u `psmu s[¼s (` $) _ Ýep_dp gp. (ApL $rñ Sy>Ap ) Å s _u X$pbu A_ S>dZu k`pv$u `f A_y¾$d σ A_ σ S> V$gu ` $rhûyscpf O_sp Dv¹$ch sp \i. (qäþs> Akf AhNZp.) () σ = 0 v B, σ = 0 v B 0 v B 0 vb σ=, σ= σ =σ = 0 vb 0 vb 0 vb σ=, σ= () σ = 0 v B, σ = 0 v B 0 v B 0 vb () σ = 0 v B, σ = 0 v B σ=, σ= 0 v B 0 vb σ=, σ= σ =σ = 0 vb 0 vb 0 vb σ =σ = 0 vb σ=, σ= 0 vb 0 vb σ=, σ=

13 Set A fighter plane of length 0 m, wing span (distance from tip of one wing to the tip of the other wing) of 5 m and height 5 m is flying towards east over Delhi. Its speed is 40 ms. The earth s magnetic field over Delhi is T with the declination angle ~0 and dip of θ such that sin θ =. If the voltage developed is V B between the lower and upper side of the plane and V W between the tips of the wings then V B and V W are close to : () V B =45 mv; V W =0 mv with right side of pilot at higher voltage V B =45 mv; V W =0 mv with left side of pilot at higher voltage V B =40 mv; V W =5 mv with right side of pilot at high voltage V B =40 mv; V W =5 mv with left side of pilot at higher voltage 6. «Ê Í Ê Ë ê Êß 0 m, πêapple apple Á UÊapple apple Ëø ŒÍ UË 5 m ÃÕÊ øêß 5 m Ò, ÊÒ U ÿ ÁŒÀ Ë apple U Ífl -ÁŒ ÊÊ apple 40 ms ªÁà apple «U Ê Ò ÁŒÀ Ë apple U ÎâflË Ê øèê Ëÿ-ˇÊappleòÊ T Ò, Á«UÁÄ Ÿapple ÊŸ ÊappleáÊ ~0 Ò, ÃÕÊ Á«U ÊappleáÊ θ apple Á ÿapple sin θ = Ò ÿᜠappleá UÃ-Áfl fl Ò V B Ê apple U fl ŸËøapple apple Ëø ; V W πêapple apple Á UÊapple apple Ëø à () V B =45 mv ; V W =0 mv ŒÊÿÊ π- Á UÊ +ve V B =45 mv ; V W =0 mv ÊÿÊ π- Á UÊ ve V B =40 mv ; V W =5 mv ŒÊÿÊ π- Á UÊ +ve V B =40 mv ; V W =5 mv ÊÿÊ π- Á UÊ ve 6. 0 m g bpc ^fphsy, 5 m `p Muep_u `lp mpc (A L$ bpsy>_u `p Muep_p R> X$p\u buæ bpsy>_p `p rmep_p R> X$p ky^u) A_ 5 m S> V$gu KQpC ^fphsy A L$ gx$pel$ rhdp_ qv$ëlu_p ` h sfa EX$u füy R>. s _u TX$` 40 ms R>. qv$ëlu D`f ` Õhu_y Qy bl$ue n Ó_y d ëe T d Á_ V$uL$ X $[¼g_ i_ ~0 A_ X$u` A ÞNg θ A hp R> L $ S> \u sin θ = \pe. Å àg p _uq _p A_ D`f_p R> X$p hãq V B S> V$gp hp ëv $S> A_ V W S> V$gp hp ëv $S> b `p Mp _p R> X$p hãq DÑ`Þ_ \sp lp e sp V B A_ V W _y d ëe ÆL$_y li.. () V B =45 mv A_ V W = `pegp V$_u S>dZu bpsy> KQp hp ëv $S> lp e s fus 0 mv V B =45 mv; V W = `pegp V$_u X$pbu bpsy> KQp hp ëv $S> lp e s fus 0 mv V B =40 mv; V W = `pegp V$_u S>dZu bpsy> KQp hp ëv $S> lp e s fus 5 mv V B =40 mv; V W = `pegp V$_u X$pbu bpsy> KQp hp ëv $S> lp e s fus 5 mv

14 Set A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as B = B0e t τ, where B 0 and τ are constants, at time t=0. If the resistance of the loop is R then the heat generated in the loop after a long time ( t ) is : () 4 4 π r B 0 τ R 4 π r B 0 τ R 4 π r B 0 R τ 4 π r B 0 τ R 7. r ÁòÊíÿÊ apple œêãè flîûêëÿ-ãê U- Í Ê Îc U, B = B0e t τ mê UÊ Œ Ãapple È øèê Ëÿ-ˇÊappleòÊ apple ê flã UπÊ Ò Ê ÿ t=0 U B 0 ÃÕÊ τ ø U Ò ÿáœ Í Ê Áà UÊappleœ R Ò, à ʻ Ë íÿêœê ÿ ( t ) ªÈ UŸapple apple ÊŒ Í apple ÒŒÊ Èß Ê Ò () 4 4 π r B 0 τ R 4 π r B 0 τ R 4 π r B 0 R τ 4 π r B 0 τ R 7. A L$ kyhpll$ ^psy_y hsy mpl$pf N Qmy L $ S> _u róäep r lp e s _ Qy bl$ue n Ó_ g bê$` d L$hpdp Aph R>. Ap Qy bl$ue n Ó kde kp\ B = B0e t τ âdpz bv$gpe R>, Äep B 0 A_ τ t=0 kde AQmp L$ R>. Å N Qmp_p Ahfp ^ R lp e sp M b S> gp bp kde ( t ) _ A s N Qmpdp DÐ`Þ_ Dódp \i. () 4 4 π r B 0 τ R 4 π r B 0 τ R 4 π r B 0 R τ 4 π r B 0 τ R

15 Set Consider an electromagnetic wave propagating in vacuum. Choose the correct statement : () For an electromagnetic wave propagating in +x direction the electric field is ( ) E= Eyz ( x, t) y z and the magnetic field is ( ) B = Byz ( x, t) y + z For an electromagnetic wave propagating in +x direction the electric field is ( ) E= Eyz ( y, z, t) y+ z and the magnetic field is ( ) B= Byz ( y, z, t) y+ z For an electromagnetic wave propagating in +y direction the electric field is E= Eyz ( x, t) y and the magnetic field is B= Byz ( x, t) z 8. ÿêapple apple ø U Ë flòlèã-ëêèê Ëÿ à Uª apple Á Ë Áfl À øèáÿ () +x ÁŒ ÊÊ apple øêá à flòlèã-øèê Ëÿ à Uª apple Á ÿapple E E ( x, t) ( y z) = yz, ( ) B = Byz ( x, t) y + z +x ÁŒ ÊÊ apple øêá à flòlèã-øèê Ëÿ à Uª apple Á ÿapple E E ( y, z, t) ( y z) = yz +, ( ) B= Byz ( y, z, t) y+ z +y ÁŒ ÊÊ apple ø U Ë flòlèã-øèê Ëÿ à Uª apple Á ÿapple B= Byz ( x, t) z E= Eyz ( x, t) y, 8. i ÞephL$pidp âkfsp rhûysqy bl$ue sf N_ Ýep_dp gp. _uq dp \u kpqy rh^p_ `k v$ L$fp. () +x -qv$ipdp Nrs L$fsp rhûysqy bl$ue sf N dpv $ rhûys n Ó ( ) E= Eyz ( x, t) y z A_ Qy bl$ue n Ó ( ) B = Byz ( x, t) y + z \i. +x -qv$ipdp Nrs L$fsp rhûysqy bl$ue sf N dpv $ rhûys n Ó ( ) E= Eyz ( y, z, t) y+ z A_ Qy bl$ue n Ó ( ) B= Byz ( y, z, t) y+ z \i. +y - qv$ipdp Nrs L$fsp rhûysqy bl$ue sf N dpv $ rhûys n Ó A_ Qy bl$ue n Ó \i. E= Eyz ( x, t) y B= Byz ( x, t) z

