# Numbers

How many ordered integral pairs (x,y) satisfy the equation 3x2 – y2 = 1747 ?
A. 0
B. 1
C. 2
D. More than 2 pairs

# Geometry

The diagonals AC and BD of quadrilateral ABCD are perpendicular to each other. If AB = 3, BC = 4 , CD = 5 , find the length of AD.

# Counting

A 10 × 10 table is formed by repeating the same number on diagonal as shown Find the sum of all numbers in the table.

# Geometry

In the figure, AB and CD  are diameters of the circle with center O, and AB⊥CD and chord DF intersect AB at E and DE = 6, EF = 2. Find the area of the circle.

A. 25π
B. 24π
C. 36π
D. None of the above

# Numbers

Find the smallest integer n such that √(n + 99) – √n  < 1.

# Geometry

ABCDEF is an equiangular hexagon ( each of its interior angle is 120°) . Find the EF + FA, if AB = 2, BC = 4, CD = 3 and DE = 5.

A. 4
B. 5
C. 6
D. 7
E. None of these

# Arithmetic

Ali sells 120 shirts at cost price of 130 shirts after giving a discount same as cost price of 26 shirts. By how much percent Ali has marked his prices up than cost price?

1. 30%
2. 20%
3. 12%
4. 26%

# Geometry

In the diagram which is not drawn to scale , the circles are tangent at A , the center of the larger circle is at B , CD = 12 , and EF = 8. What is the radius of the smaller circle  ?