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Posted Date: 28 Feb 2011 Posted By:: rohit singh G. Member Level: Bronze Points: 5 (₹ 1)
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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 y-axes 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?REC-04-(APT–SAT-II)-09-10)?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 x-axis 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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