16 Set For an electromagnetic wave propagating in +y direction the electric field is E= Eyz ( x, t) z and the magnetic field is B= Bz ( x, t) y 9. A hemispherical glass body of radius 0 cm and refractive index.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen : +y ÁŒ ÊÊ apple ø U Ë flòlèã-øèê Ëÿ à Uª apple Á ÿapple E= Eyz ( x, t) z, B= Bz ( x, t) y 9. Ê ø apple h ªÊapple Ëÿ UÊapple Ë ÁòÊíÿÊ 0 cm ÃÕÊ flã ŸÊ.5 Ò Ë fl Ëÿ à U øê ŒË Ë Uà ø Êß ªß Ò Ã Îc U apple 6 cm ŸËøapple ÃÕÊ ˇÊ U, ͡ flê Ê È È Ê ÁSÕÃ Ò Ã fl Ëÿ-Œ áê apple Ÿ U apple È È apple Ë ÁÃÁ ê ŒÍ UË Ò +y -qv$ipdp Nrs L$fsp rhûysqy bl$ue sf N dpv $ rhûysn Ó A_ Qy bl$ue n Ó \i. E= Eyz ( x, t) z B= Bz ( x, t) y 9. 0 cm _u róäep ^fphsu A_.5 h¾$uch_p L$ ^fphsp Ágpk_p A L$ A^ Np mpl$pf cpn_u h¾$ k`pv$u `f Qp v$u_p Y$p m QY$phhpdp Aph g R>. s _u ku^u k`pv$u\u 6 cm _uq, A^ Np mpl$pf_u A v$f_p cpndp, A L$ lhp_p _p_p `f`p V$p s _u An `f fl g R>. Afukp Üpfp lhp_p `f`p V$p_p ârstbb_y õ\p v$ Mpi. () 4 cm below flat surface 0 cm below flat surface 0 cm below flat surface 6 cm below flat surface () à à apple 4 cm ŸËøapple à à apple 0 cm ŸËøapple à à apple 0 cm ŸËøapple à à apple 6 cm ŸËøapple () ku^u k`pv$u_u _uq 4 cm A sf ku^u k`pv$u_u _uq 0 cm A sf ku^ k`pv$u_u _uq 0 cm A sf ku^u k`pv$u_u _uq 6 cm A sf

17 Set Two stars are 0 light years away from the earth. They are seen through a telescope of objective diameter 0 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be ( light year= m) of the order of : () 0 6 km 0 8 km 0 km 0 0 km. A photoelectric surface is illuminated successively by monochromatic light of wavelengths λ and λ. If the maximum kinetic energy of the emitted photoelectrons in the second case is times that in the first case, the work function of the surface is : () hc λ hc λ hc λ hc λ 0. ŒÊapple ÃÊ appleu ÎâflË apple 0 Ê Ê-fl Ë ŒÍ UË U Ò Ÿ Êapple appleuá S Êapple mê UÊ ŒappleπÊ ÊÃÊ Ò, Á Ê Á ŒÎ ÿ 0 cm ÿê Ê Ò Ê Ê Ë Ã UªŒÒÉÿ 600 nm Ò ( Ê Ê-fl = m) Ò appleuá S Êapple ª U Ÿ ÃÊ UÊapple Êapple ª ª Áfl appleáœã Œappleπ Ê U Ê Ò, à Ÿ apple Ëø Ë ŒÍ UË Ê order Ò () 0 6 km 0 8 km 0 km 0 0 km. Ê Ê-flÒlÈà à U Ë Ê U λ ÃÕÊ ŒÍ UË Ê U λ à UªŒÒÉÿ Ê Ê Ê «UÊ Ê ÊÃÊ Ò ÿᜠà Á Ã Ê Ê-ß appleä UÊÚŸ Ë Áœ à ªÁà - Ê ŒÍ UË Ê U apple Ë Ê U Ë ÁÃªÈŸË Êapple, Ã Ã Ê Êÿ -» Ÿ Ò () hc λ hc λ hc λ hc λ 0. b spfpap ` Õhu\u 0 âl$pihj v $f R>. s Ap _ 0 cm ìepk ^fphsp Ap bs> ¼¹$V$uh (hõsy-g Þk) hpmp V $guõl$p `\u Å hpdp Aph R>. âl$pi_u sf Ng bpc 600 nm R>. Ap b spfp_ just R >V$p `X $gp (rhc qv$s \e gp) Å hp dpv $ s d_u hãq _y A sf p ¾$d_y lp hy Å CA. ( âl$pi hj = m) () 0 6 km 0 8 km 0 km 0 0 km. A L$ ap V$p Cg ¼V²$uL$ k`pv$u_ hpfpasu A_y¾$d λ A_ λ sf Ng bpc ^fphsp A L$f Nu âl$pi\u âl$pris L$fhpdp Aph R>. buå ql$õkpdp Å DÐkÅ sp ap V$p Cg ¼V²$p u dlñd Nrs EÅ â\d ql$õkp L$fsp ÓZ NZu dmsu lp e sp k`pv$u_y hl $a ¼i \i. () hc λ hc λ hc λ hc λ

18 Set A neutron moving with a speed v makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is : () 0. ev 6.8 ev. ev 0.4 ev. To get an output of from the circuit shown in figure the input must be :. ªÁà v apple ø ÃÊ È Ê ãÿí UÊÚŸ ÁSÕ U Êß «UÊapple Ÿ U ÊáÊÈ, Êapple ŸË Êl- flsõê apple Ò, apple ê Èπ UÄ U UÃÊ Ò ãÿè UÊÚŸ Ë fl ãÿíÿã ªÁÃ Ê ÃÊÿapple Á apple ÊappleŸapple U ÿ UÄ U àÿêsõ ÊappleªË () 0. ev 6.8 ev. ev 0.4 ev. ÁŒÿapple ªÿapple Á U Õ apple ÁŸª Êåà UŸapple apple Á ÿapple Êfl ÿ ÁŸflapple Ê ÊappleŸÊ øêá ÿapple. v S> V$gu TX$`\u Nrs L$fsp ÞeyV²$p _ A L$ [õ\f A_ ^fp[õ\rsdp fl gp lpcx²$p S>_ `fdpï kp\ ku^u A\X$pdZ A_ych R>. ÞeyV²$p u A[õ\rsõ\p`L$ A\X$pdZ \pe s dpv $_u dlñd NrsEÅ \i. () 0. ev 6.8 ev. ev 0.4 ev. ApL $rñdp v$ip h g `qf`\ dpv $ ApDV$`yV$ dm s dpv $ S>ê$fu C_`yV$ \i. () a=0, b=, c=0 a=, b=0, c=0 a=, b=0, c= a=0, b=0, c= () a=0, b=, c=0 a=, b=0, c=0 a=, b=0, c= a=0, b=0, c= () a=0, b=, c=0 a=, b=0, c=0 a=, b=0, c= a=0, b=0, c=

19 Set A modulated signal C m (t) has the form C m (t)=0 sin 00πt+0 (cos 00πt cos 400πt). The carrier frequency f c, the modulating frequency (message frequency) f ω, and the modulation index µ are respectively given by : () f c =00 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =0 Hz ; f c =00 Hz ; f ω =0 Hz ; µ= µ= µ= µ= 5. A particle of mass m is acted upon by a force R F given by the empirical law F= v(t). t If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot : () v(t) against t log v(t) against t log v(t) against t log v(t) against t 4. C m (t)=0 sin 00πt+0 (cos 00πt cos 400πt) Ê«ÈUÁ à Á ÇŸ Êapple Œ ÊÊ ÃÊ Ò Ã flê ÊflÎÁûÊ f c, Ê«ÈU ÊflÎÁûÊ f ω ÃÕÊ Ê«ÈU ߟ«appleUÄ µ Ê Ò () f c =00 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =0 Hz ; f c =00 Hz ; f ω =0 Hz ; µ= µ= µ= µ= 5. m Œ ÿ ÊŸ apple áê U F ª U Ê Ò, ÊÒ U apple Á ÿapple ÊŸÈ Áfl ê œ Ò F= v(t) ß ê œ apple àÿê Ÿ apple Á ÁSÕ U flsõê apple áê Ë ªÁÃ Ê appleˇêáê (Observation) U ÁŸêŸÁ Áπà apple apple ÊÒŸ Ê ª Ê» flêapple ûê ÊappleªÊ? () t apple ÁflL h v(t) t apple ÁflL h log v(t) t apple ÁflL h log v(t) t apple ÁflL h log v(t) R t 4. dp X$éygf (Ar^rdrîs) \e gp rká_g C m (t) _uq dys>b Ap`u il$pe R>. C m (t)=0 sin 00πt+0 (cos 00πt cos 400πt) L $fuef Aph rñ f c, k v$ ip (dp X$éyg V$]N) Aph rñ f ω, A_ dp X$éyg i_ A L$ (index) µ, A_y¾$d hx $ Ap`u il$pe. () f c =00 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =50 Hz ; f c =50 Hz ; f ω =0 Hz ; f c =00 Hz ; f ω =0 Hz ; µ= µ= µ= µ= 5. m v$m ^fphsp L$Z F= v(t) _ A_ykfsp F bm_u Akf l W$m R>. Å Ap bm-r_ed_ âpep rnl$ fus, L$Z_u Nrs [õ\f [õ\rsdp \u iê$ \pe s fus QL$pkhp lp e sp p N pa A kp \u kpfp rhl$ë` \i. () v(t) rhfyý^ t log v(t) rhfyý^ t log v(t) rhfyý^ t log v(t) rhfyý^ t R t

20 Set A thin m long rod has a radius of 5 mm. A force of 50 πkn is applied at one end to determine its Young s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.0 mm, which of the following statements is false? Y () gets minimum contribution Y from the uncertainty in the length. The figure of merit is the largest for the length of the rod. The maximum value of Y that can be determined is 0 4 N/m. Y gets its maximum contribution Y from the uncertainty in strain. 6. m ê Ë Ã Ë U«Ë ÁòÊíÿÊ 5 mm Ò ÿ ª Ê«U ÁŸ Ê Ÿapple apple Á ÿapple ß apple Á appleu U 50 πkn Ê ªÊÿÊ ªÿÊ ÊŸapple Á Á È UË apple ôêêã Ò ÿᜠê ÊßÿÊapple apple Ê Ÿ apple À Ê Ê 0.0 mm Ò Ã ÁŸêŸ apple apple ÊÒŸ Ê ÕŸ ª à Ò? Y () apple ê Êß Ë ÁŸÁ øããê Ê ÿêappleªœêÿ Y ãÿíÿã Ò U«Ë ê Êß apple Á ÿapple ŒˇÊÃÊ apple «Ê Ò Y Ê Áœ à Ê# Êapple Ÿapple flê Ê ÊŸ 0 4 N/m. Y apple Áfl Î ÁÃ Ë ÁŸÁ øããê Ê ÿêappleªœêÿ Y Áœ Ã Ò 6. m gp bp A_ 5 mm róäep ^fphsp A L$ `psmp krmep R>. s _p Y$ [õ\rsõ\p`l$sp A L$ (e N dp X$éygk) ip ^hp dpv $ s _p A L$ R> X$p D`f 50 πkn S> V$gy bm gnpx$hpdp Aph R>. A hy ^pfp L $ Ap bm_y d ëe kqp V$ fus dpg d R>. Å g bpc_p b^p S> dp`_dp goyñd dp` i[¼s 0.0 mm lp e sp _uq ` L$u_y L$ey rh^p_ Mp Vy $ li? () g bpc_u AQp ½$kpC_ L$pfZ apmp Aphsp li. Y dp goyñd Y krmep_u g bpc dpv $ v$nsp L$ (figure of merit) kp \u h^pf \i. d mhu il$pe s hu Y _u dlñd ql $ds 0 4 N/m \i. Y dp dlñd apmp rhl $rsdp fl g Y AQp ½$kpC_ L$pfZ li.

21 Set A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 divisions when R=400 Ω. Deflection becomes 0 divisions when resistance taken from resistance box is 4900 Ω. Then we can conclude : 7. ªappleÀflŸÊapple Ë U U Ë S apple 50 ʪÊapple apple UË Ò Ò U UË Ê Ê ÃÁ U Áà UÊappleœ ÊÍãÿ Ò ÿᜠR=400 Ω Ò ÃÊapple ÁflˇÊapple =40 ʪ Ò ÿᜠR=4900 Ω Ò ÃÊapple ÁflˇÊapple =0 ʪ Ò Ã ÁŸœÊ Á Uà U Ãapple Ò Á 7. N ëh _p duv$fdp 50 L$p`p R>. b V$fu_p Ap sqfl$ Ahfp ^ i Þe R>. Äepf =400 Ω lp e R> Ðepf N ëh _p duv$f dp 40 L$p`p (divisions) ky^u_y Aphs _ dm R>. Äepf Ahfp ^ ` V$udp \u 4900 Ω S> V$gp L$pY$hpdp Aph R> Ðepf 0 divisions S> V$gy Aphs _ \pe R>. sp Ap`Z spfz Ap`u il$ua L $. () Resistance of galvanometer is 00 Ω. Full scale deflection current is ma. Current sensitivity of galvanometer is 0 µa/division. Resistance required on R.B. for a deflection of 0 divisions is 9800 Ω. 8. To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are : () Two Three Four Five () ªappleÀflŸÊapple Ë U U Ê Áà UÊappleœ 00 Ω Ò»È -S apple ÁflˇÊapple apple Á ÿapple œê UÊ ma Ò ªappleÀflŸÊapple Ë U U Ë œê UÊ- flappleœÿ ÊË ÃÊ 0 µa Áà ʪ Ò ÁflˇÊapple =0 ʪ apple Á ÿapple R=9800 Ω. 8. Ê ø Ë S Ò Ê ø - Êß ÊappleS Êapple mê UÊ flã ŸÊ ÁŸ Ê Ÿapple apple Á ÿapple M UË Ê ÿê Êapple Ë ãÿíÿã ÅÿÊ Ò () ŒÊapple ÃËŸ øê U Ê ø () N ëh _p duv$f_p Ahfp ^ 00 Ω li. ` Z -õl $g Aphs _ dpv $ âhpl ma li. N ëh _p duv$f_u ` hpl k h qv$sp 0 µa/division \i. 0 divisions S> V$gy Aphs _ d mhhp dpv $ Ahfp ^ ` V$udp Ahfp ^_y d ëe 9800 Ω Å Ci. 8. V²$ph g]n dpc¾$p õl$p `_u dv$v$\u Ágpk_p Qp kgp_p h¾$uch_p L$ dp`hp dpv $ Ap R>pdp Ap R>p S>ê$fu Ahgp L$_p _u k ep li. () b ÓZ Qpf `p Q

22 Set A realistic graph depicting the variation of the reciprocal of input resistance in an input characteristics measurement in a commonemitter transistor configuration is : 9. UÊ Á S U U Ê common-emitter (CE) Á ÁflãÿÊ apple ÁŸflapple Ê- Á ÊˇÊÁáÊ Ê Ÿ Á ÿê ªÿÊ Ã ÁŸflapple Ê- Áà UÊappleœ apple ÿèà Ê ÁŸêŸ apple apple ÊÒŸ- Ê ª Ê» Áøà Ò? 9. A L$ V²$p[ÞTõV$f_p common emitter (CE) k fq_pdp C_`yV$ gpnrzl$sp dpv $ C_`yV$ Ahfp ^_p ìeõs_p kp \u h^y hpõsrhl$ N pa \i. () () ()

23 Set The ratio (R) of output resistance r 0, and the input resistance r i in measurements of input and output characteristics of a transistor is typically in the range : () R~0 0 R~ 0 R~ R~0..0. The volume of 0.N dibasic acid sufficient to neutralize g of a base that furnishes 0.04 mole of OH in aqueous solution is : () 00 ml 400 ml 600 ml 800 ml 0. Á Ë UÊ Á S U U Ë ÁŸflapple Ê-ÁŸª Á ÊˇÊÁáÊ Ê Ÿapple apple Á ÿapple ÿèäã ÁŸª - Áà UÊappleœ (r 0 ) fl ÁŸflapple Ê- Áà UÊappleœ (r i ) apple ŸÈ Êà (R) Ê ÊÿÊ (range) ÊappleªÊ? () R~0 0 R~ 0 R~ R~ N ÁmˇÊÊ UËÿ ê Ê Êÿß ÄÿÊ ÊappleªÊ Êapple ª Ê ˇÊÊ U Á apple Ëÿ Áfl ÿÿ apple 0.04 Êapple OH Ò Êapple ŒÊ ËŸ UŸapple apple Á ÿapple ÿê # Ò? () 00 ml 400 ml 600 ml 800 ml 0. V²$p[ÞTõV$f_u C_`yV$ A_ ApDV$`yV$ gpnrzl$sp_p dp`_dp ApDV$`yV$ Ahfp ^ r 0 A_ C_`yV$ Ahfp ^ r i _p NyZp Ñf (R) S> V$gu f ÞS>dp lp e R>. () R~0 0 R~ 0 R~ R~ N X$peb rtl$ A rkx$_y L$v$ iy li L $ S> g b CT_p sv$õ\ul$fz L$fhp dpv $ `ep á lp e L $ S> _p S>gue ÖphZdp 0.04 dp g OH Aph gp R>? () 00 ml 400 ml 600 ml 800 ml

