Name of the Candidate (in Capital Letters): : in words

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1 This booklet contains 4 printed pages. PAPER- : CHEMISTRY, PHYSICS & MATHEMATICS Do not open this Test Booklet until you are asked to do so. Read carefully the Instructions on the Back Cover of this Test Booklet. Important Instructions :. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited.. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.. The test is of hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are There are three parts in the question paper A, B, C consisting of Chemistry, Physics and Mathematics and having 0 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. /4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue/Black Ball Point pen only for writing particulars/marking responses on Side- and Side- of the Answer Sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 0. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is give at the bottom of each page and in three pages (Pages - ) at the end of the booklet.. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.. The CODE for the Booklet is C. Make sure that the CODE printed on Side- of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet.. Do not fold or make any stray marks on the Answer Sheet. Test Booklet Code C Name of the Candidate (in Capital Letters): Roll Number : In figures : in words Examination Centre Number : Name of Examination Centre (in Capital letters) : Candidate s Signature :. Invigilator s Signature :. Invigilator s Signature : Mentors Eduserv : Plot No. : 6/7, Parus Lok Complex, Boring Road Crossing, Patna-, Ph. No. : /4/6/7

2 [ ] JEE MAIN 07 (Code-C) (0-04-7) PART-A : CHEMISTRY. The freezing point of benzene decreases by 0.45ºC when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be : (K f for benzene = 5. K kg mol ) Ans. () () 94.6% () 64.6% () 80.4% (4) 74.6% Tf 0.45ºC Tf i.k f.m 0. / i i CH COOH (CH COO) 0 i 5..7 i %association : 94.6% : Ans. (). On treatment of 00 ml of 0. M solution of CoCl.6H O with excess AgNO ;. 0 ions are precipitated. The complex is : Ans. () () [Co(H O) 5 Cl]Cl.H O () [Co(H O) 4 Cl ]Cl.H O () [Co(H O) Cl ].H O (4) [Co(H O) 6 ]Cl CoCl.6HO AgNO AgCl 00ml (excess) 0.M Mole of CoCl.6HO Mole of AgCl precipitated No. of moles of AgCl per mole of complex = Molecular formula : [Co(H O) 5 Cl]Cl.H O Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

3 JEE MAIN 07 (Code-C) (0-04-7) [ ]. Which of the following compounds will form significant amount of meta product during mono-nitration reaction? () () () (4) Acidic HNO HSO4 medium + 4. The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are : () Cl and ClO () ClO and ClO () ClO and ClO (4) Cl and ClO Cl NaOH(cold& dilute) NaCl NaOCl +H O 5. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is : () nitrates of both Li and Mg yield NO and O on heating () both form basic carbonates () both form soluble bicarbonates (4) both form nitrides Ans. () Only Magnesium forms basic Magnesium Carbonate : Mg(OH).4MgCO.6H O 6. A water sample has ppm level concentration of following anions F = 0; SO 4 = 00 ; NO = 50 The anion/anions that make/makes the water sample unsuitable for drinking is /are : () only SO 4 () only NO () both SO 4 and NO (4) only F F ion concentration above ppm causes brown mottling of teeth at the same time, excess fluoride (over 0 ppm) cause harmful effect to bones and teeth. 7. The formation of which of the following polymers involves hydrolysis reaction? () Terylene () Nylon 6 () Bakelite (4) Nylon 6, 6 Ans. () Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

4 [ 4 ] JEE MAIN 07 (Code-C) (0-04-7) 8. The Tyndall effect is observed only when following conditions are satisfied : Ans. () (a) The diameter of the dispersed particles is much smaller than the wavelength of the light used (b) The diameter of the dispersed particle is not much smaller than the wavelength of the light used (c) The refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude (d) The refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude () (b) and (c) () (a) and (d) () (b) and (d) (4) (a) and (c) (b) and (d) 9. pk a of a weak acid (HA) and pk b of a weak base (BOH) are. and.4, respectively. The ph of their salt (AB) solution is : Ans. () ().0 () 7. () 6.9 (4) 7.0 pk a (HA) =. pk b (BOH) =.4 For solution of AB(weak acid-weak base salt) ph 7 pka pkb 7 (..4) 7 (0.) The major product obtained in the following reaction is : O O DIBALH COOH OH () CHO CHO () COOH CHO OH () CHO CHO (4) COOH CHO Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

