Let α and β be two distinct roots of the equation 2x² − 6x + k = 0, such that (α + β) and αβ are the two roots of the equation x² + px + p = 0. Then the value of 8(k − p) is?

The minor angle between the hour hand and minute hand of a clock was observed at 8:48 am. The minimum deviation (in min) after 8:48 am when the angle increases by 50% is?

Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts receive…

Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of 10% is made on object B, then the profit m…

Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then…

The number of integral solutions of equation 2|x|(x² + 1) = 5x² is?

If x and y are positive real numbers such that logₓ(x² + 12) = 4 and 3 log_y(x) = 1, then x + y equals?

If x and y are real numbers such that x² + (x − 2y − 1)² = −4y(x + y), then the value of x − 2y is?

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the nth day exceeds one million, then th…