24 Set Initially, the root mean square (rms) velocity of N molecules at certain temperature is u. If this temperature is doubled and all the nitrogen molecules dissociate into nitrogen atoms, then the new rms velocity will be : () u/ u 4u 4u. Aqueous solution of which salt will not contain ions with the electronic configuration s s p 6 s p 6? () NaF NaCl KBr CaI 4. The bond angle H-X-H is the greatest in the compound : () CH 4 NH H O PH. Áfl Êapple ÃÊ U Ê Uê apple ŸÊß UÊapple Ÿ áêè Êapple (N ) Ê flª Êäÿ Í flappleª u Ò ÿáœ ß ÃÊ Êapple ŒÈªÈŸÊ U ÁŒÿÊ Êÿ ÊÒ U Ë ŸÊß UÊapple Ÿ áêè ÁflÿÊappleÁ à Êapple U ŸÊß UÊapple Ÿ U ÊáÊÈ Ÿ Ê ÃÊapple ŸÿÊ flª Êäÿ Í flappleª ÊappleªÊ () u/ u 4u 4u. Á fláê apple Ëÿ Áfl ÿÿ apple s s p 6 s p 6 ß appleä UÊÚÁŸ ÁflãÿÊ apple ÊÿŸ Ÿ Ë Êapple ªapple? () NaF NaCl KBr CaI 4. Á ÿêò᪠apple H-X-H Ê ãœ ÊappleáÊ flê Áœ Ò? () CH 4 NH H O PH. r_ròs sp`dp_ `f, iê$apsdp, N AÏAp _p kf fpi hn d m (root mean square) (rms) h N u R>. Å Ap sp`dp_ bdï (Doubled) L$fhpdp Aph sp b^p S> _pcv²$p S>_ AÏAp _y rhep S> pcv²$p S>_ `fdpïap dp \pe sp, `R>u _hy kf fpi hn d m (rms) h N iy \i? () u/ u 4u 4u. Cg ¼V²$p r_l$ rhþepk s s p 6 s p 6 ^fphsp L$ep npf_y S>gue ÖphZ Ape_p ^fphsp _\u? () NaF NaCl KBr CaI 4. L$ep k ep S>_dp H-X-H b ^M Zp khp r^l$ R>? () CH 4 NH H O PH

25 Set If 00 mole of H O decompose at bar and 00 K, the work done (kj) by one mole of O (g) as it expands against bar pressure is : HO (l) HO(l) + O (g) (R = 8. J K mol ) () An aqueous solution of a salt MX at certain temperature has a van t Hoff factor of. The degree of dissociation for this solution of the salt is : () ÿᜠH O apple 00 Êapple bar ÃÕÊ 00 K U ÁflÿÊappleÁ à Êapple ÃÊapple bar ŒÊ apple ÁflL h Êapple ÊÚÄ Ë Ÿ apple ÁflSÃÊÁ Uà ÊappleŸapple U Á ÿê È Ê Êÿ (kj apple ) ÊappleªÊ HO (l) HO(l) + O (g) (R = 8. J K mol ) () Á Ë Áfl Êapple ÃÊ U, fláê MX apple Ëÿ Áfl ÿÿ Ê flêã U ÊÚ»»Ò Ä U U Ò fláê apple ß Áfl ÿÿ apple Á ÁflÿÊapple Ÿ ÊòÊÊ ÊappleªË () Å H O _p 00 dp g bpf (bar) A_ 00 K `f rhov$us \pe sp, bpf (bar) v$bpz_p rhfyý^ dp g O (g) _p rhõsfz \hp_ gu^ \e g L$pe (kj) ip ^p. HO (l) HO(l) + O (g) (R = 8. J K mol ) () A L$ r_ròs sp`dp_ `f, npf MX _p S>gue ÖphZ_p hpþv$-lp a Aheh R>. sp npf_p Ap ÖphZ_p rhep S>_A i ip ^p. () A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperature T. The equilibrium pressure is 0 bar in this vessel. K p for this reaction is : () Œ ( ËÀ«U) ÁŸflÊ ÁÃà ÊòÊ apple UπÊ ªÿÊ UÊapple XY ÁflÉÊÁ Uà Êapple U ÃÊ T U ŒÊapple ªÒ apple X ÃÕÊ Y Ê Á üêáê ŸÊÃÊ Ò ß ÊòÊ apple Êêÿ ŒÊ 0 bar Ò ß Á Á ÿê apple Á ÿapple K p ÊappleªÊ () A L$ b ^ (sealed) r_hp rss (evacuated) `pódp fpmhpdp Aph g O_ (solid) XY rhov$us \C_ T sp`dp_ hpeyap _y rdîz X A_ Y b_ R>. Ap `pódp k syg_ v$bpz 0 bar (bpf) R>. Ap âq¾$ep dpv $ K p iy R>? ()

26 Set Oxidation of succinate ion produces ethylene and carbon dioxide gases. On passing 0. Faraday electricity through an aqueous solution of potassium succinate, the total volume of gases (at both cathode and anode) at STP ( atm and 7 K) is : ().4 L 4.48 L 6.7 L 8.96 L 9. The rate law for the reaction below is given by the expression k [A][B] A+B Product If the concentration of B is increased from 0. to 0. mole, keeping the value of A at 0. mole, the rate constant will be : () k k/ k 9k 8. ÁÄ Ÿapple U ÊÿŸ apple ÊÚÄ Ë UáÊ apple ÁÕ ËŸ ÃÕÊ Ê Ÿ «UÊß ÊÚÄ Êß«U ªÒ apple ŸÃË Ò Êapple Ò UÁ Êÿ ÁÄ Ÿapple U apple Ëÿ Áfl ÿÿ apple 0.»Ò UÊ«appleU ÁfllÈà flêá à UŸapple U ªÒ Êapple Ê È Êÿß ( Ò ÕÊapple«U ÃÕÊ ŸÊapple«U ŒÊappleŸÊapple U) STP ( atm ÃÕÊ 7 K) U ÊappleªÊ ().4 L 4.48 L 6.7 L 8.96 L 9. ŸËøapple ŒË ªß Á Á ÿê apple Á Œ U ÁŸÿ k [A][B] ÿ apple ÿäã Á ÿê ÊÃÊ Ò A+B à ÊŒ A Ë Ê㌠ÃÊ Ê ÊŸ 0. Êapple U UπÃapple È ÿᜠB Ë Ê㌠ÃÊ 0. apple Ê U 0. Êapple U ŒË ÊÃË Ò ÃÊapple Œ U ÁSÕ UÊ ÊappleªÊ () k k/ k 9k 8. k[¼k_ V$ Ape p Ap [¼kX $i_\u Cr\gu_ A_ L$pb _ X$pep ¼kpCX$ hpeyap DÐ`Þ_ \pe R>. `p V $ried k[¼k_ V$_p S>gue ÖphZdp 0. a fpx $ rhûysâhpl `kpf L$fsp, STP `f ( atm A_ 7 K) A hpey_p _y Ly$g L$v$ (L $\p X$ A_ A _p X$ b _ `f) ip ^p. ().4 L 4.48 L 6.7 L 8.96 L 9. _uq Ap` g âq¾$ep dpv $_p h N-r_ed k [A][B] ìe S>L$ \u ìe¼s (expression) L$f g R>. A+B _u`s> A _u kp Ösp 0. mole (dp g) fpmua A_ Å B _u kp Ösp 0. \u h^pfu_ 0. dp g L$fhpdp Aph sp h NAQmp L$ iy li? () k k/ k 9k 40. L $V$gpL$ L$rggp _p õhzp L$ (Np ëx$ _ bf) Ap âdpz R>. Æg V$u_ (Gelatin) : , Nd Af rbl$ (Gum Arabic) : ; Ap rga V$$ 40. Gold numbers of some colloids are : Gelatin : , Gum 40. È U Êapple Êß«UÊapple apple SfláÊÊZ Ò, Á appleá UŸ Arabic : ; Oleate : ; , ª appleuá ; Starch : 5-5. Which among these is a ÊappleÁ U ; S UÊø 5-5, ߟ apple ÊÒŸbetter protective colloid? Ê apple à U UˇÊË Êapple Êÿ«U ÊappleªÊ? () Gelatin () Á appleá UŸ Gum Arabic () Æg V$u_ (Gelatin) Oleate ª appleuá Nd Af rbl$ (Gum Arabic) Starch ÊappleÁ U Ap rga V$ (Oleate) S UÊø õv$pq (Starch) (Oleate) : ; õv$pq (Starch) : 5-5. Apdp \u L$ep kp \u h^pfp kpfp frns L$rgg R>?