5 JEE MAIN 07 (Code-C) (0-04-7) [ 5 ] Ans. () DIBAL-H converts acid and ester both to Aldehyde.. Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution? () () () (4) Ans. (). The correct sequence of reagents for the following conversion will be: () () [Ag(NH ) ] OH, CHMgBr, H / CHOH () CHMgBr, H / CHOH, [Ag(NH ) ] OH (4) [Ag(NH ) ] OH,H / CHOH,CH MgBr CHMgBr, [Ag(NH ) ] OH, H / CHOH Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

6 [ 6 ] JEE MAIN 07 (Code-C) (0-04-7) Ans. (). Which of the following species is not paramagnetic? () B () NO () CO (4) O Ans. () CO is diamagnetic, because no unpaired electrons are present in it. Paramagnetic nature of B,NO and O are explained on basis of M.O.T. 4. Which of the following, upon treatment with tert-buona followed by addition of bromine water, fails to decolourize the colour of bromine? () () () (4) Ans. () 5. Which of the following reactions is an example of a redox reaction? () XeF6 HO XeOF 4HF () XeF4 OF XeF6 O () Ans. () XeF PF 5 [XeF] PF 6 (4) XeF6 HO XeOF4 HF Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

7 JEE MAIN 07 (Code-C) (0-04-7) [ 7 ] 6. U is equal to: () Isothermal work () Isochoric work () Isobaric work (4) Adiabatic work U q W q 0 for adiabatic then U W 7. Which of the following molecules is least resonance stabilized? () () () (4) Ans. () () Stability:- Aromatic > Non-aromatic > Anti-aromatic () () (4) 8. The increasing order of the reactivity of the following halides for the S N reaction is: (I) (II) (III) Ans. () () (II) < (III) < (I) () (III) < (II) < (I) () (II) < (I) < (III) (4) (I) < (III) < (II) Rate of SN stability of carbocation formed. SN rate = Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

8 [ 8 ] JEE MAIN 07 (Code-C) (0-04-7) 9. gram of a carbonate (M CO ) on treatment with excess HCl produces mole of CO. The molar mass of M CO in g mol is: ().86 () 86 () 84. (4) 8.6 Ans. () MCO HCl MCl HO CO g excess 0.086mole moles of MCO moles of CO Mol.wt Mol.wt Sodium salt of an organic acid X produces effervescene with conc. H SO 4. X reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMnO 4. X is: () Na C O 4 () C 6 H 5 COONa () HCOONa (4) CH COONa Ans. (). The most abundant elements by mass in the body of a healthy human adult are: Oxygen (6.4%); Carbon (.9%), Hydrogen (0.0%); and Nitrogen (.6%). The weight which a 75 kg person would gain if all H atoms are replaced by H atoms is : () 0 kg () 5 kg () 7.5 kg (4) 7.5 kg 0 weight of H in body kg 00 If H is replaced by H, then wt of H is doubled weight increased by7.5 kg.. The major product obtained in the following reaction is : () ( )C 6 H 5 CH(O t Bu)CH C 6 H 5 () (+)C 6 H 5 CH(O t Bu)CH C 6 H 5 () C 6 H 5 CH=CHC 6 H 5 (4) (+)C 6 H 5 CH(O t Bu)CH C 6 H 5 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

