IIT JEE 2010 Test Series Paper 2

IIT JEE 2010 6th Test Series Paper 2 P a g e | 1 www.vidyadrishti.com An educational portal for future IITians by current IITians IIT‐JEE 2010 6th Test Series PAPER 2 21st Feb 2010 to 7th March 2010 from www.vidyadrishti.com An educational portal for future IITians by current IITians Send your feedback to www.vidyadrishti.com/feedback.php IIT JEE 2010 6th Test Series Paper 2 P a g e | 2 www.vidyadrishti.com An educational portal for future IITians by current IITians IIT JEE 2010 6th Test Series Paper 2 P a g e | 3 www.vidyadrishti.com An educational portal for future IITians by current IITians Physics Paper 2 SECTION I Single Correct Choice Type This section contains 4 multiple choice questions. Each question has four choices for its answer, out of which ONLY ONE is correct. 1. An open pipe of sufficient length is dipping in water with a speed  vertically. If at any instant l is length of tube above water then the rate at which fundamental frequency of pipe changes is (C is the speed of sound in air) (a) C /2l2 (b) C /4l2 (c) C /2 2l2 (d) C /42l2. 2. A radioactive isotope is being produced at a constant rate A. The isotope has a half‐life T. Initially there are no nuclei. After a time tT, the number of nuclei becomes constant. The value of this constant is (a) 1 (2) AT n (b) 1n(2) AT (c) AT 1n(2) (d) AT SPACE FOR ROUGH WORK  l IIT JEE 2010 6th Test Series Paper 2 P a g e | 4 www.vidyadrishti.com An educational portal for future IITians by current IITians 3. A block of mass m is at rest on an inclined plane. The coefficients of static and kinetic friction between the block and the plane are s  and k s. The angle that the plane makes with the horizontal satisfies tan . s    A string is attached to the block. Is it possible to pull on the string in such a way that the block will slide with constant velocity along a horizontal line? That is to say, can the block slide along a line of constant elevation? a) Yes b) Yes, but only if cos sin k mg   mg  c) Yes, but if cos sin k mg   mg  d) No 4. Two mirrors are joined together so that they make an angle of 60 as shown. A person stands at a point P which is on the line which bisects the 60 angle. How many images of herself does the person see? a) 1 b) 3 c) 5 d) 6 SPACE FOR ROUGH WORK P 60 IIT JEE 201 www.vidy SECTION Multiple This sectio which ON 5. Tw sh e(a (b (c (d 6. A th (a (b (c (d 7. Wpmopabc) d 10 6th Test Se yadrishti.com N II Correct Cho on contains 5 NE OR MORE i wo blocks o hown in figu longation of a) Net const b) Each bloc c) Centre of d) Centre of ball is drop he horizonta a) 5 ms1 b) 6 ms1 c) 7 ms1 d) 50 ms1 When photo hotoelectro maximum kin f energy 4. hotoelectro ) the work ) the work ) TA = 2.00 ) TB = 2.75 eries Paper 2 m oice Type multiple cho s/are correct f masses 1 m ure. Suppose f the spring b tant force on ck are pulled f mass has ze f mass move ped onto a p al as shown i ons of ene ns have a m netic energy .70 eV is T ns is B = 2 function of A function of eV eV An educ oice question t. and 2 m are e the block/s be 2F/k. Wh n the spring by a consta ero velocity. s with an ac pad at A and in the figure ergy 4.25 e maximum kin y of photoele TB = (TA – A, then is 2.25 eV B is 4.20 eV cational porta s. Each quest connected b is/are pulle ich of the fo is 2F. ant force F. cceleration m d rebounds w e. The ball wi eV strike t etic energy ectrons libe 1.50) eV. If al for future II tion has four c by an ideal s ed by applyin ollowing opt 1 2 2F .  m with a veloci ill enter the the surface TA eV and de rated from f the de B P a g e IITians by cur choices for its spring of spr ng force/s. L ion/s may be ity 0 v at an a opening BC, of a met e Broglie wa another me roglie wave 60 A | 5 rrent IITians s answer, out ring constant Let the maxi e correct? ngle 60 wit , if 0 v is tal, the eje avelength A etal B by pho elength of t B C 3 /2m t of t k as mum th ected A. The otons these 1.0 0.5m 5 m IIT JEE 2010 6th Test Series Paper 2 P a g e | 6 www.vidyadrishti.com An educational portal for future IITians by current IITians 8. A cubical block of mass m and edge a slides down a rough inclined plane of inclination θ with a uniform speed. Then (a) Torque of weight about centre is zero. (b) Torque of normal force about centre is zero. (c) Torque of friction about centre is non‐zero. (d) Torque of friction about centre is zero. 9. An ideal gas is taken from the state A (pressure P, volume V) to the state B (pressure P/2, volume V/2) along a straight line path in the PV diagram. Select the correct statement(s) from the following. a) The work done by the gas in the process A to B exceeds the work done by it if the system were taken from A to B along the isotherm. b) In the T‐V diagram, the path AB becomes part of a parabola. c) In the P‐T diagram, the path AB becomes part of a hyperbola. d) In going from A to B, the temperature T of the gas first increases to maximum value and then decreases. SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 7 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Matrix Match Type (See Physics 1, Paper 1 for instructions for Matrix Match type) 10. Match the following Column I Column II (a) Two particles A and B, each carrying charge + Q, are held with a separation d between them. A particle C having mass m and charge – q is kept at the middle of the line AB. It is displaced through a distance x perpendicular to AB. Assume x<H3PO4>H3AsO4 Acidic strength B) CuO>Na2O>K2O Basic strength C) CsOH>RbOH>KOH>NaOH Basic strength D) Mn2O3>MnO2>MnO4‐1 Acidic strength 5. What is/are the significance of the Third Law of Thermodynamics? a. The absolute entropy of a substance decreases with increasing temperature. b. The change in entropy of the universe must be positive for a spontaneous process. c. The absolute value of entropy cannot be measured for some very pure substances. d. The change in entropy of the universe equals the sum of the change in entropy of the system plus the change in entropy of the surroundings. 6. A student determined the value of Ksp for a saturated solution of borax at several different temperatures. The value for So for the dissolution of borax in water can be determined from: a. the slope of the line resulting from a plot of ln Ksp versus (1/T). b. the y‐intercept of the line resulting from a plot of ln Ksp versus T. c. the slope of the line resulting from a plot of Ksp versus (1/T). d. the y‐intercept of the line resulting from a plot of ln Ksp versus (1/T). 7. Which of the following influences the rate of a chemical reaction performed in solution? a. temperature b. activation energy c. presence of a catalyst d. concentrations of reactants 9. The magnetic moment of the fluoride complex is expected to be: a. the same as the magnetic moment of the cyanide complex. b. larger than the magnetic moment of the cyanide complex because there are more unpaired electrons in the fluoride complex. c. smaller than the magnetic moment of the cyanide complex because there are more unpaired electrons in the fluoride complex. d. larger than the magnetic moment of the cyanide complex because there are fewer unpaired electrons in the fluoride IIT JEE 2010 6th Test Series Paper 2 P a g e | 14 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Matrix Match Type 10. Match the following Column‐1 Column‐2 A) Flame colouration p) NaHCO3 B) Amphoteric character q) LiCl C) Slightly basic (pH>7) aqueous solution r) BeCl2 C) Decompose on heating s) Be(OH)2 11. Match the following Column I Column II (a) [Cr(H2O)6]Cl6 and [Cr(H2O)5Cl]Cl2.H2O (p) Can be differentiated by amount, nature, colour of ppt. Formed (b) [Co(NH3)5Br]SO4 and [Co(NH3)5SO4]Br (q) Can be differentiated by electrical conductance measurement (c) [Co(NH3)5Cl]Cl2 and [Co(NH3)6]Cl3 (r) Can be differentiated by using cryoscopic measurement. (d) [Cu(H2O)4]SO4.H20 and [Cu(H2O)6](NO3)2 (s) Can be differentiated by heating with conc. H2SO4 IIT JEE 2010 6th Test Series Paper 2 P a g e | 15 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION IV Integer Answer Type 12. Given the cell:Cd(s)| Cd(OH)2(s)| NaOH(aq,0.01M)|H2(g,1bar)|Pt(s) with Ecell = 0.0V . if EoCd2+/cd = ‐0.39V , then –logKsp of Cd(OH)2 IS : 13. The rate of the first order reaction is 0.08 moleL‐1S‐1 at 20 min and 0.06 molL‐1S‐1 at 30 min after initiation .Find the half life of the reaction in min. 14. ‘X’ is a disubstituted benzenoid aromatic compound with least molecular weight . One mole of it liberates half mole of hydrogen gas with sodium metal . It forms silver mirror with tollen’s reagent . It forms coloured complex with neutral ferric chloride solution .It has strong intramoleecula hydrogen bonding . Report the molecular weight of compound ‘X’. 15. 2 /2 . 0 2 /2 /Br Na h Br Alc KOH zone NH OH h h Zn H O Toulene  P            What is molecular weight of the final product P. 16. What is the sum of the bond order of carbon monoxide and oxyginium ion. 17. 