iitjee 2006

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Section IV :This section consists of 4 questions.Answers are to be given in between0000 to 9999 in the form of nearestinteger.Q.33 If roots of x 2 –10cx –11d = 0 are a, b and theroots of x 2 –10ax –11b = 0 are c, d, then thevalue of a+b+c+d is equal to (a,b,c,d aredifferent numbers) ………………………….Ans. [1210]Q.34 The value 50501∫∫01050 100( 1−x ) dx50101( 1−x ) dxis equal to…………………..... Ans [5051]2 33 ⎛ 3 ⎞ ⎛ 3 ⎞Q.35 Let a n = – ⎜ ⎟ + ⎜ ⎟ – ………………4 ⎝ 4 ⎠ ⎝ 4 ⎠n(–1) n–1 ⎛ 3 ⎞⎜ ⎟⎠ and b⎝ 4n= 1–a nthen find thenatural number n 0such that b n>a n, n > n 0.is………. Ans [0005]Q.36 If f(x) is twice differentiable and f(a) = 0,f(b) = 2, f(c) = –1, f(d) = 2, f(e) = 0,where a < b < c < d < e then the minimumnumber of zeroes of g(x)= {f ′(x)}2 + {f ′′(x)f(x)} in [a,e] is ?Ans.[0006]Section V: This section consists of 4 questions.Each having two columns with 4entries in each column. Entries ofcolumn I are to be matched withcolumn II. One entry of column I mayhave more than one matching incolumn II.Ans.–(a) → (p)(b) → (s)(c) → (r)(d) → (q)Q.38 Column I(a) Area bounded by (p) 0–4y 2 = x and x–1= – 5y 2(b) cosine of the angle (q) 6 ln 2of intersection of curvesy= x x –1 and y = 3 x–1 log xAns.–(c) / cos xsin x( sin x) ( cos x.cot x – log(sin x) )∫ π 20(r) 4/3,(d) Not available (s) 1,(a) → (r)(b) → (s)(c) → (s)Q.39 (a) –1⎛1 ⎞∑ ∞ tan ⎜ ⎟ = t , (p) 02i=1 ⎝ 2i ⎠then tan t =(b) A line perpendicular to (q) 35x + 2y + 2z = 0 and passesthrough (0, 1, 0) then theperpendicular distance ofthe line from origin is(c) Not available (r) 1(d) Not available (s) 2/3dxQ.37 Three normals drawn at P,Q and R on theparabola y 2 = 4x intersect at (3, 0). ThenColumn I Column II(a) Radius of circumcircle (p) 5/2of ∆ PQR(b) Area of ∆ PQR (q) (5/2, 0)(c) Centroid of ∆ PQR (r) (2/3, 0)(d) circumcentre of ∆ PQR (s) 2Ans.–(a) → (r)(b) → (s)CAREER POINT, 112, SHAKTI NAGAR , KOTA (RAJ) PH. 250049218PAPER - IIT-JEE-<strong>2006</strong>
Column IQ.40(a) Two rays in the Ist quadrant ax–y = 1and x + y = |a| cut each other in theInterval a ∈ (a 0 , ∞) the value of a 0 is(b) sinA sinB sinC + cosAcosB = 1then sinC =(c)10(1 − y2 )dy + (y2∫−1)dy01∫(d) Let a = α î + β ĵ + γ kˆ , kˆ ×(kˆ × a ) = 0and a point (α,β,γ) lies on planex + y + z = 2, then γ =Column II(p) 4/3(q)11∫− xdx + 1∫+00–1x dx(r) 1(s) 2Ans.–(a) → (r)(b) → (r)(c) → (p) & (q)(d) → (s)CAREER POINT, 112, SHAKTI NAGAR , KOTA (RAJ) PH. 250049219PAPER - IIT-JEE-<strong>2006</strong>
Page 1 and 2: Section I:Multiple Choice Questions
Page 3 and 4: Section II: Multiple Choice Questio
Page 5: Q.25 Resultant wave is given as y R
Page 8 and 9: IIT-JEE (2006)(Memory Based Questio
Page 10: Q.16Q.17CH 3CH 3-CH-CH 2-CH3Cl /hv
Page 13 and 14: Q.36 K spof AgBr = 12 × 10 -14 . T
Page 15 and 16: Q.8 If ω = α+iβ where β ≠ 0 a
Page 17: Passage - IITotal n urns each conta

iitjee 2006

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