September 2011 - Career Point

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⎛ dy ⎞∴ arc AP = s =∫ 21+⎜ ⎟ dx.⎝ dx ⎠xaP(x,y)A(x = a)Using the above information, answer the followingquestions :13. Length of the arc of the parabola y 2 = 4x cut off byits latus-rectum is :(A) 2[ 2 + log e ( 2– 1)](B) 2[ 2 + ln( 2+ 1)](C) [ 2 + ln( 2+1)](D) [ 2 + ln( 2–1)]14. Whole length of the astroid x 2/3 + y 2/3 = 4 is :(A) 12 (B) 48(C) 6(D) none of these15. Length of the curve y = log e (sec x) between x = 0to x = π/3 is :(A) ln(2 + 3 ) (B) ln(1 + 3 )(C) 21 ln 3 (D) ln(2 – 3 )Passage # 2 (Ques. 16 to 18)Multinomial theorem states that for n ∈ N anda 1 , a 2 ,...........,a p ∈ C, then(a 1 + a 2 + ...+ a p ) nn!= ∑n1n2n pa 1 a2..... a pn1 ! n2!....... n p !where n 1 , n 2 ,...,n p are non-negative integers suchthat n 1 + n 2 + .... + n p = nAnswer the following questions :16. If x 1 , x 2 ,.....x n are independent, then number ofterms in the expansion of (x 1 + x 2 + .... + x n ) 5 is :(A) n+1 C 5 (B) n+4 C 5 (C) n+5 C 4 (D) n+4 C 417. Coefficient of x 3 y 3 z in the expansion of (1 + x – y + z) 9is :(A) 2520 (B) 2800 (C) – 2800 (D) – 140018. Coefficient of a 3 b 4 c 5 in the expansion of (ab + bc +ca) 6 is :(A) 60 (B) 40 (C) 0 (D) NonesThis section contains 2 questions (Questions 19, 20).Each question contains statements given in twocolumns which have to be matched. Statements (A, B,C, D) in Column I have to be matched withstatements (P, Q, R, S, T) in Column II. The answersto these questions have to be appropriately bubbledas illustrated in the following example. If the correctmatches are A-P, A-S, A-T; B-Q, B-R; C-P, C-Q andD-S, D-T then the correctly bubbled 4 × 5 matrixshould be as follows :ABCDP Q R S TP Q R S TP Q R S TP Q R S TP Q R S TMark your response in OMR sheet against thequestion number of that question in section-II.+ 8 marks will be given for complete correct answer(i.e. +2 marks for each correct row) and No Negativemarks for wrong answer.19. Match the column :Column-IColumn-II(A) The largest value of n such (P) 2that 2010 n divides 2010!6r12 C(B) N = ∑ (–1)r=0r (Q) 3(C) The number of positive (R) 5integer triplets (a,b,c)such that a + b + c ≤ 0(D) A set contains 6 elements. (S) 7The number of ordered pairs(A,B) such that A ∩ B = φ (T) 1120. Match the column :Column-IColumn-II(A) Area of the region defined (P) 0by the inequality1|y| + ≤ 2 1– | x | is p/q,then p – q =(B) Sum of the values of α for (Q) 5/6which the system of inequalitiesx 2 + 2x + α ≤ 0; x 2 – 4x – 6α ≤ 0has unique solution iscos nx(C) If I n =∫dx, thensin x(R) 12cos pxI 7 – I 5 = , where p =p(D) The number of 5 digit (S) 4/5numbers made up of thedigits 3, 4, 5, 6,7 withoutrepetitions which are multipleof 11 is ab. Then b – a = (T) 1/6XtraEdge for IIT-JEE 62 SEPTEMBER <strong>2011</strong>
Based on New PatternIIT-JEE 2013XtraEdge Test Series # 5Time : 3 HoursSyllabus : Physics : Laws of motion, Friction, Work Power Energy, Gravitation, S.H.M., Laws of Conservations ofMomentum, Rotational Motion (Rigid Body), Elasticity, Fluid Mechanics, Surface Tension, Viscosity.Chemistry : Gaseous state, Chemical Energetic, Oxidation-Reduction, Equivalent Concept, Volumetric Analysis.Mathematics : Logarithm & Modulus Function, Quadratic Equation, Progressions, Binomial Theorem, Permutation &Combination, Complex Number.Instructions : [Each subject contain]Section – I : Question 1 to 8 are multiple choice questions with only one correct answer. +3 marks will be awardedfor correct answer and -1 mark for wrong answer.Section – II : Question 9 to 12 are multiple choice question with multiple correct answer. +4 marks will be awarded for correctanswer and -1 mark for wrong answer.Section – III : Question 13 to 18 are passage based single correct type questions. +4 marks will be awarded forcorrect answer and -1 mark for wrong