TARGET - AIEEE PHYSICS, CHEMISTRY & MATHEMATICS

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1 RS -11- A -1 TARGET - AIEEE PHYSICS, CHEMISTRY & MATHEMATICS Physics : Laws of conservation, Rigid body dynamics Chemistry : Gaseous state, Chemical energetic, Surface chemistry Mathematics : Tangent normal, Rolle's theorem, Rate measure Duration : 1 :30 Hrs. Ma. Marks : 135 Name : Roll No. : Date : GENERAL: Instructions to Candidates 1. This paper contains 45 Qs. in all. All questions are compulsory.. There is Negative Marking. Guessing of answer is harmful. 3. Write your Name, Roll No. & Date in the space provided on this cover page of question paper. 4. The question paper contains blank space for your rough work. No additional sheet will be provided for rough work. 5. The answer sheet, machine readable Optical Mark Recognition (OMR) is provided separately. 6. Do not break the seals of the question paper booklet before being instructed to do so by the invigilator. 7. Blank papers, Clipboards, Log tables, Slide Rule, Calculators, Cellular Phones, Pagers and Electronic Gadgets in any form are not allowed to be carried inside the eamination hall. SEAL MARKING SCHEME: 1. Each Question has four options, only one option is correct. For each incorrect response, one-third of the weightage marks allotted to the question would be deducted.. In Physics : Q carry 3 marks each, In Chemistry : Q carry 3 marks each, In Mathematics : Q carry 3 marks each, CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.) Ph: , Fa (0744) info@careerpointgroup.com ; Website : Now, Schedule practice questions are available on internet also, Visit

2 Q.1 Si identical balls are lined in a straight groove made on a horizontal frictionless surface as shown. Two similar balls each moving with a velocity v collide elastically with the row of 6 balls from left. What will happen? v PHYSICS Q.1 N%,dleku sans n'kkz;s vuqlkj,d {ksfrt?k"kz.kghu lrg ij cus,d lh/kh iafdr esa [kk pksa (groove) esa j[kh tkrh gsaa os v ls freku nks leku sansa ck ;s ls vkdj 6 sanksa dh iafdr ls izr;klfk :i ls VDdj djrh gsa D;k gksk? v One ball from the right rolls out with a speed v and the remaining balls will remain at rest Two balls from the right roll out with speed v each and the remaining balls will remain stationary All the si balls in the row will roll out with speed v/6 each and the two colliding balls will come to rest The colliding balls will come to rest and no ball rolls out from right Q. A wooden block of mass M rests on a horizontal surface. A bullet of mass m moving in the horizontal direction strikes and gets embedded in it. The combined system covers a distance on the surface. If the coefficient of friction between wood and the surface is µ, the speed of the bullet at the time of striking the block is (where m is mass of the bullet) : Mg µ m M + m µ g m µmg M µ m M + m nk ;h vksj ls,d san v pky ls yq<+dsh rfkk 'ks"k sansa fojke ij jgsah nk ;h vksj ls izr;sd sanksa esa ls izr;sd v pky ls yq<+dsh rfkk 'ks"k sansa flfkj jgsah iafdr dh lhkh N% sansa v/6 pky ls yq<+dsah rfkk nks VDdj djus okyh sansa fojke flfkfr esa vk tk;sah Vdjkus okyh sansa fojke esa vk tk;sah rfkk nk ;s ls dksbz san ugha yq<+dsh Q. nzo;eku M dk,d ydm+h dk CykWd,d {ksfrt lrg ij fojke esa gsa {ksfrt fn'kk esa freku m nzo;eku dh,d ksyh Vdjkdj blesa /k l tkrh gsa la;qdr fudk; lrg ij nwjh r; djrk gsa ;fn ydm+h o lrg ds e/;?k"kz.k q.kkad µ gs, CykWd ls Vdjkrs le; ksyh dh pky gs (tgk m ksyh dk nzo;eku gs) : Mg µ m M + m µ g m µmg M µ m M + m CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page #

