For a real number x the condition |3x − 20| + |3x − 40| = 20 necessarily holds if

For all possible integers n satisfying 2.25 ≤ 2 + 2ⁿ⁺² ≤ 202, the number of integer values of 3 + 3ⁿ⁺¹ is

Suppose one of the roots of the equation ax² − bx + c = 0 is 2 + √3, where a, b and c are rational numbers and a ≠ 0. If b = c³ then |a| equals

Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu's share of profit increa…

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank bec…

For a sequence of real numbers x₁, x₂, ..., xₙ, if x₁ − x₂ + x₃ − ... + (−1)⁽ⁿ⁺¹⁾xₙ = n² + 2n for all natural numbers n, then the sum x₄₉ + x₅₀ equals

Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then z − x equals

Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the ga…

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is: