A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals

Let C be the circle x² + y² + 4x − 6y − 3 = 0 and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to 60 degree. Then, the point at which L touches the line x = 6 is?

For some positive and distinct real numbers x, y and z, if 1/(√y + √z) is the arithmetic mean of 1/(√x + √z) and 1/(√x + √y), then the relationship which will always hold true, is?

If √(5x + 9) + √(5x − 9) = 3(2 + √2), then find the value of √(10x + 9)?

The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the r…

In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible d…

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Git…

The equation x³ + (2r + 1)x² + (4r − 1)x + 2 = 0 has −2 as one of the roots. If the other roots are real, then the minimum possible non-negative integer value of r is?

Let n be the least positive integer such that 168 is a factor of 1134ⁿ. If m is the least positive integer such that 1134ⁿ is a factor of 168ᵐ, then m + n equals