9 JEE MAIN 07 (Code-C) (0-04-7) [ 9 ] Ans. (). Given C O (g) CO (g); (graphite) o rh 9.5kJ mol H (g) O (g) HO( ); o H 85.8 kj mol r CO (g) H O( ) CH (g) O (g); 4 o rh 890. kj mol Based on the above thermochemical equation, the value of o r H C(graphite) H (g) CH 4(g) will be: () 44.0 kj mol () kj mol () kj mol (4) 74.8 kj mol o graphite 4 98k C H (g) CH (g) : H? Given, () 0 graphite C O (g) CO (g) : H 9.5 kj / mol o () H (g) ½O (g) H O(l) : H 85.8kJ/ mol o () CO (g) H O(g) CH (g) O (g) : H 890. kj / mol 4 : at 98 K for the reaction Cgraphite H (g) CH 4(g) = 74.8 kj/mol o o o o H H H H 98k Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

10 [ 0 ] JEE MAIN 07 (Code-C) (0-04-7) 4. In the following reactions, ZnO is respectively acting as a/an : (a) ZnO + Na O Na ZnO (b) ZnO + CO ZnCO () acid and base () base and acid () base and base (4) acid and acid Ans. () ZnO NaO NaZnO (Acidic) (Basic) (Basic) ZnO CO ZnCO (Acidic) 5. The radius of the second Bohr orbit for hydrogen atom is : (Planck s Const. h = Js; mass of electron = kg; charge of electron e = C; permittivity of vacuum kg m A ) (). Å ().65 Å () 4.76 Å (4) 0.59 Å Ans. () r n,z n 0.59Å. z rz,n 0.59Å..Å 6. Two reactions R and R have identical pre-exponential factors. Activation energy of R exceeds that of R by 0 kj mol. If k and k are rate constants for reactions R and R respectively at 00 K, then In(k /k ) is equal to: (R = 8.4 J mol K ) () 4 () 8 () (4) 6 Ans. () E E 0 0 k k a a A.e A.e Ea /RT Ea /RT k k Ea Ea Ea / RT Ea / RT RT e e k k e k ln k A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is a, the closest approach between two atoms in metallic crystal will be: () a () a () a (4) a Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

11 JEE MAIN 07 (Code-C) (0-04-7) [ ] Ans. () In FCC 4r r a a a Closest distance between two atom = r = 8. The group having isoelectronic species is : a Ans. () () () O,F,Na,Mg O,F,Na,Mg () O,F,Na,Mg (4) O, F, Na, Mg + O,F,Na,Mg all species have 0 electrons. 9. Given o o Cl /Cl Cr /Cr E.6 V, E 0.74 V o o CrO 7 /Cr MnO 4/Mn E. V, E.5V Among the following, the strongest reducing agent is: () Cl () Cr () Mn + (4) Cr + Ans. () Reducing power Reduction Potential 0. -Methyl-pent -ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is : Ans. () () Four () Six () Zero (4) Two No. of stereoisomers = n = 4 where n = No. of chiral carbon(*) Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

12 [ ] JEE MAIN 07 (Code-C) (0-04-7) PART-B : MATHEMATICS. The integral 4 dx is equal to: cosx 4 () 4 () () (4) I 4 4 dx dx I cos x cos x /4 /4 I I cosec x dx cot x 4 I 4 I n. Let In tan x dx, n. If 5 5 I4 I6 a tan x bx C, where C is a constant of integration, then the ordered pair (a,b) is equal to: (), 5 (),0 5 (), 5 (4),0 5 n In tan x sec x dx n tan x I n C n n tan x In In C n For n = 6 5 tan x I6 I4 C 5. The area (in sq. units) of the region x,y :x 0, x y, x 4y and y x is: () Ans. () 7 () 5 () 59 (4) Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

13 JEE MAIN 07 (Code-C) (0-04-7) [ ] x x A x dx x dx A box contains 5 green and 0 yellow balls. If 0 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is: Ans. () () 4 () 6 5 () 5 (4) 6 Probability of success in each trial p, q, n Variance npq If dy sinx y cos x 0 and y 0, then y dx is equal to: () () 4 () (4) Ans. () dy cosx dx y sin x n y n sinx nc y sin x C Since; y 0 C 4 4 y Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

