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

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…

If \(\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\cdots\) upto \(\infty = \frac{\pi^2}{6}\), then the value of \(\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\cdots\) upto \(\infty\) 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…

The value of \(\cos^2\frac{\pi}{8}+\cos^2\frac{3\pi}{8}+\cos^2\frac{5\pi}{8}+\cos^2\frac{7\pi}{8}\) 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,…

The equation of the straight line passing through the point M (-5, 4), such that the portion of it between the axes is divided by the point M into two equal halves, is

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…