The number of friends that like Countryside Sightseeing is ____

Let \(S\) denote an arithmetic progression whose first term is either 132 or 158, and the common difference is an even integer less than 10. If the \(n^{\text{th}}\) term of \(S\) is 174, then the number of possible distinct values of \(n\) is ______

If \(n\) is an integer such that \(\frac{|n+6| - |n-3|}{\sqrt{100 - n^3}} \geq 0\), then the number of possible values of \(n\) is _______

Two locations A and B are at diametrically opposite ends of a circular track. Rekha starts running along the track from location A in the clockwise direction. Sajal starts running simultaneously along the track in the anticlockwise direction from location B. If the length of the…

The number of ways in which three distinct integers can be chosen from the set \(\{1, 2, \ldots, 9\}\) such that their product is divisible by 4, is _________

The number of integers \(n\) such that \(1 \leq n \leq 10^7\) and \(\gcd(n, 10^7) = 10^3\) is _____

Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

The Celsius scale of temperature can be converted to Fahrenheit scale using the relationship \(F = 1.8C + 32\), where \(F\) and \(C\) are temperature recorded in degrees Fahrenheit and Celsius, respectively. Ajay noted down the temperature of a chemical reaction as \(x\) degrees…

Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is