14 [ 4 ] JEE MAIN 07 (Code-C) (0-04-7) 6. Let be a complex number such that z where z. If k, 7 then k is Ans. () equal to: () () () z (4) z is the complex cube root of unity. 7 Applying, C C C C 4 0 z k z 0 7. Let a i ˆ ˆj kˆ and b ˆi ˆj. Let c be a vector such that c a, a b c 0 between c and a b be 0. Then a c is equal to: and the angle () 5 () a b c 0 ab c sin0 8 Now, a i ˆ ˆj kˆ and b ˆi ˆj from (i) c Now, c a c a 9...(i) c a c a 9 a c a b () 5 8 (4) 8. The radius of a circle, having minimum area, which touches the curve y = 4 x and the lines, y = x is: Ans. () () 4 () 4 () (4) Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

15 JEE MAIN 07 (Code-C) (0-04-7) [ 5 ] Required circle will be as shown in figure. Let the centre be 0,, then the radius r Now, radius r 4 9. If for x 0, 4, the derivative of 6x x tan is x g(x) 9x, then g(x) equals: x () 9x () 9x 9 () 9x x x (4) 9x Ans. () 6x x tan tan x x 9x d 6x x d 9 x tan tan x x dx dx 9x 9x 9 g(x) 9x 40. If two different numbers are taken from the set {0,,,,...,0}; then the probability that their sum as well as absolute difference are both multiple of 4, is: () 4 45 () 7 55 () 6 55 (4) 55 Ans. () The number of elements in sample space = C 55. Now, the favourable cases are those when the numbers chosen are any two from 0, 4, 8 or from, 6, 0, therefore, favourable cases C C 6 Hence, the required probability = 6 55 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

16 [ 6 ] JEE MAIN 07 (Code-C) (0-04-7) cot x cos x 4. lim ( x) x () 8 equals : () 4 () 4 (4) 6 t t x, x t t tan cos t cos t tan lim t0 = lim t t0 t. t The value of ( C C ) ( C C ) ( C C ) ( C C )... ( C C ) is : Ans. () () () 0 0 () (4) 0 C C C C C C... C C ( ) ( ) 4. For three events A, B, C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) and 4 P(All the three events occur simultaneously). 6 Then the probability that at least one of the events occurs, is () 7 64 () P(A) P(B) P(A B) 4 P(B) P(C) P(B C) 4 P(C) P(A) P(A C) 4 Add all 6 P(A) P(B) P(C) P(A B) P(B C) P(C A) 8 7 P(A B C) () 7 (4) 7 6 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

17 JEE MAIN 07 (Code-C) (0-04-7) [ 7 ] 44. Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = AB. If BPC, then tan is equal to : () 9 () 4 9 () 6 7 (4) 4 Ans. () AP = 4 tan 4 4 tan( ) 4 tan 4 tan 4 4 tan 4 tan 8 tan 4 tan tan The eccentricity of an ellipse whose centre is at the origin is.if one of its directrices is x = 4, then the equation of the normal to it at, is : () 4x y 7 () x y 4 () y x (4) 4x y e, centre (0,0) and a 8 a e and b a ( e ) b equation of ellipse will be x y 4 slope of tangent at, will be and slope of normal is, then equation of normal is (x ) y 4x y Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

18 [ 8 ] JEE MAIN 07 (Code-C) (0-04-7) 46. If, for a positive integer n, the quadratic equation, x(x ) (x )(x )... (x n )(x n) 0n has Ans. () two consecutive integral solutions, then n is equal to : () 0 () () (4) 9 nx n x ( (n )n) 0n n(n ) nx n x 0n 0 nx n x n(n ) 0n 0 x nx (n ) 0 4(n ) n n 4n 4 n n 47. The following statement (p q) [(~ p q) q] is: Ans. () () equivalent to p ~ q () a fallacy () a tautology (4) equivalent to ~ p q (p q) (~ p q) q (~ p q) (p q) q (~ p q) ~ (p q) q (~ p q) (~ p ~ q) q (~ p q) (~ p q) (~ q q) (~ p q) [(~ p q) t ] where t = tautology (~ p q) (~ p q) ~ (~ p q) (~ p q) t 48. The normal to the curve y(x ) (x ) = x + 6 at the point where the curve intersects the y-axis passes through the point : (), (), (), (4), Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