27 Set The following statements concern elements in the periodic table. Which of the following is true? () All the elements in Group 7 are gases. The Group elements are all metals. Elements of Group 6 have lower ionization enthalpy values compared to those of Group 5 in the corresponding periods. For Group 5 elements, the stability of +5 oxidation state increases down the group. 4. Extraction of copper by smelting uses silica as an additive to remove : () Cu S FeO FeS Cu O 4. ÁŸêŸ ÕŸ Êflà ÃÊÁ Ê apple ÁSÕà ÃàflÊapple apple ê ÁœÃ Ò ÁŸêŸ apple apple ÊÒŸ- Ê àÿ Ò? () ª È 7 apple Ë Ãàfl ªÒ Ò ª È apple Ë Ãàfl œêãè Ò ª È 5 apple ÃàflÊapple Ë ÃÈ ŸÊ apple ªÃ Êflà apple ª È 6 apple ÃàflÊapple apple ÊÿŸŸ ãõòà Ë Ê ÊŸ U ÃÊ Ò ª È 5 apple ÃàflÊapple apple Á, ª È apple ŸËøapple ÊŸapple U +5 ÊÚÄ Ë UáÊ flsõê Ê SÕÊÁÿàfl ÃÊ Ò 4. S appleáà Uª mê UÊ ÊÚ U apple ÁŸc áê apple Á Á Ê ÿêappleíÿ apple M apple ÁŸêŸ apple apple Á Êapple UÊŸapple apple Á Ë ÊÃË Ò? () Cu S FeO FeS Cu O 4. _uq _p rh^p_p Aphs L$p ô$dp _p sòhp _ k b r^s R>. _uq _pdp \u L$ey kpqy R>? () kd l 7 dp b^p S> sòhp hpeyap R>. kd l dp b^p S> sòhp ^psyap R>. Aphs _ A_ygnu_ kd l 5 _p sòhp _u syg_pdp kd l 6 _p sòhp _u â\d Ape_uL$fZ A Þ\pë`u Ap R>u R>. kd l 5 _p sòhp dpv $, kd ldp _uq S>CA s d +5 Ap [¼kX $i_ Ahõ\p_u [õ\fsp h^ R>. 4. âöphz (smelting) Üpfp L$p `f_y r_ól$j Z L$fsu hms Dd f g rkrgl$p_p D`ep N _uq _pdp \u iy v $f L$fhp \pe R>? () Cu S FeO FeS Cu O 4. Identify the reaction which does not liberate hydrogen : () Reaction of zinc with aqueous alkali. Electrolysis of acidified water using Pt electrodes. Allowing a solution of sodium in liquid ammonia to stand. Reaction of lithium hydride with B H Á Á ÿê Êapple ÃÊß Á apple Êß«UÊapple Ÿ à Á à Ÿ Ë ÊappleÃË Ò () Ëÿ ˇÊÊ U apple ÊÕ Á Ë Á Á ÿê å appleá UŸ ß appleä UÊapple«UÊapple Ê ÿêappleª U apple ê Ë Î Ã Ê ÁfllÈà ÉÊ UŸ Œ fl ÊappleÁŸÿÊ apple ÊappleÁ«Uÿ apple Áfl ÿÿ Êapple ÁSÕ U ÊappleŸapple apple Á UÊapple«ŒappleŸÊ B H 6 apple ÊÕ ËÁÕÿ Êß«UÊß«U Ë Á Á ÿê 4. âq¾$ep Ap mmu bsphp L $ S> dp lpcx²$p S>_ DÐkS> _ \sp _\u. () S>gue ApëL$gu_u T]L$ kp\ _u âq¾$ep Pt Cg ¼V²$p X$p _p D`ep N L$fu_ A rkqx$l$ `pzu_y rhûysrhcps>_ âhplu A dp r_epdp kp qx$ed_p ÖphZ_ fpmu_ R>p X$u v$ hy B H 6 kp\ rgr\ed lpcx²$pcx$_u âq¾$ep

28 Set The commercial name for calcium oxide is : () Milk of lime Slaked lime Limestone Quick lime 45. Assertion : Among the carbon allotropes, diamond is an insulator, whereas, graphite is a good conductor of electricity. Reason : Hybridization of carbon in diamond and graphite are sp and sp, respectively. () Both assertion and reason are correct, and the reason is the correct explanation for the assertion. Both assertion and reason are correct, but the reason is not the correct explanation for the assertion. Assertion is incorrect statement, but the reason is correct. Both assertion and reason are incorrect. 46. Identify the incorrect statement : () S is paramagnetic like oxygen. Rhombic and monoclinic sulphur have S 8 molecules. S 8 ring has a crown shape. The S-S-S bond angles in the S 8 and S 6 rings are the same. 44. Ò ÁÀ Êÿ ÊÚÄ Êß«U Ê ÿêfl ÊÁÿ ŸÊ Ò () Á À ÊÚ» Êß S ÒÄ«U Êß Êß S UÊappleŸ ÁÄfl Êß 45. ÕŸ Ê Ÿ apple UM Êapple apple, «UÊÿ «U È øê Ò Á ª apple» Êß U ÁfllÈà ÈøÊ Ò Ê UáÊ «UÊÿ ã«u ÃÕÊ ª apple» Êß U apple Ê Ÿ Ê UáÊ Ê sp ÃÕÊ sp Ò () ÕŸ ÃÕÊ Ê UáÊ ŒÊappleŸÊapple Ë Ò ÃÕÊ Ê UáÊ ÕŸ Ë Ë ÿêåÿê Ò ÕŸ ÃÕÊ Ê UáÊ ŒÊappleŸÊapple Ë Ò UãÃÈ Ê UáÊ, ÕŸ Ë Ë ÿêåÿê Ÿ Ë Ò ÕŸ àÿ Ò UãÃÈ Ê UáÊ àÿ Ò ÕŸ ÃÕÊ Ê UáÊ ŒÊappleŸÊapple Ë àÿ Ò 46. àÿ ÕŸ Êapple øêáÿ () ÊÚÄ Ë Ÿ Ë Ã U S ŸÈøÈê Ëÿ Ò UÊÁê (Áfl ÊˇÊ) ÃÕÊ ÊappleŸÊappleÄ ËÁŸ À» U apple S 8 áêè Ò S 8 fl ÿ Ê Ê Ê U È È U Ë Ã U Ò S 8 ÃÕÊ S 6 fl ÿêapple apple S-S-S Ê ãœ ÊappleáÊ Ò apple Ò 44. L $ëiued Ap ¼kpCX$_y ìep`pfu ^p fz _pd Ap`p. () v $r^ep Q _p (rdël$ Ap a gpcd) (Milk of lime) ap X $gp Q _p (Slaked lime) Q _p_p `Õ\f (Limestone) L$mu Q _p (Quick lime) 45. L$\_ : L$pb p blºê$`p dp, lufp A AhplL$ R> Äepf N apcv$ A rhûys_p kyhpll$ R>. L$pfZ : lufpdp A_ N apcv$dp L$pb y k L$fZ A_y¾d sp A_ sp R>. () L$\_ A_ L$pfZ b _ kpqp R>, s\p L$pfZ A L$\_ dpv $_u kpqu kds >su R>. L$\_ A_ L$pfZ b _ kpqp R>, `Z L$pfZ A L$\_ dpv $_u kpqu kds >su _\u. L$\_ A AkÐe rh^p_ R>. `Z L$pfZ kðe R>. L$\_ A_ L$pfZ b _ AkÐe R>. 46. Mp Vy $ rh^p_ ip ^u bsphp. () S A Ap [¼kS> u dpal$ A_yQy bl$ue R>. f¹lp [çbl$ A_ dp _p [¼gr_L$ këafdp S 8 AÏAp R>. S 8 hge_p ApL$pf dynv$ (¾$pD_) S> hp R>. S 8 A_ S 6 hgep dp S-S-S b ^ M ZpAp A L$kfMp R>.

