Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the parallelogram are (5.5, 7.5) and (13.5, 16). Find the lengths of the diagonals.

In the diagram below, CD = BF = 10 units and ∠CED = ∠BAF = 30°. What would be the area of triangle AED? (Note: Diagram below may not be proportional to scale.) (Figure: A at top, AD vertical with B and C on it; BF ⟂ AD at B; ED ⟂ AD at D; E, C, F collinear.) [Figure: see page 17…

If f(x² - 1) = x⁴ - 7x² + k₁ and f(x³ - 2) = x⁶ - 9x³ + k₂ then the value of (k₂ - k₁) is

A circular road is constructed outside a square field. The perimeter of the square field is 200 ft. If the width of the road is 7√2 ft. and cost of construction is Rs. 100 per sq.ft. Find the lowest possible cost to construct 50% of the total road.

In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs. 10,000 and in the beginning of 2010, the accumulated interest becomes Rs. 25,000. The interest rate is compounded annually and the annual interest…

Product M is produced by mixing chemical X and chemical Y in the ratio of 5 : 4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 : 3. Chemical Y is prepared by mixing raw materials, B and C, in the ratio of 2 : 1. Then the final mixture is prepared…

The tax rates for various income slabs are given below. Income Slab (Rs.) | Tax rate ≤ 500 | Nil > 500 to ≤ 2000 | 5% > 2000 to ≤ 5000 | 10% > 5000 to < 10000 | 15% There are 15 persons working in an organization. Out of them, 3 to 5 persons are falling in each of the income slab…

Find the equation of the graph shown below. (Graph: an upward parabola with minimum about -20 near x ≈ -0.75, crossing the x-axis near x ≈ -3.9 and x ≈ 2.4, y-intercept about -19.) [Figure: see page 16 of source PDF]

If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of [(a + b) + (c + d)] / [(a + b) + (c - d)] would be: