ALL INDIA TEST SERIES

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1 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 In JEE Advanced 06, FIITJEE Students bag 6 in Top 00 AIR, 75 in Top 00 AIR, 8 in Top 500 AIR. 54 Students from Long Term Classroom/ Integrated School Program & 44 Students from All Programs have qualified in JEE Advanced, 06 FIITJEE ALL IDIA TEST SERIES JEE(Advanced)-07 ASWERS, HITS & SOLUTIOS COCEPT RECAPITULATIO TEST I (Paper-) Q. o. PHYSICS CHEMISTRY MATHEMATICS. A C B. B C C. A C B 4. A A C 5. B B B 6. CD ABC AD 7. AB BC CD 8. AD BD AB 9. ABC ACD AD 0. ABD BCD AC. BD CD BD. ABD AC BCD. BD B AB FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

2 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 Physics PART I SECTIO A. A For C 5mg kx = 0 kx 5mg For B kx mg k.x kx 7mg For A kx mg kx If spring is cut kx = 0 mg + kx = ma B 7 mg = ma B 7 ab g( ). B v = V cos 0 sin 0 ( ˆi) + V(cos 0 sin 0 ) ĵ. A 75 min 0.0 Å. Hence wavelength less than 0.0 Å is not possible. 40, A r Potential energy U = ev = ev0 ln r du ev Force F 0 dt r The force will provide the necessary centripetal force. mv ev0 ev0 Hence, v r r m (i) nh and mvr (ii) nh m From equations (i) and (ii), mr ev or r n B y = A sin (kx) cos (t) k length of sting U = du = x x0 x (dm) A sin and m dm dx FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

3 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 6. CD Particle P will have a velocity in vertical direction. i.e. R cos = V cos V R Required angle is cos And in second case Rcos V V cos R, V cos R V R R V R V 7. AB dv v dt R dv v v ds R 8. AD Property of friction. 9. ABC Work energy theorem. 0. ABD By conservation of angular momentum, I I I f i f E E i f / I i I I f Ratio of the heat produced to initial kinetic energy Ei E f E i. BD E m and r m. ABD Bernoulli s theorem for an orifice at depth x in liquid d. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

4 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 4 H P o + dg dg.x = P o + d v z () H x gt () R = Vt Solve for R and apply maxima/minima. (). BD Stopping potential does not depend on intensity and saturation current depends on intensity. Intensity I due to point source r where r is distance from the source. SECTIO C. For m not to slide over M, acceleration of the triangular block should be g tan if the required mass in m 0, then m g T m gtan 0 0 & T M m gtan & T = g tan & cot = m 0 = kg. PT = k dv V dt (i) nrt T k V T k V T V k (ii) dv T dt K (iii) From (i), (ii) and (iii) k T T k T. B r Q dr r R T0D. QR B T D R 0 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

5 5 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/ Consider energy losses in successive collisions, find, i.e. maximum deflection after 0 each collision you will get cos will satisfy 60 this condition will be met after nth collision. After st collision, K.E. = mghe = 0.8 mgh After nd collision, K.E. = 0.64 mgh After rd collision, K.E. = 0.5 mgh After 4 th collision, K.E. < mgh i.e., < i 5 (6) i() ir 5 i i ir 5 i 5 R 5 P i R R 5 R P i R dp 0 dr R 5. i/ + 5 V V - i/ i a R i b FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

6 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 6 Chemistry PART II SECTIO A. C CaCO H SO CaSO CO H O Moles of CaCO = Moles of H SO 4 = = Moles of CaCO = = ml water contains =.5 0 g CaCO 0 6 ml(0 6 g) water will contain = 5 g of CaCO Hardness of sample = 5 ppm. C aoh is not used as a bleaching agent.. C A g 4B g Cg At t 0 : P 0 0 o o At t 0min : P x 4x x P x 4x x 400 P 6x 400 6x o x = K 5.70 sec t 060 o 4 4. A The acidic strength of the acids is HW > HX > HY > HZ 5. B o. of X + ions per unit cell = o. of Y ions per unit cell = 8 Y Y 8 Hence the formula is XY. 6. ABC Dipole moment of H > F, SCl > BeCl (zero value) SF 4 > CF 4 (zero value) 7. BC It is an endothermic reaction as the equilibrium constant increases with increasing temperature. 8. BD FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

7 7 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 H O Be C Be OH CH 4 H O 4 4 Al C Al OH CH 9. ACD Sxz Sx y Sy z (Enthalpy is a state function and hence additive) H H (State function, depend in initial and final state) W x yz x z W (work done in y z is zero as it is an isochoric process) x y z x y 0. BCD Gr-III radicals are precipitated with ammonia solution.. CD For i + the configuration is t 6 e and Zn + is t 6 e 4.. AC cos [When two diploes are identical] g g g g. B (i) Loses aromaticity if it gives away lone pair H H + (ii) H + + H H H Conjugate acid is resonance stabilized but attached to sp carbon atoms, which shows I effect and destabilize the conjugate acid. SECTIO C. The valence electrons are s p for which = 0 and.. The structure of H SO 5 is: O HO - O - O - S - OH. Total charge on four oxide ions = - 4 = -8 Let n no. of X -8/ ions will replace O ions 8 n 8 n FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

8 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/ One vacancy will be created. T f = K f n 000 W 5. 9 Or, 4 = W W = 46.5 g Mass of water converted to ice = = 4 g Charge = = coulomb = F F deposits g eq = 9 g of aluminium FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

9 9 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/7 Mathematics PART III SECTIO A. B A B 0. C 4 circles touch sides of any given triangle formed by tangents.. B Required number C Let common root be and ow P 0 and 5. B P P P 0 one of the roots must be. x iy 8 6i x xy 8 x y y 6 Use y tx and solve P x x bx c 6. AD f x h f x f ' x lim x n0 h Hence, f (x) is differentiable for all x R but not twice differentiable at x = CD xn Fx x n as x Range of Fx is n, 8. AB Consider a number system with base and using only the digits 0 or. 9. AD Take A and B B B A A P FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

10 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/ AC Second diagonal will pass through the centre of the hyperbola.. BD n m k k m and n m 00. BCD Let r ˆ ˆ ˆ ai bj ck and r ˆ ˆ ˆ i 4j 5k r r r r and. AB Radical axis of S 0 and S 0 is the line L 0, the point of concurrency of family of lines ax by c 0 if a,b,c are in A.P. is (,-). g. 8 e h lim gx x 6 f lim gx x Since, g x is continuous at x g lim g x lim g x x x g f h 0 Area 6 f x dx f x dx 0 SECTIO C Feasible region is FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

11 AITS-CRT-I-(Paper-)-PCM (Sol)-JEE(Advanced)/ Focus is 4, x 7x 4x 0 x 4 x x 9x 6 x 4 x 4 Take the curve y x. Both square roots can be interpreted as distances. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, ew Delhi -006, Ph , , Fax 6594

FIITJEE JEE(Main)

FIITJEE JEE(Main) AITS-FT-II-PCM-Sol.-JEE(Main)/7 In JEE Advanced 06, FIITJEE Students bag 6 in Top 00 AIR, 75 in Top 00 AIR, 8 in Top 500 AIR. 54 Students from Long Term Classroom/ Integrated School Program & 44 Students