Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is

Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixtu…

In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of student…

Consider the following statements: (i) When 0 < x < 1, then \(\frac{1}{1+x} < 1 - x + x^2\). (ii) When 0 < x < 1, then \(\frac{1}{1+x} > 1 - x + x^2\). (iii) When -1 < x < 0, then \(\frac{1}{1+x} < 1 - x + x^2\). (iv) When -1 < x < 0, then \(\frac{1}{1+x} > 1 - x + x^2\). Then th…

Given \(f(x) = x^2 + \log_3 x\) and \(g(y) = 2y + f(y)\), the value of g(3) equals

If \(\log_5\log_8(x^2-1)=0\), then a possible value of x is

A \(2 \times 2\) matrix is filled with four distinct integers randomly chosen from the set {1,2,3,4,5,6}. Then the probability that the matrix generated in such a way is singular is

A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is

Ashok started a business with a certain investment. After few months, Bharat joined him investing half amount of Ashok's initial investment. At the end of the first year, the total profit was divided between them in ratio 3:1. Bharat joined Ashok after