3 Q.3 A ball moving with speed v hits another identical ball at rest. The two balls stick together after collision. If specific heat of the material of the balls is S, the temperature rise resulting from the collision is : v v v v 8S 4S S S Q.4 A bag of sand of mass M is suspended by a string. A bullet of mass m is fired at it with velocity v and gets embedded into it. The loss of kinetic energy in this process is : 1 1 mv 1 mv M + m 1 mv M m 1 M mv M + m Q.5 A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to K / r, where K is a constant. The total energy of the particle is : K r K r K K r r Q.6 The displacement of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t = + 3, where is in meters and t is in seconds. The work done by the force in the first 6 seconds is : 9 J 6 J 0 J 3 J Q.3 v pky ls freku,d san fojke ij flfkr,d nwljh le:i san ls Vdjkrh gsa nksuksa sansa VDdj ds i'pkr~ vkil esa fpid tkrh gsaa ;fn sanksa ds inkfkz dh fof'k"v Å"ek S gs, VDdj ds dkj.k rki esa o`f) gs : v v v v 8S 4S S S Q.4 M nzo;eku dk,d jsar dk cs,d Mksjh ls yvdk;k ;k gsa m nzo;eku dh,d ksyh os v ls bl ij pyk;h tkrh gs rfkk blesa /k l tkrh gsa bl izøe esa frt ÅtkZ esa {k; gs : 1 1 mv mv 1 M + m 1 mv M m 1 M mv M + m Q.5 m nzo;eku dk,d d.k K / r ds,d vfhkdsunzh; cy ds vurzr r f=kt;k ds,d {ksfrt o`ùk esa freku gs] tgk K,d fu;rkad gsa d.k dh dqy ÅtkZ gs : K r K r K K r r Q.6,d fu;r cy ds vurzr,d fn'kk esa freku,d d.k dk folfkkiu, le; t ls lehdj.k t = + 3 }kjk lecfu/kr gs] tgk ehvj esa rfkk t lsds.mksa eas gsa izfke 6 lsd.mksa esa cy }kjk fd;k ;k dk;z gs : 9 J 6 J 0 J 3 J CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 3

4 Q.7 A force F = K(y î + ĵ ) (where K is a positive constant) acts on a particle moving in the y-plane. Starting from the origin, the particle is taken along the positive -ais to the point (a, 0) and then parallel to the y-ais to the point (a, a). The total work done by the force F on the particles is : Ka Ka Ka Ka Q.8 A particle free to move along the -ais has potential energy given by U ( ) = k[1 ep( ) ] for +, where k is a positive constant of appropriate dimensions. Then : At point away from the origin, the particle is in unstable equilibrium For any finite non-zero value of, there is a force directed away from the origin If its total mechanical energy is k/, it has its minimum kinetic energy at the origin For small displacements from = 0, the motion is simple harmonic Q.9 A set of n identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed v towards the net one at time t = 0. All collisions are completely inelastic, then : ( n 1) L The last block starts moving at t = v n( n 1) L The last block starts moving at t = v The centre of mass of the system will have a final speed v The centre of mass of the system will have a final speed nv Q.7,c cy F = K(y î + ĵ ) (tgk K,d /kukred fu;rkad gs) y-ry esa freku,d d.k ij dk;zjr gsa ewy fcunq ls izkjehk djds d.k dks /kukred -v{k ds vuqfn'k fcunq (a, 0) rd ys tk;k tkrk gs rfkk fqj y-v{k ds lekurj fcunq (a, a) rd ys tk;k tkrk gsa d.kksa ij cy F }kjk fd;k ;k dqy dk;z gs : Ka Ka Ka Ka Q.8 -v{k ds vuqfn'k fr djus ds fy;s LorU=k,d d.k + ds fy;s U ( ) = k[1 ep( ) ] }kjk nh ;h flfkfrt ÅtkZ j[krk gs] tgk k mi;qzdr foekvksa dk,d /kukred fu;rkad gs] rks : ewy fcunq ls nwj fcunq ij] d.k vlfkk;h lke;kolfkk esa gs ds fdlh Hkh ifjfer v'kwu; eku ds fy;s] ewy fcunq ls nwj,d cy funszf'kr gs ;fn bldh dqy ;kaf=kd ÅtkZ k/ gs] rks bldh U;wure frt ÅtkZ ewy fcunq ij gksrh gs = 0 ls FkksM+s ls folfkkiu ds fy;s] fr ljy vkorz fr gs Q.9 n le:i?kukhk CykWd dk,d leqpp;,d fpduh {ksfrt lrg ij,d js[kk ds vuqfn'k,d&nwljs ds lekurj fojke ij flfkr gsa fdugha Hkh nks layxu CykWd dh utnhdh lrgksa ds e/; nwjh L gsa,d fljs ij flfkr CykWd dks t = 0 le; ij vys okys dh vksj v pky iznku dh tkrh gsa lhkh VDdjsa iw.kzr;k vizr;klfk gsa] rks : ( n 1) L vafre CykWd t = ij fr djuk izkjehk djrk gs v n( n 1) L vafre CykWd t = ij fr djuk izkjehk v djrk gs fudk; ds nzo;eku dsunz dh vafre pky v gksh fudk; ds nzo;eku dsunz dh vfure pky nv gksha CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 4