19 JEE MAIN 07 (Code-C) (0-04-7) [ 9 ] x 6 y, intersects y-axis at (0,) x 5x 6 dy (x 5x 6) (x 6)(x 5) dx (x 5x 6) dy 6 0 dx 6 (0,) slope of normal = y (x 0) x y 49. For any three positive real numbers a,b and c, 9(5a b ) 5(c ac) 5b(a c). Then : () a,b and c are in A.P () a,b and c are in G.P () b,c and a are in G.P. (4) b,c and a are in A.P. 5a 9b 5c 75ac 45ab 5bc 0 (5a) (b) (5c) (5a.5c) (5a.b) (b.5c) 0 (5a b) (b 5c) (5c 5a) 0 a b c 5a b 5c (say) 5 a,b 5,c b,c,a are in A.P. 50. If the image of the point P(,,) in the plane, x + y 4z + = 0 measured parallel to the line, x y z is Q, then PQ is equal to 4 5 () 4 () 6 5 () 5 (4) 4 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

20 [ 0 ] JEE MAIN 07 (Code-C) (0-04-7) equation of PQ: x y z 4 5 Any point S on line PQ is given by (r +, 4r, 5r +) point S lies on plane r 4r 4 5r 0 6r 6 0 r S,,8 PS ( ) ( ) (8 ) units 5. If PQ PS 4 units 5 tan x cos x cos x 9, then the value of cos 4x is : () Ans. () 9 () 7 9 () 5 (4) 5 sec x cos x cos x 9 cosx 5 cosx 9 cosx, cos x t let t 5 t 9 t t t 0 t, So, cosx, cosx Hence, cos 4x cos x Let a, b, c R. If f x ax bx c is such that a b c and f x y f x f y xy, x,y R, then Ans. () 0 f n is equal to : n () 90 () 55 () 0 (4) 65 f x ax bx c f a b c Now, f x y f x f y xy Put x y f 7 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

21 JEE MAIN 07 (Code-C) (0-04-7) [ ] Put x, y f 7 Put x, y f Now, Series is S t n S 7... t t n n n to n terms t t n upto n terms n 6 n 0 0 n n n n n 5 n 5n n 5n f n 0 6 Ans. n 5. The distance of the point (,, 7) from the plane passing through the point (,, ), having normal perpendicular to both the lines x y z 4 and x y z 7, is : () 5 8 () Let the equation of plane is a x b y c z 0 Since a b c 0 a. b c 0 a b c a b c 5 7 Hence equation of plane is 5 x 7 y z 0 5x 7y z 5 0 Hence distance () 0 8 Ans. 54. If S is the set of distinct values of b for which the following system of linear equations x y z x ay z ax by z 0 has no solution, then S is : () a finite set containing two or more elements () a singleton () an empty set (4) an infinite set 0 74 (4) 0 8 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

22 [ ] JEE MAIN 07 (Code-C) (0-04-7) Ans. () The system of equations has no solution Hence, a 0 a b a 0, a = 55. If Now equations become x y z, x y z, x by z 0 For, b =, rd plane is parallel to first two coinciding plane. A, 4 then adj A A is equal to : () () () (4) A A Now, A A 4 Hence adj A A is Ans A hyperbola passes through the point P, and foci at,0. Then the tangent to this hyperbola at P also passes through the point : (), (), (), (4), Let the hyperbola is x y a b...(i) It passes through, a b...(ii) Also, ae b a e b a e a b 4 a...(iii) From (ii) & (iii) b a a b 4 a a a 4 a a 4 9a 8 0 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

