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Math Faculty Test Paper

This document contains a faculty recruitment test for mathematics. It provides instructions for a 60 minute test with 40 total marks. The test contains two parts - Part I contains 10 multiple choice questions worth 2 marks each, and Part II contains 4 longer form questions worth 5 marks each. Calculators and log tables are not permitted. The document provides the questions and response fields for the test.

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Arijit Singh
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© Attribution Non-Commercial (BY-NC)
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587 views2 pages

Math Faculty Test Paper

This document contains a faculty recruitment test for mathematics. It provides instructions for a 60 minute test with 40 total marks. The test contains two parts - Part I contains 10 multiple choice questions worth 2 marks each, and Part II contains 4 longer form questions worth 5 marks each. Calculators and log tables are not permitted. The document provides the questions and response fields for the test.

Uploaded by

Arijit Singh
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016. Ph: 46106000/10/13/15 Fax : 26513942.

FACULTY RECRUITMENT TEST


CATEGORY - A
APT, SAT-II, IITJEE & IO

(MATHEMATICS)

PAPER A


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 maximum value of (cos o
1
) (cos o
2
) (cos o
n
) under the restriction
0 s o
1
, o
2
, , o
n
s
2
t
and (cot o
1
) (cot o
2
) (cot o
n
) = 1

2. For all complex numbers z
1
, z
2
satisfying |z
1
| = 12 and |z
2
3 4i| = 5, find the minimum value of |z
1

z
2
|

3. For the equation 3x
2
+ px + 3 = 0, p > 0, if one of the roots is square of the other then find p

4. Suppose a, b, c are in A.P. and a
2
, b
2
, c
2
are in G.P. If a < b < c and a + b + c =
2
3
, then find the
value of a

5. If a > 2b > 0, then find the positive value of m for which y = mx b
2
m 1+ is a common tangent to x
2

+ y
2
= b
2
and (x a)
2
+ y
2
= b
2



FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016. Ph: 46106000/10/13/15 Fax : 26513942.
FACREC-(SAT-II, IITJEE&IO-1112)-PAPERA MA2
6. Evaluate,
x
x
2 x
3 x
lim |
.
|

\
|
+


, for xeR

7. Evaluate
}
2
e
e / 1
x
x ln
dx

8. If a
n
=

=
n
0 r r
n
C
1
, then prove that

=
=
n
0 r
n
r
n
2
na
C
r


9. Find the number of values of k for which the system of equations
(k + 1) x + 8y = 4k and kx + (k + 3) y = 3k 1 has infinitely many solutions.

10. Let f (x) = (1 + b
2
) x
2
+ 2bx + 1 and let m (b) be the minimum value of f (x). As b varies, find the range
of m (b)

PART II

1. A tennis match of best of 5 sets is played by two players A and B. The probability that first set is
won by A is
1
2
and if he looses the first then probability of his winning of next set is
1
4
otherwise it
remains same. Find the probability that A wins the match.

2. Find the area between the curve y =
2
4 x and the locus of the point P which moves such that the
sum of its distances from the coordinate axes is equal to its distance from the curve y =
2
4 x .

3. Evaluate
( )
2
cosec xln cosx cos2x dx
}
.

4. Let P be any point in the first quadrant on a curve passing through (3, 3) and the slope of the curve at
any point in the first quadrant is negative. The foot of the perpendicular from P to x-axis is the point A
and to y-axis is the point B. Tangent at P intersects with x-axis at point R and with y-axis at point Q.
Now if 2(Area (APAR)) + Area (ABPQ) =
2
3
(Area of rectangle OAPB), for all positions of P, where O
is the origin, then find all possible curves on which P can lie. Also find the minimum distance of P from
the origin on each curve.

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