10ml of 0.1M triprotic acid H3A is Titrated with 0.1M NaOH solution . What is the ratio of [H3A]/[A3‐] at second equivalence point . given K1 = 8 x 10‐4 ;k2 =10‐8;k3 = 10‐12 18. The decomposition of HI to yield H2 and I2 at 508oC has a half life of 138 minutes When PHI = 0.1 atm (initially), which comes down to one tenth of the value when the initial pressure is 1 atm . Calculate the rate constant and give your answer in terms of k(atm‐1min‐1)x1000 19. The carbon‐14 activity of some ancient Peruvian corn was found to be 10 disintegrations per minute per gram. If present‐day plant life shows 15 disintegrations/minute/gram, how old is the Peruvian corn? The half‐life of carbon‐14 is 5,730 years. IIT JEE 2010 6th Test Series Paper 2 P a g e | 16 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 17 www.vidyadrishti.com An educational portal for future IITians by current IITians Mathematics Paper 2 SECTION I Single Correct Choice Type This section contains 4 multiple choice questions. Each question has four choices for its answer, out of which ONLY ONE is correct. 1. Given 2 0 en n sec tand 1 e       then the value of n can be a) 34 b) 54 c) 74 d) None of these 2. If f (x)is continuous and 90  f(x)dx4then the value of the integral 3 2 0  x.f(x )dx is a) 9 b) 8 c) 4 d) 2 3. The value of the integral 16 4 1 dx x  x  is a) 4ln 32 b) 4ln 3 1 2  c) 4ln 3 2 2  d) None of these IIT JEE 2010 6th Test Series Paper 2 P a g e | 18 www.vidyadrishti.com An educational portal for future IITians by current IITians 4. A differentiable function satisfies f '(x)f(x)2ex with initial conditions f (0)  0 . The area enclosed by f (x) and the x‐axis is a) 1 sq. unit b) 2 sq. units c) 3 sq. units d) 4 sq. units SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 19 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION II Multiple Correct Choice Type This section contains 5 multiple choice questions. Each question has four choices for its answer, out of which ONE OR MORE is/are correct. 5. If ampz1z20 and z1  z2 1 then a) 1 2 z z 0 b) 1 2 z z  1 c) 1 2 z z d)     1 2 ampz ampz 6. If     , , '0 2 2 f x y f x f y x y R f a          and f b  0then a)   10 2 f x dx  a b b) f'4 f'0 c) Max f x ab d) Min f x ab 7. The angle between the two curves y sinxcosx and x2y2 5 , where [x] denotes the greatest integer function is a) 2  b) The curves are orthogonal. c) tan1 2 d) cos 1 25        IIT JEE 2010 6th Test Series Paper 2 P a g e | 20 www.vidyadrishti.com An educational portal for future IITians by current IITians 8. If   /2 22 0 sin sin fn nxdx x    then a) 1 2 f   b) sinf7cosf71 c) tan2f2cot2f24 d) f1,f2,...,fn are in A.P. 9. If cba and bca then       a) a,b,c    are coplanar vectors when a,b,c    are non zero vectors. b) a  is perpendicular to both b  and c  . c) a  is perpendicular to both bc   . d) a  is perpendicular to both bc   . SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 21 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION III Matrix Match Type 10. Ten dice are tossed. Assume that all combinations of tosses are equiprobable. Match Column I with Column II. Column I Column II (A) Not a single 6 is obtained (P) (5 /6)10 (B) Exactly three 6 are obtained (Q) 7 3 10 7 5 1 6 6 C             (C) At least one six is obtained (R) 6 4 10 4 5 1 6 6 C             (D) Exactly four six is obtained (S) 1(5/6)10 (T) 3 7 10 3 5 1 6 6 C             SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 22 www.vidyadrishti.com An educational portal for future IITians by current IITians 11. Match the following Column I Column II (A) The number of triangles can be drawn through 10 given points on a circle is (P) 2n 1 (B) The value of 1 ! r n n r r P r   is (Q) 120 (C) The number of positive divisors of 10! is (R) 45 (D) The maximum number of points at which 10 straight lines intersect is (S) 270 (T) 2n 1 SPACE FOR ROUGH WORK IIT JEE 2010 6th Test Series Paper 2 P a g e | 23 www.vidyadrishti.com An educational portal for future IITians by current IITians SECTION IV Integer Answer Type 12. Given f xy  f x f y. f  x is continuous at x = a. Find x at which is f  x not continuous. 13. If 3n is a factor of the determinant 3 6 1 1 1 3 6 2 2 2 1 1 1 C C C n n n n n n C C C     then find the maximum value of n . 14. If 1 2 (z, z )and 3 4 (z , z )are two pairs of none zero conjugate complex numbers then find the value of arg 13 zz      + arg 24 zz       . 15. If       sin   2 tan   4cosec    14 then at 4, 2 cos 4sec 2cot xy xy xy dy xy xy xy dx      is x. Find the value of |x|. 16. Find the distance of the point i2j3k from the planeri jk   5   , measured parallel to the vector2i3j6k . 17. If the line x y 1 touches the parabola y2  kx , then find the value of k . 18. An integer is chosen from the first 200 positive integers. The probability that the integer is divisible by 6 ir 8 is p. Find the value of 1/p. 19. Find the degree of the polynomial of expression     5 5 x x31  x x31 IIT JEE 2010 6th Test Series Paper 2 P a g e | 24 www.vidyadrishti.com An educational portal for future IITians by current IITians SPACE FOR ROUGH WORK