5 Q.10 A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at = 0, its velocity at = 1m is : F(N) 10 (m) m/s 0 m / s 0 3 m / s 40 m / s Q.11 The potential energy of a system is represented in the first figure. The force acting on the system will be represented by : U() Q kg nzo;eku ds,d d.k ij,d cy dk;zjr gs tks nwjh ds lkfk fp=k esa n'kkz;s vuqlkj ifjofrzr gksrk gsa ;fn ;g = 0 ij fojke ls bldh ;k=kk izkjehk djrk gs] rks = 1m ij bldk os gs : F(N) 10 (m) m/s 0 m / s 0 3 m/ s 40 m / s Q.11,d fudk; dh flfkfrt ÅtkZ izfke fp=k esa iznf'kzr gsa fudk; ij dk;zjr cy ftl fp=k }kjk n'kkz;k tk;sk] gs : U() F() a a F() a F() a a F() a F() a F() a F() a F() a CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 5

6 Q.1 The graph between E and energy and p = momentum) : 1 is (E=kinetic p Q.1 E rfkk p 1 ds e/; vkjs[k gs : (E = frt ÅtkZ rfkk p = laos) E E E E 1/p 1/p 1/p 1/p E E E E 1/p 1/p 1/p 1/p Q.13 The position of a particle is given by : r = ( iˆ + ˆj kˆ) and momentum P = ( 3ˆ i + 4 ˆj kˆ ). The angular momentum is perpendicular to : X-ais Y-ais Z-ais Line at equal angles to all the three aes Q.14 Two discs of moment of inertia I 1 and I and angular speeds ω 1 and ω are rotating along collinear aes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same ais, the rotational KE of system will be : I1ω1 + I ω ( I + I ) 1 ( I + I ) ( ω1 + ( I1ω1 + I ω ) ( I1 + I ) None of these 1 ω ) Q.13,d d.k dh flfkfr : r = ( iˆ + ˆj k) rfkk laos P = ( 3ˆ i + 4 ˆj kˆ) }kjk nh tkrh gsa dks.kh; laos yecor~ gs : X-v{k ds Y-v{k ds Z-v{k ds rhuksa v{kksa ds cjkcj dks.kksa ij js[kk ds Q.14 I 1 o I tm+ro vk?kw.kz dh nks pdfr;k muds ry ds yecor~ rfkk muds nzo;eku dsunz ls qtjus okys,d gh js[kk ij flfkr v{kksa ds vuqfn'k dks.kh; pky ω 1 o ω ls?kw.kzu dj jgh gsaa ;fn nksuksa dks leku v{k ds vuqfn'k,d lkfk?kw.kzu djok;k tk;s rks fudk; dh?kw.kzu frt ÅtkZ gksh : I1ω1 + I ω ( I + I ) 1 ( I1 + I ) ( ω1 + ω ) ( I1ω1 + I ω ) ( I1 + I ) buesa ls dksbz ugha ˆ CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 6

7 Q.15 A smooth uniform rod of length L and mass M has two identical beads of negligible size, each of mass m, which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity ω 0 about an ais perpendicular to the rod and passing through the mid point of the rod (see figure). There are no eternal forces. When the beads reach the ends of the rod, the angular velocity of the system is : Q.15 yeckbz L o nzo;eku M dh,d fpduh le:i NM+ m nzo;eku ds nks u.; vkdkj okys le:i eksrh j[krh gs] tks NM+ ij LorU=k :i ls fqly ldrs gsaa izkjehk esa nksuksa eksrh NM+ ds dsunz ij gsa rfkk fudk; NM+ ds yecor~ rfkk NM+ ds e/; fcunq ls qtjus okys v{k ds lkis{k dks.kh; os ω 0 ls?kw.kzu dj jgk gs (fp=k esa ns[ksa)a dksbz cká cy dk;zjr ugha gsa tc eksrh NM+ ds fljksa ij igq prs gsa] rks fudk; dk dks.kh; os gs : L/ L/ L/ L/ ω 0 Mω 0 M + m Mω 0 M + 1m Mω 0 M + 6m ω 0 Mω 0 M + m Mω0 M + 1m Mω 0 M + 6m CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 7

8 CHEMISTRY Q.16 The heat of combustion of benzene at 7 C found by bomb calorimeter i.e. for the reaction - 1 C 6 H 6 (l) + 7 O (g) 6 CO (g) + 3 H O (l) is 780 kcal mol 1. The heat evolved on burning 39 g of benzene in an open vessel will be kcal kcal kcal 780 kcal Q.17 Calculate S for the combustion of glucose at 5 C from the following data - comb (glucose) = kj mol 1 f f f G (glucose) = 900 kj mol 1 G (CO, g) = 395 kj mol 1 G (H O, l) = 31 kj mol JK 1 mol J mol 1 K J mol 1 K 1 56 J K 1 mol 1 Q.18 PbO PbO, G 98 < 0 SnO SnO, G 98 > 0 Most probable oidation state of Pb and Sn will be Pb 4+, Sn 4+ Pb 4+, Sn + Pb +, Sn + Pb +, Sn 4+ Q.19 The lattice energy of NaCl (s) is 756 kj/mole. The dissolution of the solid in water to form ions is endothermic to the etent of 4 kj/mol. If the hydration energy of Na + and Cl are in the ratio 6 : 5, then the heat of hydration value of Na + ion is kj mol 1 75 kj mol 1 80 kj mol kj mol 1 Q.16 7 C ij fueu vfhkfø;k 1 C 6 H 6 (l) + 7 O (g) 6 CO (g) + 3 H O (l) ds fy, ce dsyksjhehvj }kjk csathu ds ngu dh Å"ek 780 kcal mol 1 ik;h tkrh gsa,d [kqys ik=k esa 39 g csathu dks tykus ij eqdr Å"ek gksh & 390 kcal kcal kcal 780 kcal Q.17 fueufyf[kr vk dm+ks ds vuqlkj 5 C ij Xywdksl ds ngu ds fy, S dh.kuk djks & comb (glucose) = kj mol 1 f f f G (glucose) = 900 kj mol 1 G (CO, g) = 395 kj mol 1 G (H O, l) = 31 kj mol JK 1 mol J mol 1 K J mol 1 K 1 56 J K 1 mol 1 Q.18 PbO PbO, G 98 < 0 SnO SnO, G 98 > 0 Pb o Sn dh lokzf/kd LFkk;h vkwdlhdj.k volfkk gksh Pb 4+, Sn 4+ Pb 4+, Sn + Pb +, Sn + Pb +, Sn 4+ Q.19 NaCl (s) dh tkyd ÅtkZ 756 kj/mole gsa Bksl dk ty esa?kqyuk Å"ek'kks"kh izøe gs ftldk eku 4 kj/mol gsa ;fn Na + rfkk Cl dh ty;kstu ÅtkZ dk vuqikr 6 : 5, gs] rks Na + vk;u dh ty;kstu Å"ek dk eku gs kj mol 1 75 kj mol 1 80 kj mol kj mol 1 CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 8

9 Q.0 Calculate free energy change when one mole of NaCl is dissolved in water at 5 C. Lattice energy = 700 kj/mole, S at 5 C = 0.40 J mol 1, Hydration energy of NaCl = 696 kj/mol 4 kj 8 kj 1 kj 16 kj Q.1 Critical temperatures of N, CO and CH 4 are 16, 134 and 190 K respectively. The increasing order of adsorption on the surface of activated charcoal is N < CH 4 < CO N < CO < CH 4 CH 4 < CO < N CO < N < CH 4 Q. A graph between log m and log P is a straight line at angle of 45 with the intercept on the y-ais equal to Under a pressure of 0.3 atmosphere, the amount of the gas adsorbed per gram of adsorbent is Q.3 The coagulation of 00 ml of a positive colloid took place when 0.73 g HCl was added to it without changing the volume much. The flocculation value of HCl for the colloid is Q.4 An evacuated glass vessel weighs 50 gm when empty, 148 g when filled with a liquid of density 0.98 g/ml and 50.5 gm when filled with an ideal gas at 760 mm Hg at 300 K. The molar weight of the gas is g 13 g 00 g 31 g Q.5 N and unknown gas are leaked for 10 minutes into a common vessel of 3 litre capacity at 7 C. If resulting pressure is 4.18 bar and the miture contains 0.4 mol of N, the molar mass of unknown gas is g 4 g 11 g 896 g Q.0 5 C ij tc,d eksy NaCl dks ty esa?kksyk tkrk gs rks eqdr ÅtkZ esa ifjorzu dh.kuk djksa tkyd ÅtkZ = 700 kj/mole, 5 C ij S = 0.40 J mol 1, NaCl dh ty;kstu ÅtkZ = 696 kj/mol 4 kj 8 kj 1 kj 16 kj Q.1 N, CO o CH 4 ds Økafrd rki Øe'k% 16, 134 o 190 K gsa lfø;r pkjdksy dh lrg ij vf/k'kks"k.k dk c<+rk Øe gs & N < CH 4 < CO N < CO < CH 4 CH 4 < CO < N CO < N < CH 4 Q. log rfkk log P ds e/; zkq,d lh/kh js[kk gs] m ftldk dks.k 45 gs rfkk y-v{k ij vur% [k.m gsa 0.3 ok;qe.my nkc ij] vf/k'kks"kd ds izfr zke }kjk vf/k'kksf"kr Sl dh ek=kk gs & Q.3 tc,d /kukred dksykbm ds 00 ml vk;ru esa vf/kd ifjorzu fd;s fcuk 0.73 g HCl feyk;k tkrk gs rks dksykwbm dk Ldanu gksrk gsa dksykwbm ds fy;s HCl dk m.kzu eku gs Q.4,d fuokzfrr dk p ufydk dk Hkkj 50 gm gs tc og fjdr gsa tc bls 0.98 g/ml?kuro ds,d nzo ls Hkjrs gs rks Hkkj 148 g rfkk 760 mm Hg 300 K ij,d vkn'kz Sl Hkjus ij 50.5 gm gksrk gsa rks Sl dk eksyj Hkkj gs& 100 g 13 g 00 g 31 g Q.5 7 C ij 3 yhvj {kerk dh,d lkeku; ufydk esa 10 feuv ds fy, N rfkk vkkr Sl fudyrh gsa ;fn ifj.kkeh nkc 4.18 ckj gs rfkk fej.k esa 0.4 eksy N ds gs rsk vkkr Sl dk eksyj nzo;eku gs & 448 g 4 g 11 g 896 g CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 9