29 Set Identify the correct statement : () Iron corrodes in oxygen-free water. Iron corrodes more rapidly in salt water because its electrochemical potential is higher. Corrosion of iron can be minimized by forming a contact with another metal with a higher reduction potential. Corrosion of iron can be minimized by forming an impermeable barrier at its surface. 48. Which of the following is an example of homoleptic complex? () [Co(NH ) 6 ]Cl [Pt(NH ) Cl ] [Co(NH ) 4 Cl ] [Co(NH ) 5 Cl]Cl 49. The transition metal ions responsible for color in ruby and emerald are, respectively : () Cr + and Co + Co + and Cr + Co + and Co + Cr + and Cr Ë ÕŸ Êapple øêáÿÿapple () Êÿ UŸ ÊÚÄ Ë Ÿ- ÈÄà apple ˇÊÊÁ Uà ÊappleÃÊ Ò fláêëÿ apple Êÿ UŸ ÀŒË apple ˇÊÊÁ Uà ÊappleÃÊ Ò ÄÿÊapple Á ß Ê ÁfllÈà UÊ ÊÿÁŸ Áfl fl ìê Ò Êÿ UŸ Ê ˇÊÊ UáÊ ß Êapple ìê øÿÿ Áfl fl flê apple œêãè apple ê apple ÊŸapple U Á ÿê Ê ÃÊ Ò Êÿ UŸ Ê ˇÊÊ UáÊ ß apple à U Ê Uªêÿ fl UÊappleœ ŸÊ U Á ÿê Ê ÃÊ Ò 48. ÁŸêŸ apple apple ÊÒŸ Êapple Êapple appleáå U (homoleptic) È Ê ŒÊ UáÊ Ò? () [Co(NH ) 6 ]Cl [Pt(NH ) Cl ] [Co(NH ) 4 Cl ] [Co(NH ) 5 Cl]Cl 49. M Ë fl ß apple UÊÀ«U apple Á Ÿ áê œêãè Êapple apple ÊÿŸÊapple Ë ÁSÕÁà apple Ê UáÊ Uª ÊappleÃÊ Ò, flapple Ê Ò () Cr + ÃÕÊ Co + Co + ÃÕÊ Cr + Co + ÃÕÊ Co + Cr + ÃÕÊ Cr kpqy rh^p_ ip ^p. () Ape_ (gp M X$) Ap [¼kS>_-dy¼s `pzudp npqfs \pe R>. npfhpmp `pzudp Ape_ (gp M X$) M b S> TX$`\u npqfs \pe R> L$pfZ L $ s _p rhûysfpkperzl$ `p V $[Þieg KQp R>. Ape_ (gp M X$) _y npfz, Äepf s _p buæ KQp fux$n_ `p V $[Þieg ^fphsu ^psy kp\ k `L $ L$fsp Ap Ry> L$fu il$pe R>. Ape_ (gp M X$) _y npfz, s _u k`pv$u `f A`pfNçe Ahfp ^ b_phu_ Ap Ry> L$fu il$pe R>. 48. _uq Ap` gpap dp \u L$ey A L$ lp dp g àv$ul$ (homoleptic) kdp_ul $s k L$uZ _y Dv$plfZ R>? () [Co(NH ) 6 ]Cl [Pt(NH ) Cl ] [Co(NH ) 4 Cl ] [Co(NH ) 5 Cl]Cl 49. dpz L$ (Ruby) A_ `Þ_p (emerald) dp f Np dpv $ S>hpbv$pf k ¾$p rs ^psy Ape_p A_y¾$d _uq _pdp \u ip ^p. () Cr + A_ Co + Co + A_ Cr + Co + A_ Co + Cr + A_ Cr +

30 Set Which one of the following substances used in dry cleaning is a better strategy to control environmental pollution? () Tetrachloroethylene Carbon dioxide Sulphur dioxide Nitrogen dioxide 5. Sodium extract is heated with concentrated HNO before testing for halogens because : () Silver halides are totally insoluble in nitric acid. Ag S and AgCN are soluble in acidic medium. S and CN, if present, are decomposed by conc. HNO and hence do not interfere in the test. Ag reacts faster with halides in acidic medium. 50. «UÊß Ä ËÁŸ ª apple ÿèäã ÁŸêŸ ŒÊÕÊappleZ apple apple Á Ê ÿêappleª flêãêfl UáÊ ŒÍ áê apple ÁŸÿ òêáê Ë apple à U Êÿ ŸËÁà Ò? () appleu UÊÄ Êapple UÊapple ÁÕ ËŸ Ê Ÿ «UÊß ÊÚÄ Êß«U À» U «UÊß ÊÚÄ Êß«U ŸÊß UÊapple Ÿ «UÊß ÊÚÄ Êß«U 5. Ò Êapple Ÿ Ë Ê ø apple apple ÊappleÁ«Uÿ ÄS ÒUÄ U Êapple Ê㌠HNO apple ÊÕ ª Á ÿê ÊÃÊ Ò ÄÿÊapple Á () Á Àfl U Ò Êß«U ŸÊßÁ U ê apple ÍáÊ M appleáê ÉÊÈ Ÿ ÊË Ò ê Ëÿ Êäÿ apple Ag S ÃÕÊ AgCN ÉÊÈ Ÿ ÊË Ò ÿᜠS ÃÕÊ CN ÁSÕÃ Ò ÃÊapple Ê㌠HNO apple ÁflÉÊÁ Uà Êapple ÊÃapple Ò ß Á ÿapple UˡÊáÊ apple SÃˇÊapple Ÿ Ë UÃapple ê Ëÿ Êäÿ apple Á Àfl U, Ò Êß«UÊapple apple ÊÕ Ãapple Á Á ÿê UÃÊ Ò 50. X²$pe¼gu_]Ndp _uq Ap` gp `v$p\p dp \u L$ep A L$_p D`ep N hpsphfzue âv $jz_ r_e ÓZ L$fhpdp h^y L$pe nd R>? () V $V²$p¼gp fp Cr\rg_ L$pb _ X$pep ¼kpCX këaf X$pep ¼kpCX$ _pcv²$p S>_ X$pep ¼kpCX$ 5. l gp S>_p _u L$kp V$u L$fsp `l gp kp qx$ed AL $ (extract) _ kp Ö HNO _u kp\ Nfd L$fhpdp Aph R> L$pfZ L $... () rkëhf l gpcx$p _pcv²$ul$ A rkxdp k ` Z fus AÖpìe R>. A rkqx$l$ dpýeddp Ag S A_ AgCN Öpìe \pe R>. Å S A_ CN lps>f lp e sp kp Ö HNO \u rhov$_ \pe R>. s \u `funzdp (L$kp V$udp ) v$mgnufu L$fsp _\u. A rkqx$l$ dpýeddp Ag _u âq¾$ep l gpcx$p kp\ TX$`u \pe R>.

