Geometry

In the figure A is the centre of the circle . B is a point on the circumference and AFBE is a rectangle . AE and AF produced meet the circle at D and C respectively . If EF = 10 and ED = 2 . Find FC .

Algebra

The roots of the quadratic equation x² – nx + 2n = 0  are integers. What is the sum of all possible values of n ?

A. 16
B. 17
C. 18
D. None of the above

Counting

27 unit cubes are assembled together to form a 3 × 3 × 3 cube. How many sets of 3 cubes can you find such that the centres of the 3 cubes lie in a straight line?
a) 76
b) 32
c) 49
d) 44
e) 50

Arithmetic

An explorer is going on a 10 day march. He is hiring bearers to carry food and supplies for him. Each person including himself can carry food and supplies of one man for 6 days. Bearers will die if they don’t have enough food and supplies on their way back.
How many bearers does Burton need if he’s to complete his march and the bearers are to return safely?
a) 3
b) 4
c) 5
d) 8
e) more than 8 

Counting 

Find the number of ways in which 5 members can be selected from three teams (each having three members) such one member is selected from each team. 

Geometry

In triangle ABC, BF and CF are angle bisectors meeting at F, and DE is a segment parallel to BC through F. If AB has length 10, BC has length 15, and AC has length 17, what is the perimeter of triangle ADE?

Counting

Find the number of  positive integral solution of the equation 12x + 28y + 84z = 2520.

A. 406
B. 604
C. 496
D. None of these

Geometry

An acute angle triangle has altitudes a, b, c, then which of the following is a possible triplet (a, b, c) :-
a) (1, 1, 2)
b) (1, 2, 2)
c) Both are possible
d) None of the above