10 Q.6 Vanderwaal's constant of gases are given a b gas A: gas B : (i) (V c ) A > (V C ) B (ii) (P C ) A > (P C ) B (iii) (T C ) A < (T C ) B (iv) (Rate of liquefaction) A > (rate of liquefaction) B correct relation is/are (i), (ii) (i), (iii), (iv) (ii), (iii), (iv) (i), (iii) Q.7 1 mol of N at 0.8 atm takes 38 seconds to diffuse through a pin Hole, whereas 1 mol of unknown compound of Xe with fluorine at 1.6 atm takes 57 seconds to diffuse through same hole. The molecular formula of the compound may be [F = 19] [Xe = 131] XeF XeF 6 XeF 4 None of these Q.6 nks Slks ds fn,, okumj oky flfkjkad gs & a b gas A: gas B : (i) (V c ) A > (V C ) B (ii) (P C ) A > (P C ) B (iii) (T C ) A < (T C ) B (iv) (nzohdj.k dh nj) A > (nzohdj.k dh nj) B lgh lecu/k gs & (i), (ii) (i), (iii), (iv) (ii), (iii), (iv) (i), (iii) Q.7,d lw{e fnnz ls N ds 1 eksy 0.8 atm ij folfjr gksus esa 38 lsd.m ysrs gs tcfd Xe ds lkfk yksjhu ds vkkr ;ksfd ds 1 eksy dks 1.6 atm ij mlh fnnz ls folfjr gksus esa 57 lsd.m yrs gs rks ;ksfd dk vkf.od lq=k D;k gksk - [F = 19] [Xe = 131] XeF XeF 6 XeF 4 buesa ls dksbz ugha Q.8 He Ne 0.63 atm 3.4 L 1. L.8 atm Two gas bulbs are connected by a thin tube. The partial pressure of He after the connective valve is opened at a constant temp. of 7 C is - 1 atm 0.38 atm 1.64 atm atm Q.8 He Ne 0.63 atm 3.4 L 1. L.8 atm nks Sl cyc,d iryh uyh ls tqm+s gsa fu;r rki 7 C ij okyo dks [kksyus ds i'pkr~ He dk vkaf'kd nkc gs - 1 atm 0.38 atm 1.64 atm atm CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 10

11 Q.9 Q.9 fraction of total molecules T 3 T T 1 dqy v.kqvks dh fhkuu T 3 T T 1 speed total area under the curve for graph plotted at temp. T 1, T & T 3 are - area T 1 = area T 1 > area T 1 < area T 3 = area T = area T > area T < area T 1 + area T 3 area T 3 area T 3 area T Q.30 Select the incorrect conditions indicated below - fr T 1, T rfkk T 3 rki ij [khaps, vkjs[k gsrq dqy {ks=kqy fueu esa ls gs & {kséqy T 1 = {kséqy T = {kséqy T 3 {kséqy T 1 > {kséqy T > {kséqy T 3 {kséqy T 1 < {kséqy T < {kséqy T 3 {kséqy T 3 = {kséqy T 1 + {kséqy T Q.30 uhps iznf'kzr flfkfr;ksa esa vlr; dk p;u dhft, & P V 3 V V 1 Vol. P 3 P P 1 P V 3 V V 1 Vol. P 3 P P 1 T (V 1 >V >V 3 ) T (P 1 <P <P 3 ) T (V 1 >V >V 3 ) T (P 1 <P <P 3 ) P T 3 T T 1 V (T 1 <T <T 3 ) P.V T 3 T T 1 P (T 1 <T <T 3 ) P T 3 T T 1 V (T 1 <T <T 3 ) P.V T 3 T T 1 P (T 1 <T <T 3 ) CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 11

12 Q.31 In which of the following functions Rolle s theorem is applicable?, 0 < 1 f() = on [0, 1] 0, = 0 sin, f() = 0, f() = π < 0 = 0 6 on [,3] f() = 1 6 MATHEMATICS on [ π, 0] if 1,on [,3] if = 1 Q.3 The tangent to the graph of the function y = f() at the point with abscissa = a forms with the -ais an angle of π/3 and at the point with abscissa = b at an angle of π/4, then the value of the integral, b a f '().f"() d is equal to [ assume f () to be continuous ] Q.31 fueu esa ls fdu Qyuksa eas jksys izes; ykw gksh?, 0 < 1 [0, 1] ij f() = 0, = 0 sin, [ π, 0] ij f() = 0, [,3] ij f() = 6 1 π < 0 = [,3] ij f()= 1 6 ;fn 1 ;fn = 1 Q.3 Qyu y = f() ds vkys[k ij Hkqt = a okys fcunq ij Li'kZ js[kk -v{k ds lkfk π/3 dk dks.k cukrh gs,oa Hkqt = b okys fcunq ij Li'kZ js[kk -v{k ds lkfk b π/4 dks.k cukrh gs] rc lekdyu f '().f"() d a dk eku cjkcj gksk [;g ekurs gq, fd f () larr~ gs] Q.33 Two curves C 1 : y = 3 and C : y = k, k R intersect each other at two different points. The tangent drawn to C at one of the points of intersection A (a,y 1 ), (a > 0) meets C 1 again at B(1, y )(y 1 y ). The value of a is Q.33 nks oø C 1 : y = 3 rfkk C : y = k, k R,d nwljs dks nks vy-vy fcunqvksa ij izfrpnsfnr djrs gsa,d izfrpnsfnr fcunq A (a,y 1 ), (a > 0) ls C ij [khph bz Li'kZ js[kk C 1 ds fcunq B(1, y )(y 1 y ) ij feyrh gsa a dk eku gksk - (A) 4 (B) 3 (C) (D) 1 CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 1

13 Q.34 The -intercept of the tangent at any arbitrary point a b of the curve + = 1 is proportional to - y square of the abscissa of the point of tangency square root of the abscissa of the point of tangency cube of the abscissa of the point of tangency cube root of the abscissa of the point of tangency Q.35 Let be the length of one of the equal sides of an isosceles triangle, and let θ be the angle between them. If is increasing at the rate (1/1) m/hr, and θ is increasing at the rate of π/180 radians/hr then the rate in m /hr at which the area of the triangle is increasing when = 1 m and θ = π/4 1/ π / 3 1 π + 1/ 1 π Q.36 Number of solution of the equation 3 tan + 3 = π in 0, is Q.37 Consider f() = t + dt and g() = f () for t 0 1, 3. If P is a point on the curve y = g() such that the tangent to this curve at P is parallel to 1 1 a chord joining the points, g and (3, g) of the curve, then the coordinates of the point P can't be found out (7/4, 65/8) (1, ) 3 5, 6 a b Q.34 oø + = 1 ds fdlh LosPN fcunq ij Li'kZ js[kk y }kjk dkvk ;k -vur%[k.m fueu ds lekuqikrh gksk - Li'kZ fcunq dh Hkqt ds oz ds Li'kZ fcunq dh Hkqt ds ozewy ds Li'kZ fcunq dh Hkqt ds?ku ds Li'kZ fcunq dh Hkqt ds?kuewy ds Q.35 ekuk,d lef}ckgq f=khkqt dh cjkcj Hkqtkvksa esa ls,d dh yeckkbz gs rfkk θ muds e/; cuk dks.k gsa ;fn ; (1/1) eh-/?k.vs dh nj ls c<+ jgk gs rfkk θ ; π/180 jsfm;u/?k.vs dh nj ls c<+ jgk gs] rc og nj ftl ij f=khkqt dk {ks=kqy c<+ jgk gs tc = 1 m rfkk θ = π/4 gs] gksh - (A) 1/ π (B) 1/ 5 (C) 3 1 π + (D) 1/ 1 π π Q.36 0, esa lehdj.k 3 tan + 3 = ds gyksa dh 4 la[;k gksh Q.37 ekuk, 3 ds fy, f() = t + dt rfkk t 0 g() = f () gs ;fn oø y = g() ij P fcunq bl izdkj gs fd bl oø ds fcunq P ij Li'kZ js[kk oø ds 1 1 fcunq, g rfkk (3, g) dks tksm+us okyh thok ds lekurj gs] rc fcunq P ds funsz'kkad gkss - Kkr ugha fd;k tk ldrk (7/4, 65/8) (1, ) 3 5, 6 CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 13

