The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

The probability that a randomly chosen factor of \(10^{19}\) is a multiple of \(10^{15}\) is

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

Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is ____________.

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

Two friends run a 3 kilometer race along a circular course of length 300 meters. If their speeds are in ratio 3:2, the number of times the winner passes the other is ____________.

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

Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C and at most 20 students passed C and M. The maximum number of s…

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