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

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

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

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…

The average marks of 6 students in a test is 64. All the students got different marks, one of the students obtained 70 marks and all other students scored 40 or above. The maximum possible difference between the second highest and the second lowest marks is

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,…

From the passage: The table below presents the quoted buy and sell prices of five stocks...

If an investor had Rs. 36,00,000 to invest in any particular single stock, and she could buy the stock only on Monday and sell it off only on Friday, then the stock she should buy on Monday to earn the maximum possible profit during the week 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…

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…