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Posted Date: 28 Feb 2011 Posted By:: rohit singh G. Member Level: Bronze Points: 5 (₹ 1)

2009 Fiitjee maths paper 2 Question paper
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FACULTY RECRUITMENT TEST MATHEMATICS APT & SAT–II PAPER – II Time: 60 Minutes. Maximum Marks: 40 Name:.................................................................................................... Subject: ................................................................................................ Marks: Instructions: ? Attempt all questions. ? This question paper has two Parts, I and II. Each question of Part I carries 2 marks and of Part II carries 5 marks. ? Calculators and log tables are not permitted PART – I 1. Find the expression of integral without evaluating which represents the area enclosed by the smaller loop of the graph r = 1 + 2sin?. 2. Find the third degree Taylor polynomial about x = 0 of ln(1 – x). 3. A solid has a rectangular base that lies in the first quadrant and is bounded by the x and yaxes and the lines x = 2 and y = 1. The height of the solid above the point (x, y) is 1 + 3x. Find the Riemann sum approximation for the volume of the solid. 4. Evaluate h 3 3 cos h cos 2 2 lim ?? h ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? . 5. Find the solution of the differential equation dy 4x dx y ? , where y(2) = – 2. 6. Evaluate 2 x 2 x 4 lim ?? 2 x 4x ? ? ? . 7. A particle travels along a straight line with a velocity of v(t) = 3e–t/2 sin2t meters per second. What is the total distance, in meters, traveled by the particle during the time interval 0 ? t ? 2 seconds? FIITJEE Ltd., FIITJEE House, 29 – A, Kalu Sarai, Sarvapriya Vihar, New Delhi  110016, Ph : 26515949 , 26569493, Fax :011 26513942. FAC?REC04(APT–SATII)0910)?MA?2 8. A differentiable function f has the property that f(5) = 3 and f?(5) = 4. What is the estimate for f(4.8) using the local linear approximation for f at x = 5? 9. Oil is leaking from a tanker at the rate of R(t) = 2000e–0.2t gallons per hour, where t is measured in hours. How much oil leaks out of the tanker from time t = 0 to t = 10? 10. Which of the following series converge to 2? I. n 1 2n n 3 ? ? ? ? II. ? ?n n 1 8 3 ? ? ? ? ? III. n n 0 1 2 ? ? ? PART – II 1. What are all values of x for which the series n n n 1 n3 x ? ? ? converges? 2. For a series S, let S = n 1 1 1 1 1 1 1 1 1 1 ... a ... 9 2 25 4 49 8 81 16 121 ? ? ? ? ? ? ? ? ? ? ? ? , where an = ? ? ? ? n 1 / 2 1 ,if n is odd 2 1 , if n is even n 1 ? ? ??? ? ? ?? ? which of the following statements are true? Justify. I. S converges because the terms of S alternate and n n lim a 0 ?? ? II. S diverges because it is not true that an + 1 < an for all n. III. S converges although it is not true that an + 1 < an for all n. 3. A particle moves along the xaxis so that at any time t ? 0 its velocity is given by v(t) = ln(t + 1) – 2t+ 1. The total distance traveled by the particle from t = 0 to t = 2 is 4. Draw the slope field for the differential equation dy x dx y ? ?
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