FACULTY RECRUITMENT TEST
CATEGORY-D
Formal School Education/ VIII
MATHEMATICS
PAPER – B
Time: 1 Hour
Maximum Marks: 40
Name:.................................................................................
Marks:
Subject:…………………………...........................................
Instructions

Attempt all questions.

PAPER-B has only one part. Each question carries two marks.

Calculators and log tables are not permitted.
1.
In the given figure, ABCO is a rhombus, three of
whose vertices lie on a circle with centre O. If the
3
area of the rhombus is 32 3 cm , find the radius
of the circle.
A
B
O
C
th
th
2.
If the m term of an A.P. is 1/n and the n term is 1/m, find the sum of mn terms.
3.
A semicircular region and a square region have equal perimeter. The area of the square region
2
exceeds that of the semicircular region by 4 cm . Find the areas of two regions.
4.
The medians of a right triangle which are drawn from the vertices of the acute angles are 15 cm and
40 cm, find the length of the hypotenuse.
5.
If sec  + tan  = x, what is the value of sin  in terms of x.
6.
Factorize : (a + b + c)  a  b  c .
7.
Determine the set of integers n for which n + 19n + 92 is a square.
8.
If ABCD be a convex quadrilateral in which BAC = 50, CAD = 60, CBD = 30 and BDC = 25.
If E is the point of intersection of AC and BD, then find AEB.
9.
Find the value of
3
3
3
3
2
3 5 
2  3 
FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016. Ph: 46106000/10/13/15 Fax : 26513942.
FACREC-NTSE-P2-B-MATH-2
10.
If 2x =
a
1
x2  1
, then find the value of
a
x
x
2

.
1
11.
Find the sum upto n terms of the series: 6 + 66 + 666 + …
12.
Three circles each of radius ‘r’ touch one another. Find the radius of the circle touching all the three
given circles internally.
13.
If a = bc, b = ca, c = ab, then find xyz.
14.
Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. Find
the total number of persons in the room.
x
y
z
15.
1

2
2
If a + b = 7ab, then find the value of log   a  b  .
3

16.
Find the LCM of
17.
If the sides of the triangles are 5k, 6k, 5k and radius of incircle is 6, then find the value of k.
18.
The sides of a triangle are 7 cm, 4 3 cm and 13 cm, then find the smallest angle.
19.
If x = 7  4 3 and xy = 1, then find
2 3
5
,
and .
7 14
3
1
x
20.
If
2

1
y2
.
x a x b x c


 3 , then find x.
bc c a ab
FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 110016. Ph: 46106000/10/13/15 Fax : 26513942.