answerSection – III : Question 19 to 20 are Column Matching type questions. +8 marks will be awarded for the completecorrectly matched answer (i.e. +2 marks for each correct row) and No Negative marks for wronganswer.PHYSICSQuestions 1 to 8 are multiple choice questions. Eachquestion has four choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct. Mark your response inOMR sheet against the question number of thatquestion. + 3 marks will be given for each correctanswer and – 1 mark for each wrong answer.1. A child is standing at one end of a long trolleymoving with a speed v on a smooth horizontaltrack. If the child starts running towards the otherend of the trolley with a speed u, the centre of massof the system (trolley + child) will move with aspeed -(A) zero (B) (v + u) (C) (v – u) (D) v2. A particle strikes a horizontal frictionless floor witha speed u, at an angle θ with the vertical, andrebounds with a speed v, at an angle φ with thevertical. The coefficient of restitution between theparticle and the floor is e. The angle φ is equal to –uθ φ v3. Two blocks A and B of mass m and 2m areconnected by a massless spring of force constant k.They are placed on a smooth horizontal plane.Spring is stretched by an amount x and thenreleased. The relative velocity of the blocks whenthe spring comes to its natural length is –⎛(A) ⎜⎝(C)3k⎞⎟ x2m⎠2kxmA B⎛(B) ⎜⎝(D)2k3m3km2x⎞⎟ x⎠4. Three identical blocks A, B and C are placed onhorizontal frictionless surface. The blocks B and Care at rest but A is approaching towards B with aspeed 10 m/s. The coefficient of restitution for allcollisions is 0.5. The speed of the block C just aftercollision is –A B C(A) θ (B) tan –1 [e tan θ](C)− ⎡1⎤tan 1⎢ tan θ⎥⎣e⎦(D) (1 + e)θ(A) 5.6 m/s(C) 8 m/s(B) 6 m/s(D) 10 m/sXtraEdge for IIT-JEE 63 SEPTEMBER <strong>2011</strong>
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Volume - 7 Issue - 3September, 2011
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challenges for both high school and
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KNOW IIT-JEEBy Previous Exam Questi
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CHEMISTRY6. A hydrated metallic sal
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Given that K sp for Ag 2 C 2 O 4 =
Page 14 and 15: π(1 - cos kx)1 - cos( k - 1) x= 2
Page 16 and 17: 8Questions1. ConceptualOption [A,B,
Page 18 and 19: (ii) Prove that the harmonic oscill
Page 20 and 21: θωConsider a radius of the shell
Page 22 and 23: PHYSICS FUNDAMENTAL FOR IIT-JEECurr
Page 24: (b) Real cellr,EiRise upr,EDrop upE
Page 27 and 28: Sol. The circuit is shown in fig.10
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Page 31 and 32: z =∫∫z dm=dm∫z dmMwhere M is
Page 33 and 34: Problem Solving Strategy: Equilibri
Page 35 and 36: OrganicChemistryFundamentalsALIPHAT
Page 37 and 38: oxymercuration - demercuration of 3
Page 39 and 40: The free molecule, in the gas phase
Page 41 and 42: UNDERSTANDINGInorganic Chemistry1.
Page 43 and 44: Sol. All the above information can
Page 45 and 46: MATHEMATICAL CHALLENGESSOLUTION FOR
Page 47 and 48: let y = 1 in it2. f (x/2) = f (x) (
Page 49 and 50: Now, cos α ==2 +BG CG - BC2BG .CG2
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Page 53 and 54: MATHSBINOMIAL THEOREMMathematics Fu
Page 55 and 56: XtraEdge for IIT-JEE 53 SEPTEMBER 2
Page 57 and 58: f = 20 cm(0, 0)5mmf = -10Principle
Page 59 and 60: 16. Value of k 2 is -8(A) (B)332(C)
Page 61 and 62: 10. 0.5 M KI solution reacts with e
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Page 69 and 70: 10. Select the correct statement -(
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Page 73 and 74: Subscription Offer for Students'Xtr
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September 2011 - Career Point

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