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(C)25 / 6πI = x dxn ∫sec πl 327 / 6π5 / 6I = ln| sec πx+ tan πx|πln37 / 6πI = ⋅ ln3= πln3(D) ∴ |z| = 1z = cos θ + i sin θ. ∀ θ∈ (– π. π] and θ ≠ 0.1Arg(1 − z)⎛ θ ⎞⎜ icot⎟⎛ 1 ⎞⎜1= Arg ⎜⎟ = Arg + 2 ⎟⎝1− cosθ − isinθ ⎠ ⎜ 2 2 ⎟⎝ ⎠=π − θ2so maximum value is π.60. Match the statements given in Column-I with theintervals/union of intervals given in Column-II.Column-I(A) The set⎧ ⎛ 2iz ⎞⎫⎪Re⎜⎟;z is a complex number,2⎪⎨ ⎝1− z ⎠⎬ is⎪⎪⎩| z | = 1, z ≠ ± 1 ⎭(B) The domain of the function⎛ x−2⎞−1⎜8(3)f ( x)= sin⎟ is2( x−1)⎝1−3 ⎠1(C) If f ( θ)= − tan θ−1tan θ1− tan θ1tan θ , then the⎧π⎫set ⎨ f ( θ) : 0 ≤ θ < ⎬ is⎩2 ⎭3/ 2(D) If f ( x)= x (3x−10),x ≥ 0 , then f(x) isincreasing inColumn-II(p) (– ∞, –1) ∪ (1, ∞)(q) (– ∞, 0) ∪ (0, ∞)(r) [2, ∞)(s) ( – ∞, –1] ∪ [1, ∞)(t) (– ∞, 0] ∪ [2, ∞)Ans. [A → p, r, s ; B → r, t ; C → r ; D → r]1Sol.(A) Let z = cos θ + i sin θ2iz2i(cos+isinθ)so == −cosecθ21−z 1−cos2θ − isin 2θ∀ θ ≠ (2n + 1) 2π⎛ 2iz ⎞so Re⎜⎟ = − cos ec θ∈(−∞,−1]∪ [1, ∞)2⎝1− z ⎠x−28×3 8×3(B) =2x−22x1−3 9 − 3Let 3 x = t⎛So f(x) = sin –1 ⎜8 3⎝ 9 − 3x⎞⎟ = sin⎠×x−12x8t−1≤ 129 − t≤ on solvingx ∈ (– ∞, 0] ∪ [2, ∞) ∪ {1}(C) f(θ) = 2 sec 2 θso f(θ) ∈[2, ∞)(D) f(x) = 3x 5/2 – 10x 3/215 xf'(x) = ( x − 2)2So f(x) is increasing for f '(x) ≥ 0x ∈ [2, ∞)Random Facts⎛ 8t⎜⎝ 9 − t• As a gas' temperature is raised to over10,000°, its molecules collide so violentlythat they are broken apart into individualatoms.• When the tsunami reaches the coast andmoves inland, the water level can risemany meters. In extreme cases, water levelhas risen to more than 15 m (50 ft) fortsunamis of distant origin and over 30 m(100 ft) for tsunami waves generated nearthe earthquake’s epicenter.• Some minerals, notably quartz, arepiezoelectric--that is, they produceelectricity when subjected to pressure orstress. This same phenomenon is probablyalso responsible for "earthquake lights,"the luminescence sometimes reported (and,on occasion, photographed) in the skyduring earthquakes.2⎟⎠⎞XtraEdge for IIT-JEE 96 MAY 2011
XtraEdge Test SeriesANSWER KEYIIT- JEE 2012 (May issue)PHYSICSQues 1 2 3 4 5 6 7 8Ans D C C B A B A A,B,CQues 9 10 11 12 13 14 15 16Ans B,C B,C A,B,C,D B C C B CNumerical Ques 17 18 19 20 21 22 23Response Ans 3 1 2 1 2 3 4CHEMISTRYQues 1 2 3 4 5 6 7 8Ans C B D D B A C B,CQues 9 10 11 12 13 14 15 16Ans B,D B,D D C D B D BNumerical Ques 17 18 19 20 21 22 23Response Ans 1 6 7 2 8 4 6MATHEMATICSQues 1 2 3 4 5 6 7 8Ans A A D A C C A B,DQues 9 10 11 12 13 14 15 16Ans A,B,C A,B,C,D B,D D C A A ANumerical Ques 17 18 19 20 21 22 23Response Ans 9 0 2 5 1 1 0IIT- JEE 2013 (May issue)PHYSICSQues 1 2 3 4 5 6 7 8Ans B A A D A B A A,B,C,DQues 9 10 11 12 13 14 15 16Ans A,B,C A,B,D A,C,D C B C B BNumerical Ques 17 18 19 20 21 22 23Response Ans 6 9 1 5 6 4 5CHEMISTRYQues 1 2 3 4 5 6 7 8Ans A B D B A C D A,B,CQues 9 10 11 12 13 14 15 16Ans A,B,C A,D A,C,D A B A B ANumerical Ques 17 18 19 20 21 22 23Response Ans 3 1 1 5 0 2 3MATHEMATICSQues 1 2 3 4 5 6 7 8Ans A C C C D A C A,B,DQues 9 10 11 12 13 14 15 16Ans C,D A,C A,B,C,D C C B A BNumerical Ques 17 18 19 20 21 22 23Response Ans 5 9 3 2 6 3 2XtraEdge for IIT-JEE 97 MAY 2011
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Volume - 6 Issue - 11May, 2011 (Mon
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Volume-6 Issue-11May, 2011 (Monthly
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KNOW IIT-JEEBy Previous Exam Questi
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Physics Challenging ProblemsSet # 1
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PHYSICSStudents'ForumExpert’s Sol
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PHYSICS FUNDAMENTAL FOR IIT-JEEElec
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the indivual forces. It's often hel
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Hence, E x = -∴∂V∂ xE = - ayi
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For (x - a) 2 + (y - b) 2 = r 2 , t
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KEY CONCEPTPhysicalChemistryFundame
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Kinetic Isotope Effects :The kineti
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MATHSCOMPLEX NUMBERMathematics Fund
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MATHSMATRICES &DETERMINANTSMathemat
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Page 50 and 51: dxO12. The time of crossing the riv
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Page 54 and 55: 7. If the equation 3x 4 - 16x 3 + 3
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Page 62 and 63: 17. Ifsin 3θcos 2θ2-147137= 0Then
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Page 70 and 71: 1 2 × 8∆U = × [V - 0]22 2 + 81
Page 72 and 73: shown in the figure. We use the sig
Page 74 and 75: 40. A block is moving on an incline
Page 76 and 77: MATHEMATICSSECTION - ISingle Correc
Page 78 and 79: Ans.Sol.[A,D]r = xiˆ + yj ˆ + zk
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Page 84 and 85: Ans. [A]Sol. ∆T = k f × m × i
Page 86 and 87: SECTION - IVMatrix match TypeThis s
Page 88 and 89: Ans.[D]m 1 = 0.01 kgvH = 5mm 2 = 0.
Page 90 and 91: 31. A series R-C circuit is connect
Page 92 and 93: P3PBAColumn-I(A) Pipe closed at one
Page 94 and 95: 21/ x45. If lim [1 + xl n(1 + b )]
Page 96 and 97: So f(x) is monotonically decreasing
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