31 Set Bromination of cyclohexene under conditions given below yields : 5. ŸËøapple ÁŒÿapple ªÿapple Áà ãœêapple apple ÊßÄ Êapple appleä ËŸ Ê Êapple ËŸapple ÊŸ ŒappleÃÊ Ò 5. kpe¼gp l ¼Tu y b p rd_ i_ Ap` g _uq _u `qf[õ\rsap dp L$C _u`s> Ap`i? Br /hν Br /hν Br /hν Br Br Br () () () Br Br Br Br Br Br Br Br Br Br Br Br Br Br Br Br Br Br

32 Set Consider the reaction sequence below : 5. ŸËøapple ŒË ªß Á Á ÿê U ÁfløÊ U ËÁ 5. _uq Ap` g âq¾$ep_p ¾$d Ýep_dp gp. OCH OCH OCH X X is : Ò X iy R>? H CO OH H CO OH H CO OH () OH () OH () OH OCH OH OCH OH OCH OH OH OH OCH OCH OCH OH

33 Set - 0 H CO H CO H CO 54. Which one of the following reagents is not suitable for the elimination reaction? Br () NaOH/H O NaOEt/EtOH NaOH/H O-EtOH NaI 55. The correct statement about the synthesis of erythritol (C(CH OH) 4 ) used in the preparation of PETN is : () The synthesis requires four aldol condensations between methanol and ethanol. The synthesis requires two aldol condensations and two Cannizzaro reactions. The synthesis requires three aldol condensations and one Cannizzaro reaction. Alpha hydrogens of ethanol and methanol are involved in this reaction. 54. Áfl Êapple Ÿ Á Á ÿê apple Á ߟ Á Ê U Êapple apple apple ÊÒŸ- Ê ÿèäã Ÿ Ë Ò? 54. _uq Ap` gpdp \u L$ep âq¾$el$ A rhgp `_ âq¾$ep dpv $ kyk Ns _\u? Br () NaOH/H O NaOEt/EtOH NaOH/H O-EtOH NaI 55. PETN apple ŸÊŸapple apple ÿèäã ß UËÁÕ UÊÚ (C(CH OH) 4 ) apple apple áê apple ê 㜠apple Ë ÕŸ Ò () apple áê apple appleõappleÿêú ÃÕÊ ÕappleŸÊÚ apple Ëø øê U À«UÊapple ÉÊŸŸ Ë Êfl ÿ ÃÊ ÊappleÃË Ò apple áê apple ŒÊapple À«UÊapple ÉÊŸŸ ÃÕÊ ŒÊapple Ò ÁŸ Ê UÊapple Á Á ÿê Ë M Uà ÊappleÃË Ò apple áê apple ÃËŸ À«UÊapple ÉÊŸŸ ÃÕÊ Ò ÁŸ Ê UÊapple Á Á ÿê Ë Êfl ÿ ÃÊ ÊappleÃË Ò ß Á Á ÿê apple ÕappleŸÊÚ apple À» Ê Êß«UÊapple Ÿ ÃÕÊ appleõappleÿêú ʪ appleãapple Ò Br () NaOH/H O NaOEt/EtOH NaOH/H O-EtOH NaI 55. PETN _u b_phv$dp h`fpsp Cfu\ uv$p g (C(CH OH) 4 ) _p k ïg jz dpv $ L$ey rh^p_ kpqy R>? () k ïg jz dpv $ rd\ _p g A_ C\ _p g_u hãq Qpf ApëX$p g k O u AphíeL$sp lp e R>. k ïg jzdp b ApëX$p g k O A_ b L $r_tpfp âq¾$ep_u AphíeL$sp R>. k ïg jzdp ÓZ ApëX$p g k O A_ A L$ L $r_tpfp âq¾$ep_u AphíeL$sp R>. Ap âq¾$epdp C\ _p g_p Apëap lpcx²$p S>_ A_ rd\ _p g cpn g R>.

34 Set Fluorination of an aromatic ring is easily accomplished by treating a diazonium salt with HBF 4. Which of the following conditions is correct about this reaction? () Only heat NaNO /Cu Cu O/H O NaF/Cu 57. Which of the following polymers is synthesized using a free radical polymerization technique? () Teflon Terylene Melamine polymer Nylon 6,6 58. The N which does not contribute to the basicity for the compound is : N 6 N 5 () N 7 N 9 N N 7 N 8 4 N 9 H 56. Á Ë UÊÒ ÒÁ U fl ÿ Ê ç È Êapple UË UáÊ Ê ÊŸË apple fl ÊappleÃÊ Ò ÿᜠapple «UÊß ÊappleÁŸÿ fláê Êapple HBF 4 apple ÊÕ øêá Uà Á ÿê Êÿ ß Á Á ÿê apple ê 㜠apple ÁŸêŸÁ Áπà apple apple ÊÒŸ Ë Á UÁSÕÁà ÿèäã Ò? () apple fl c Ê NaNO /Cu Cu O/H O NaF/Cu 57. ÁŸêŸÁ Áπà apple apple ÊÒŸ- Ê È ÈÄÃ Í È Ë UáÊ ÁflÁœ mê UÊ appleá à Á ÿê ÊÃÊ Ò? () appleuç ÊÚŸ ÒU UË ËŸ Ò Ò Êߟ È ŸÊÿ ÊÚŸ 6,6 58. fl N Êapple ÁŸêŸ ÿêòáª Ë ˇÊÊ UËÿ flîáûê apple ÿêappleªœêÿ Ÿ Ë ŒappleÃÊ Ò, fl Ò N 6 N 5 () N 7 N 9 N N 8 4 N 9 H 56. L$p C A fp d qv$l$ hge_y ãgp qf_ i_ M b S> kl gpc\u k ch lp e R>, Äepf s _p X$peTp _ued npf_ HBF 4 kp\ âq¾$ep L$fhpdp Aph R>. D`f_u ` q¾$ep dpv $ _uq _p Ap` gpdp \u L$C `qf[õ\rs kpqu R>? () a¼s Dódp NaNO /Cu Cu O/H O NaF/Cu 57. _uq Ap` gpdp \u L$ep blºgl$_y k ïg jz A dy¼s dygl$ blºgul$fz sl$_ul$_p D`ep N L$fu_ L$fhpdp Aph R>? () V $agp _ V $qfrg_ d g dpc_ blºgl$ _pegp _ 6,6 58. N L $ S> Ap` g k ep S> u b rtl$spdp cpn g sp _\u s bsphp. 7 N N 6 N 5 () N 7 N 9 N N 7 N 8 4 N 9 H

35 Set Which of the following is a bactericidal antibiotic? () Erythromycin Tetracycline Chloramphenicol Ofloxacin 60. Observation of Rhumann s purple is a confirmatory test for the presence of : () Reducing sugar Cupric ion Protein Starch 6. Let P = { θ : sinθ cosθ = cos θ } and Q = { θ : sinθ + cosθ = sin θ } be two sets. Then : () P Q and Q P φ Q P P Q P = Q 59. ÁŸêŸ apple apple ÊÒŸ- Ê ÒÄ UËÁ UÿÊŸÊ ÊË Áà ÒÁfl Ò? () Á UÕ Êapple Êß ËŸ appleu UÊ ÊÿÄ ËŸ Ä Êapple U ê»ò ÁŸ Ê ÊÚ» ÊappleÄ Ò ËŸ 60. L ÒŸ ŸË ÊappleÁ à ( ) Ê U ÊappleŸÊ ÁŸêŸÁ Áπà apple apple Á Ê ÈÁc U UˡÊáÊ Ò? () øêÿ Ê UÊ ÄÿÍ Á U ÊÿŸ Êapple UËŸ S UÊø ( «U) 6. ÊŸÊ P = { θ : sinθ cosθ = cos θ } ÃÕÊ Q = { θ : sinθ + cosθ = sin θ } ŒÊapple Èëøÿ Ò, ÃÊapple () P Q ÃÕÊ Q P φ Q P P Q P = Q 59. _uq _pdp \u L$ey A L$ b ¼V $qfep_pil$ ârsæhuap (antibiotic) R>? () Cqf\ p dpeku_ V $V²$pkpe¼gu_ ¼gp fa ça r_l$p g Ap ãgp ¼k rk_ 60. ""fyldp_ Å byx$uep ''(`` g) (Rhumann s purple) Ahgp L$_ A r_zp el$ L$kp V$u _uq _pdp \u L$p _u lps>fu k Qh R>? () fux$éyk]n il $fp ¼eyâuL$ Ape_ âp V$u_ õv$pq 6. ^pfp L $ P = { θ : sinθ cosθ = cos θ } A_ Q = { θ : sinθ + cosθ = sin θ } b NZp R>. sp : () P Q A_ Q P φ Q P P Q P = Q