14 Q.38 At the point P(a, a n ) on the graph of y = n (n N) in the first quadrant a normal is drawn. The normal intersects the y-ais at the point (0, b). If 1 Limb =, then n equals - a Q.39 Let f : [ 1, ] R be differentiable such that 0 f ' (t) 1 for t [ 1, 0] and 1 f ' (t) 0 for t [0, ]. Then - f f( 1) 1 1 f f( 1) 3 f f( 1) 0 f f( 1) 0 Q.4035 Consider f () = 1 1 and g () = f () + b sin π, 1 < < then which of the following is correct? Rolle's theorem is applicable to both f, g and 3 b = LMVT is not applicable to f and Rolle's 1 theorem if applicable to g with b = LMVT is applicable to f and Rolle's theorem is applicable to g with b = 1 Rolle's theorem is not applicable to both f, g for any real b. Q.41 Let C be the curve y = 3 (where takes all real values). The tangent at A meets the curve again at B. If the gradient at B is K times the gradient at A then K is equal to Q.38 y = n (n N) ds zkq ij flfkr fcunq P(a, a n ) ij ls izfke prqfkkaz'k esa,d vfhkyec Mkyk ;k gsa vfhkyec y-v{k dks fcunq (0, b) ij izfrpnsfnr djrk gsa ;fn 1 Limb = gs] rc n cjkcj gksk - a Q.39 ekuk vodyuh; Qyu f : [ 1, ] R bl izdkj gs fd t [ 1, 0] ds fy, 0 f ' (t) 1 rfkk t [0, ] ds fy, 1 f ' (t) 0 rc - f f( 1) 1 1 f f( 1) 3 f f( 1) 0 f f( 1) 0 Q.4035 ekuk f () = 1 ; 1 rfkk π g () = f () + b sin, 1 < < rc fueu esa ls dksulk dfku lr; gs? f, g nksuksa ds fy, jksys izes; ifjhkkf"kr gs rfkk 3 b = 1 b = ij f ds fy, yszk t ek/;eku izes; ifjhkkf"kr ugha gs rfkk g ds fy, jksys izes; ifjhkkf"kr gs b = 1 ij f ds fy, yszk t ek/;eku izes; ifjhkkf"kr gs rfkk g ds fy, jksys izes; ifjhkkf"kr gsa fdlh oklrfod b ds fy, f, g nksuksa ds fy, jksys izes; ifjhkkf"kr ugha gsa Q.41 ekuk C oø y = 3 gs (tgk lhkh oklrfod eku zg.k djrk gs) oø ds fcunq A ij [khaph bz Li'khZ oø dks iqu% B ij feyrh gsa ;fn B ij izo.krk] A ij izo.krk dh K quk gs] rks K cjkcj gksk CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 14

