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FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016. Ph: 46106000/10/13/15 Fax : 26513942.

FACULTY RECRUITMENT TESTFormal School Education/IX, X / NSEJS/NTSE/ Foundation

for KVPY, Senior Olympiads & IIT-JEE

CATEGORY-D (MATHEMATICS)

PAPER BTime: 1 Hour Maximum Marks: 40

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

Subject:...........................................

Marks:

Inst ruct ions

Attempt all questions.

PAPER-B has two parts I and II. Each question of partI carries 2 marks and that ofpartII carries 4 marks.

Calculators and log tables areno t permit ted.

PARTI1. If tan

2= 2 tan

2+ 1, then find the value of cos 2+ sin

2.

2. If3

log 5 a and3

log 2 b , then find the value of3

log 300 .

3. In the given figure, AD is the trisector of

BAC, prove that AB AC = BD DC = AD2

.

A

B CD

4. In the triangles having same bases and equal area. The triangle that is isosceles has minimumperimeter. Prove it.

5. Prove that cos A cos 2A cos 22A cos 2

3A cos 2

n1A =n

n

sin2 A

2 sin A.

6. P (x) = x4+ bx

3+ cx

2+ dx + e is a polynomial of degree 4. If P (1) = P (2) = P (3) = 0, then find the

value of P (4) + P (0).

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