8/9/2019 Cat-A Jee Main,Jee Advanced & Io Maths Paper A_2

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FACULTY RECRUITMENT TESTCATEGORY-A

JEE Main/JEE Advanced & IOMATHEMATICS

PAPER  – A

Time: 60 Minutes. Maximum Marks: 40

Name: ........................................................................................................

Subject: .....................................................................................................Marks:

Instruct ions:

  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 domain of the function f(x) =

x 21

2 x 1

8 3sin

1 3

.

2. Let f(x) = x2 and g(x) = sinx for all x  R. Then find the set of all x satisfying (fogogof)(x) = (gogof)(x),

where (fog)(x) = f(g(x)).

3. Let z = x + iy be a complex number where x and y are integers. Then find the area of the rectangle

whose vertices are the roots of the equations 3 3zz zz 350 .

4. Let a, b, c be the sides of a triangle where a  c and   R. If the roots of the equation x2 + 2(a + b +

c)x + 3(ab + bc + ca) = 0 are real, then find the interval in which  lies.

5. Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations3x  – y  – z = 0 – 3x + z = 0 – 3x + 2y + z = 0.

Then find the number of such points for which x2 + y

2 + z

2  100.

6. Given an isosceles triangle, whose one angle is2

3

 and the radius of its incircle = 3 . Then find the

area of the triangle.

8/9/2019 Cat-A Jee Main,Jee Advanced & Io Maths Paper A_2

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FIITJEE Ltd., FIITJEE House, 29 –  A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016, Ph : 26515949 , 26569493, Fax :011- 26513942. 

FACREC-(SAT-II, IITJEE&IO-1112)-PAPER A MA 2

7. Find the locus of the orthocentre of the triangle formed by the lines(1 + p)x  – py + p(1 + p) = 0(1 + q)x  – qy + q(1 + q) = 0 and

y = 0, where p  q.

8. Let ABCD be quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD. Let AD

be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all thesides, then find its radius.

9. A line with positive direction cosines passes through the point P(2,  – 1, 2) and makes equal angleswith the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. Then find the length ofthe line segment PQ.

10. Let g(x) =n

m

( x 1)

logcos (x 1)

; 0 < x < 2, m and n are integers, m  0, n > 0, and let p be the left hand

derivative of |x  – 1| at x = 1. If x 1lim g x p,

 then find the value of m and n.

PART –

 II

1. Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and2x 0

p(x)lim 1 2

x

. Then find

the value of p(2).

2. Evaluate/ 3   3

/ 3

4x

2 cos | x |3

dx. 

3. a, b, c, d   are four distinct vectors satisfying the conditions a b c d  and a c b d , then prove

that a b c d a c b d .

4. Tangents are drawn to the circle x2 + y

2 = 9 from a point on the hyperbola

2 2x y1

9 4 . Find the locus

of mid –point of the chord of contact.