23 JEE MAIN 07 (Code-C) (0-04-7) [ ] But a a 8 a 8 0 a or 8 a 4 (from (iii)) a b Hyperbola is x y Now, Equation of the tangent at P, is x y y x This tangent passes through the point, Ans. 57. Let k be an integer such that the triangle with vertices (k, k), (5, k) and ( k, ) has area 8 sq. units. Then the orthocentre of this triangle is at the point : (), 4 (), (), (4), 4 Ans. () Area of the ABC = k k 5 k k k k 8 k k 0 5k k k 5k k 0 56 If 5k k 0 56 or, 5k k K K 0 K, 5 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

24 [ 4 ] JEE MAIN 07 (Code-C) (0-04-7) OR 5k k k K 66 0 k k I k A, 6, B 5,, C, Equation of AD is x 0... () Equation of BE is y x 0... () From () & (), orthocentre is, 58. Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is : Ans. () () 5 () 0 ().5 (4) 0 Let r be the radius, be the angle and A the area of the sector, then r r r 0 r 0 0 r 0 A. r.r r 0r r 5 r 5 Maximum area is 5 m when r = 5 m Ans. 59. The function x f : R, defined as f x, is : x Ans. () () surjective but not injective () neither injective nor surjective () invertible (4) injective but not surjective Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

25 JEE MAIN 07 (Code-C) (0-04-7) [ 5 ] f ' x x x.x x x x f is increasing in [, ] and decreasing in,, f is not injective. Also lim f x 0, f and f x Range, is co-domain of f f is surjective. 60. A man X has 7 friends, 4 of them are ladies and are men. His wife Y also has 7 friends, of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting ladies and men, so that friends of each of X and Y are in this party, is : Ans. () () 469 () 484 () 485 (4) 468 Let X invites x ladies and x men and Y invites y ladies and y men, then x x, y y,x y, x y. Total no. of ways = 485 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

26 [ 6 ] JEE MAIN 07 (Code-C) (0-04-7) PART-C : PHYSICS 6. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 0 GHz. What is the frequency of the microwave measured by the observer? Ans. () 8 speed of light 0 ms (). GHz () 7. GHz () 5. GHz (4) 0. GHz f ' f c u c u 0GHz c c / 7. GHz c c / 6. The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, D.5 0 m ; rise of water, h.45 0 m. Using g 9.80m / s and the rhg simplified relation T 0 N / m, the possible error in surface tension is closest to : ().5% ().4% () 0% (4) 0.5% Ans. () rhg Drhg T T D h (g is given, not the part of measurement) T r h T % error 00.49%.5% T 6. Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r /, is given by : () r () r () 4 r (4) 4 r Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

27 JEE MAIN 07 (Code-C) (0-04-7) [ 7 ] Ans. () hc 4E E E...(i) hc E E E...(ii) Dividing equation (i) by equation (ii) We get, 64. A body of mass m 0 kg is moving in a medium and experiences a frictional force F k. Its initial Ans. () speed is 0 0ms. If, after 0 s, its energy is () 0 kg s F ma m 8 0, the value of k will be : 4 () () (4) dv kv m dt 0 kg m 0 kg m s 0 kg m Now v mv mv v k dt m v 0 / 0 v0 dv v v0 k(0) 0 v v0 k(0) 0 v0 v0 4 k 0 kgm Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

28 [ 8 ] JEE MAIN 07 (Code-C) (0-04-7) 65. C p and C are specific heats at constant pressure and constant volume respectively. It is observed that Cp C a for hydrogen gas ; Cp C b for nitrogen gas. The correct relation between a and b is : Ans. () () a b () a 4b () a 8 b (4) a b 4 for H C p R C (MH ) R a...(i) For N C p R C MN 8 8 R b...(ii) 8 From (i) and (ii) a 4 b a 4b 66. The moment of inertia of a uniform cylinder of length and radius R about its perpendicular bisector is. What is the ratio / R such that the moment of inertia is minimum? () () () (4) MR M 4 R M M R MR M M 4 R 4 M M R 4 R 4 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

29 JEE MAIN 07 (Code-C) (0-04-7) [ 9 ] d M 4M R dr 4 R 5 For to be minimum d 0 dr R 4M 5 R R R R 67. A radioactive nucleus A with a half life T, decays into a nucleus B. At t 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.. Then, t is given by : () log. t T () t T log(.) () log T t (4) log(.) T log t log. Ans. () A B at t 0,N 0 0 at t t, N N N 0 No N 0. N No.N N o. N e o t n(.) t n. t t T og(.) og() Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

30 [ 0 ] JEE MAIN 07 (Code-C) (0-04-7) 68. Which of the following statements is false? Ans. () () In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed. () A rheostat can be used as a potential divider. () Kirchhoff s second law represents energy conservation. (4) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude. Conceptual. 69. A capacitance of F is required in an electrical circuit across a potential difference of.0 kv. A large Ans. () number of F capacitors are available which can withstand a potential difference of not more than 00V. The minimum number of capacitors required to achieve this is : () 6 () 4 () (4) To get capacitance F such that P.D. across any one should not be more than 00 V can be arranged as below : Total number of minimum capacitors required In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be : () r CE r r () r CE r r () r CE r r (4) CE Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

31 JEE MAIN 07 (Code-C) (0-04-7) [ ] Ans. () In steady state no current will pass through capacitor current through cell, i E r r P. D across capacitor = P. D. across r V ir Er r r Charge on capacitor = CV CEr r r 7. In the above circuit the current in each resistance is : () 0.5 A () 0.5 A () 0 A (4) A Ans. () Let potential of A is 0 V B = V G = V, V C = V F = 4 V, V D = 6 V and V H = 0 As there is no any P.D. across either resistor and hence no current will flow. 7. In amplitude modulation, sinusoidal carrier frequency used is denoted by and the signal frequency is c denoted by. The bandwidth ( ) of the signal is such that. Which of the following m m m c frequencies is not contained in the modulated wave? () c () m c () c m (4) m Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

32 [ ] JEE MAIN 07 (Code-C) (0-04-7) In amplitude modulation frequencies from ( c m ) to ( c m ) are obtained. Band width, m ( c m ) ( c m ) m As m c m c Hence in the frequency range only m can not be obtained. 7. In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be : Ans. () () 90º () 5º () 80º (4) 45º Conceptual 74. A copper ball of mass 00 gm is at a temperature T. It is dropped in a copper calorimeter of mass 00 gm, filled with 70 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75ºC. T is given by : Ans. () (Given : room temperature = 0ºC, specific heat of copper = 0. cal/gmºc) () 885ºC () 50ºC () 85ºC (4) 800ºC From principle of calorimetry, Heat lost by copper sphere = Heat gained by calorimeter + Heat gained by water (T 75) T T 885º C 75. In a Young s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 50 cm away. A beam of light consisting of two wavelengths 650 nm and 50 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is : Ans. () () 7.8 mm () 9.75 mm () 5.6 mm (4).56 mm Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

33 JEE MAIN 07 (Code-C) (0-04-7) [ ] Let n th order maxima of wavelength 50 nm coincides with n th order maxima wavelength 650 nm. i.e. n 50 = n 650 n 5 n 4 So 5 th order maxima of wavelength 50 nm coincides with 4 th order maxima of wavelength 650 nm. Then the least distance from central maxima is, 5D Y d (50 0 ) = 7.8 mm An electric dipole has a fixed dipole moment p, which makes angle with respect to x-axis. When subjected to an electric field E ˆ Ei, it experiences a torque T ˆ k. When subjected to another electric field E Eˆ j it experiences a torque T T. The angle is : Ans. () () 45º () 60º () 90º (4) 0º PE sin =P Esin(90 ) tan = = 60º 77. A slender uniform rod of mass M and length is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is : () g sin () g cos () g cos (4) g sin Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