36 Set If x is a solution of the equation, x + x =, x, then () 4 x is equal to : 4 6. ÿáœ Ë UáÊ x x, x, + = Ê x Ò, ÃÊapple 4 x UÊ U Ò () 4 6. Å kdul$fz x x, x + = _p A L$ DL $g x R>, sp 4 x () 4 = \pe. 6. Let z=+ai be a complex number, a > 0, such that z is a real number. Then the sum +z+z +...+z is equal to : () 50 i 50 i 65 i 65 i 6. ÊŸÊ z=+ai, a > 0 apple Ë Áê üê ÅÿÊ Ò, Á z flêsãáfl ÅÿÊ Ò, ÃÊapple ÿêappleª +z+z +...+z UÊ U Ò () 50 i 50 i 65 i 65 i 6. ^pfp L $ z=+ai, a > 0, A L$ A hu k L$f k ep R> L $ S> \u z hpõsrhl$ k ep \pe. sp kfhpmp +z+z +...+z = \pe. () 50 i 50 i 65 i 65 i

37 Set Let A be a matrix such that A 5A+7I=O. Statement - I : A = (5I A ). 7 Statement - II : The polynomial A A A+I can be reduced to 5(A 4I). Then : () Statement-I is true, but Statement-II is false. Statement-I is false, but Statement-II is true. Both the statements are true. Both the statements are false If A =, then the determinant of the matrix (A 06 A 05 A 04 ) is : () ÊŸÊ A, Ê apple Ê Ê ÿí Ò Á A 5A+7I=O Ò 65. ÿᜠ՟ - I : A = (5I A ). 7 ÕŸ - II : È Œ A A A+I Êapple 5(A 4I) apple Á UflÁà à Á ÿê Ê ÃÊ Ò ÃÊapple, () ÕŸ - I àÿ Ò appleá Ÿ ÕŸ - II àÿ Ò ÕŸ - I àÿ Ò appleá Ÿ ÕŸ - II àÿ Ò ŒÊappleŸÊapple ÕŸ àÿ Ò ŒÊappleŸÊapple ÕŸ àÿ Ò A 4 = Ò, ÃÊapple Ê ÿí (A 06 A 05 A 04 ) Ê Ê UÁáÊ Ò () ^pfp L $ A A L$ î rzl$ R> L $ S> \u 65. Å A 5A+7I=O. rh^p_ - I : A = (5I A ). 7 rh^p_ - II : blº`v$u A A A+I _ 5(A 4I) dp ê$`p sqfs L$fu il$pe R>. sp. () rh^p_-i kðe R>, `f sy rh^p_-ii AkÐe R>. rh^p_-i AkÐe R>, `f sy rh^p_-ii kðe R>. b _ rh^p_p kðe R>. b _ rh^p_p AkÐe R>. A 4 =, sp î rzl$ (A 06 A 05 A 04 ) _p r_òpel$ R>. ()

38 Set n+ C 66. If 6=, then n satisfies the n P equation : () n +n 08=0 n +5n 84=0 n +n 80=0 n +n 0=0 66. ÿᜠn+ C6 n P = Ò, ÃÊapple n ÁŸêŸ apple apple Á, Ë UáÊ Êapple ÃÈc U UÃÊ Ò? () n +n 08=0 n +5n 84=0 n +n 80=0 n +n 0=0 66. Å n+ C6 n P k `p j? = sp n _uq _pdp \u L$ey kdul$fz, () n +n 08=0 n +5n 84=0 n +n 80=0 n +n 0=0 67. If the coefficients of x and x 4 in the expansion of x m and n respectively, then m n () , (x > 0), are x is equal to : 68. Let a, a, a,..., a n,... be in A.P. If a +a 7 +a +a 5 =7, then the sum of its first 7 terms is equal to : () ÿᜠx 8 +, (x > 0), apple Ê U apple x x ÃÕÊ x 4 apple ªÈáÊÊ Ê m ÃÕÊ n Ò, ÃÊapple m n UÊ U Ò () ÊŸÊ a, a, a,..., a n,... Ê Ã U üêapple Ë apple Ò ÿᜠa +a 7 +a +a 5 =7 Ò, ÃÊapple apple Õ 7 ŒÊapple Ê ÿêappleª UÊ U Ò () Å x +, (x > 0) _p rhõsfzdp x x A_ x 4 _p klnyzl$p A_y¾$d m A_ n lp e sp, m n = \pe. () ^pfp L $ a, a, a,..., a n,... kdp sf î Zudp R>. Å a +a 7 +a +a 5 =7, sp s _p â\d 7 `v$p _p kfhpmp \pe. ()

39 Set The sum ( r ) r= () ()! 0 (!) 0 (0!) (!) + ( r!) is equal to : ÿêappleª» ( r + ) ( r!) UÊ U Ò r= () ()! 0 (!) 0 (0!) (!) ( r ) r= + ( r!) =. () ()! 0 (!) 0 (0!) (!) 70. ( cosx) lim is : x 0 x tan x x tan x 70. ( cosx) lim UÊ U Ò x 0 x tan x x tan x 70. ( cosx) lim =. x 0 x tan x x tan x () () ()

40 Set Let a, b R, (a 0). If the function f defined as x, 0 x < a f ( x) = a, x < b 4 b, x < x is continuous in the interval [0, ), then an ordered pair (a, b) is : () (, ) (, + ) (, + ) (, ) 7. Let f(x)=sin 4 x+cos 4 x. Then f is an increasing function in the interval : π () 0, 4 π π, 4 π 5π, 8 5π π, ÊŸÊ a, b R, (a 0) ÿ᜻ Ÿ f Êapple, ÁŸêŸ mê UÊ Á U ÊÁ Ã Ò x, 0 x < a f ( x) = a, x < b 4 b, x < x à UÊ [0, ) apple Ãà Ò, ÃÊapple Á à ÿèç (a, b) Ò () (, ) (, + ) (, + ) (, ) 7. ÊŸÊ f(x)=sin 4 x+cos 4 x Ò, ÃÊapple ÁŸêŸ apple apple Á à UÊ apple f flœ ÊŸ» Ÿ Ò? π () 0, 4 π π, 4 π 5π, 8 5π π, ^pfp L $ a, b R, (a 0). Å rh^ e x, 0 x < a f ( x) = a, x < b 4 b, x < x A sfpg [0, ) dp kss lp e, sp ¾$dey¼s Å X$ (a, b) = R>. () (, ) (, + ) (, + ) (, ) 7. ^pfp L $ f(x)=sin 4 x+cos 4 x. sp _uq _pdp \u L$ep A sfpgdp f h^sy rh^ e R>? π () 0, 4 π π, 4 π 5π, 8 5π π, 8 4

41 Set Let C be a curve given by y ( x) = + 4 x, x >. If P is a point 4 on C, such that the tangent at P has slope, then a point through which the normal at P passes, is : () (, ) (4, ) (, 7) (, 4) 7. ÊŸÊ C fl Ò Êapple y ( x) 4 x = +, x > mê UÊ ŒûÊ Ò ÿᜠC U P apple Ê Á ŒÈ Ò 4 Á P U πë øë ªß S Ê appleuπê Ë Ê Ò, ÃÊapple fl Á ŒÈ Á apple P U πë øê ªÿÊ Á ªÈ$ UÃÊ Ò, Ò () (, ) (4, ) (, 7) (, 4) 7. ^pfp L $ A L$ h¾$ C A y ( x) = + 4 x, x > Üpfp v$ip h g R>. Å C `f A L$ A hy tbvy$ P R> 4 L $ S> \u tbvy$ P ApNm_p õ`i L$_p Y$pm \pe, sp P ApNm_p Arcg b tbvy$dp \u `kpf \pe R>. () (, ) (4, ) (, 7) (, 4) 74. The integral dx ( ) + x x x to : (where C is a constant of integration.) () + x + C x x + C + x x + C + x + x + C x is equal 74. Ê ( ) + x x x dx ( Ê C Ê Ÿ ø U Ò ) () + x + C x x + C + x x + C + x + x + C x UÊ U Ò 74. dx ( ) + x x x (Äep C k L$g p AQmp L$ R>.) () + x + C x x + C + x x + C + x + x + C x =.