Let C be a circle of radius √20 cm. Let L1, L2 be the lines given by 2x − y − 1 = 0 and x + 2y − 18 = 0, respectively. Suppose that L1 passes through the center of C and that L2 is tangent to C at the point of intersection of L1 and L2. If (a, b) is the center of C, which of the following is a possible value of a + b?

Let P be the point of intersection of the lines 3x + 4y = 2a and 7x + 2y = 2018, and Q the point of intersection of the lines 3x + 4y = 2018 and 5x + 3y = 1. If the line through P and Q has slope 2, the value of a is:

log(97 − 56√3) / log √(7 + 4√3) equals which of the following?

When opening his fruit shop for the day a shopkeeper found that his stock of apples could be perfectly arranged in a complete triangular array: that is, every row with one apple more than the row immediately above, going all the way up ending with a single apple at the top. Durin…

In the trapezium ABCD the sides AB and CD are parallel. The value of sin∠BAC / sin∠BAD is

A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly installments. If the rate of interest charged is 12% per annum, then the amount of each installment (nearest to a rupee) is:

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles (each built outward on a side of ABCD, with apex at a corner of EFGH). What is the ratio of the area of the square EFGH to that of ABCD? [Figure: see page 16 of source PDF]

An article is marked x% above the cost price. A discount of (2/3)x% is given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is?

What is the maximum number of points that can be placed on a circular disk of radius 1 metre (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 metre from each other?