34 [ 4 ] JEE MAIN 07 (Code-C) (0-04-7) M Mg sin gsin 78. An external pressure P is applied on a cube at 0ºC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by ; () P K () PK () PK (4) P K dv V( )dt (i) P K dv V (ii) P from (i) and (ii) dt K 79. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm from a converging lens of magnitude of focal length 0 cm. A beam of parallel light falls on the diverging lens. The final image formed is : () virtual and at a distance of 40 cm from convergent lens. () real and at a distance of 40 cm from the divergent lens. () real and at a distance of 6 cm from the convergent lens. (4) real and at a distance of 40 cm from convergent lens. Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

35 JEE MAIN 07 (Code-C) (0-04-7) [ 5 ] For L image will be formed at 5 cm from L (Left) For L u = 40 cm f = + 0 cm v = + 40 cm (using lens formula) real image will be formed at 40 cm from L i.e converging lens (right of L ). 80. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If min is the smallest possible wavelength of X-ray in the spectrum, the variation of log min with log V is correctly represented in : () () () (4) min hc ev log min log(hc) log(ev) hc log log V e Hence, correct answer is (4). Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

36 [ 6 ] JEE MAIN 07 (Code-C) (0-04-7) 8. The temperature of an open room of volume 0 m increases from 7 C to 7 C due to the sunshine. The atmospheric pressure in the room remains 0 5 Pa. If n i and n f are the number of molecules in the room before and after heating then n f n i will be: Ans. () ().8 0 () () (4).6 0 Using PV = NRT (N = number of moles) = N i R 90 and = N f R 00 N f N i = R = R = 5 0 R 90 For molecules n n N N N f i 0 f i = = In a coil of resistance 00, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is: () 5 Wb () 50 Wb () 75 Wb (4) 00 Wb Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

37 JEE MAIN 07 (Code-C) (0-04-7) [ 7 ] Ans. () ir d ir dt d R idt = 00 0 = 50 Wb 8. When a current of 5 ma is passed through a galvanometer having a coil of resistance 5, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 0 V is () ().55 0 () (4) (R 5) R + 5 = 000 R A time dependent force F = 6t acts on a particle of mass kg. If the particle starts from rest, the work done by the force during the first sec. will be: () J () 9 J () 8 J (4) 4.5 J a = 6t dv dt 6t v dv 6 t dt 0 0 6t v V0 t t ms W KE mv 4.5 J 0 Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

38 [ 8 ] JEE MAIN 07 (Code-C) (0-04-7) 85. A magnetic needle of magnetic moment Am and moment of inertia kg m is performing simple harmonic oscillations in a magnetic field of 0.0 T. Time taken for 0 complete oscillations is: () 8.89 s () 6.98 s () 8.76 s (4) 6.65 s I T = s MB For 0 oscillations, time = 0 T = 6.65 s 86. The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth s radius): () () () (4) Ans. () For d R GM g d R For d R GM g d 87. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? () () () (4) Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

39 JEE MAIN 07 (Code-C) (0-04-7) [ 9 ] Ans. () V = u gt 88. A particle A of mass m and initial velocity collides with a particle B of mass m which is at rest. The collision is head on, and elastic. The ratio of the de-broglie wavelengths A to B after the collision is: () A B () A B () A B (4) A B Ans. () m mv mv v v v v...(i) Also v v v e v = v v...(ii) (i) + (ii) v v v v v 4v From (ii) 4v v v Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

40 [ 40 ] JEE MAIN 07 (Code-C) (0-04-7) 4v v v v P mv mv A m PB v = m 4v mv PB h P PA B P B A mv mv B A A B 89. A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like : () () () (4) Ans. () Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7

41 JEE MAIN 07 (Code-C) (0-04-7) [ 4 ] V V cost max KE mvmax cos t 90. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of: () 9 () 8 () 8 (4) 9 Strees = F mg LgA Lg A A A Now when length increases ' mg A '9Lg 9Lg A ' A' Mentors Eduserv: Parus Lok Complex, Boring Road Crossing, Patna- Helpline No. : /4/6/7