Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one speciality. The total number of biologists, geologists, and explorers are equal. The following additional information is available. - Every team has at least 2 members from each of the three skill sets. - Team C and D have 6 biologists each, and Team A has 6 geologists. - Every team except A has more biologists than explorers. - The number of explorers in each team is distinct and decreases in the order A, B, C, D and E. The median number of biologists across five teams is ________ .

Eight teams take part in a tournament where each team plays against every other team exactly once. In a particular year, one team got suspended after playing 3 matches, due to a disciplinary issue. The organizers decide to proceed, nonetheless, with the remaining matches. The tot…

If \(\log_3 (x^2 - 1)\), \(\log_3 (2x^2 + 1)\) and \(\log_3 (6x^2 + 3)\) are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is _______________.

If \(A = \begin{bmatrix} 2 & n \\ 4 & 1 \end{bmatrix}\) such that \(A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix}\), then \(p + q + r\) equals ______________ .

If m and n are two positive integers such that 7m + 11n = 200, then the minimum possible value of m + n is _________.

Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by tea…

If a, b, c are three distinct natural number, all less than 100, such that |a - b| + |b - c| = |c - a|, then the maximum possible value of b is______________.

Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by tea…

A circle of radius 13 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 18 cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is___________.