15 Q.4 Which of the following si statements are true about the cubic polynomial P() = ? (i) It has eactly one positive real root. (ii) It has either one or three negative roots. (iii) It has a root between 0 and 1. (iv) It must have eactly two real roots. (v) It has a negative root between and 1. (vi) It has no comple roots. only (i), (iii) and (vi) only (ii), (iii) and (iv) only (i) and (iii) only (iii), (iv) and (v) Q.43 A cube of ice melts without changing shape at the uniform rate of 4 cm 3 /min. The rate of change of the surface area of the cube, in cm /min, when the volume of the cube is 15 cm 3, is /5 16/6 8/15 Q.44 The ordinate of all points on the curve 1 y = where the tangent is sin + 3cos horizontal, is - always equal to 1/ always equal to 1/3 1/ or 1/3 according as n is an even or an odd integer. 1/ or 1/3 according as n is an odd or an even integer. Q.45 The tangent to the curve = a cos θ. cos θ, y = a cos θ. sin θ at the point corresponding to θ = π/6 is - Parallel to the -ais Parallel to the y-ais Parallel to line y = None of these Q.4 fueu N% dfkuksa esa ls dksuls dfku f=k?kkrh; cgqin P() = ds fy, lr; gksas? (i) ;g Bhd,d /kukred oklrfod ewy j[krk gs (ii) ;g ;k rks,d ;k rhu _.kkred ewy j[krk gs (iii) ;g 0,oa 1 ds e/; ewy j[krk gs (iv) ;g Bhd nks oklrfod ewy j[krk gs (v) ;g,oa 1 ds e/; _.kkred ewy j[krk gs (vi) ;g dksbz lfeej ewy ugha j[krk gs dsoy (i), (iii) rfkk (vi) dsoy (ii), (iii) rfkk (iv) dsoy (i) rfkk (iii) dsoy (iii), (iv) rfkk (v) Q.43 cqz dk,d VqdM+k vkd`fr esa fcuk dksbz ifjorzu fd;s 4 cm 3 /min dh,dleku nj ls fi?ky jgk gs] rks tc cqz ds VqdM+s dk vk;ru 15 cm 3 gs] rc VqdM+s ds i`"bh; {ks=kqy esa ifjorzu dh nj (cm /min es) gksh /5 16/6 8/15 1 Q.44 oø y = ij flfkr lhkh fcunqvksa dh sin + 3cos dksfv] tgk Li'khZ {ksfrt gs] gksh - lnso 1/ ds cjkcj lnso 1/3 ds cjkcj 1/ ;k 1/3 ; n ds le ;k fo"ke iw.kk±d gksus ds vuqlkj 1/ ;k 1/3 ; n ds fo"ke ;k le iw.kk±d gksus ds vuqlkj Q.45 oø = a cos θ. cos θ, y = a cos θ. sin θ dh θ = π/6 ds lar fcunq ij Li'kZ js[kk gs - -v{k ds lekurj y-v{k ds lekurj js[kk y = ds lekurj buesa ls dksbz ugha CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 15

16 HkkSfrd fokku : lja{kh fu;e] n`<+ fi.m frdh jlk;u fokku : Slh; volfkk] jklk;fud ÅftZdh] i`"bh; jlk;u f.kr : Li'kZ-js[kk vfhkyec] jksy izes;] nj ekiu Duration : 1 : 30 Hrs. Ma. Marks : 135 fueu funsz'kksa dks /;kuiwozd if<+;s: ijh{kkffkz;ksa ds fy;s funsz'k SEAL 1. bl iz'u i=k esa dqy 45 iz'u gsaa lhkh iz'u gy djus vfuok;z gsaa. blesa _.kkred vadu gs vr% mùkj vuqekfur djuk gkfudkjd gks ldrk gsa 3. bl iz'u i=k ds doj ist ij fn;s ;s LFkku esa viuk uke] jksy uecj rfkk fnukad fyf[k;sa 4. bl iz'u i=k esa gh jq odz ds fy, [kkyh LFkku fn;k ;k gsa jq odz ds fy, dksbz vfrfjdr 'khv ugha nh tk,sha 5. mùkj O.M.R.(Optical Marks Recognisation) 'khv esa vafdr djus gsaa ;g vy ls nh bz gsa 6. iz'u i=k dh lhy rc rd u [kksysa tc rd,slk djus ds fy, ifjoh{kd }kjk dgk u tk,sa 7. [kkyh dk+t] fdyi cksmz] ykw lkj.kh] LykbM :y] dsydqysvj] lsy;qyj Qksu] istj ;k fdlh Hkh izdkj dk vu; bysdvªkwfud midj.k fdlh Hkh :i esa ijh{kk gkwy ds vunj ys tk;s tkus dh vuqefr ugha gsa vadu i)fr : 1. izr;sd iz'u esa pkj fodyi fn;s ;s gsa] dsoy,d fodyi lgh gsa izr;sd yr mùkj ds fy, ml iz'u ds fy, fu/kkzfjr vadksa esa ls,d&frgkbz dkv fy, tk,sasa. HkkSfrd fokku esa : Q izr;sd ds fy, 3 vad, jlk;u fokku esa : Q izr;sd ds fy, 3 vad, Xkf.kr esa : Q izr;sd ds fy, 3 vad, CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.) Ph: , Fa (0744) info@careerpointgroup.com ; Website : Now, Schedule practice questions are available on internet also, Visit CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.), Ph: Page # 16