The number of ways in which a pair of friends can be chosen for a trip from those who like Adventure Sports 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…

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 _________

Savitri borrowed 10000 rupees from a bank for a period of two years at a fixed interest rate of 10% per annum, compounded semi-annually, and paid back 5025 rupees at the end of first year. Then, the amount, in rupees, to be paid at the end of second year is _________

Let \(M = \begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{bmatrix}\) where \(a\), \(b\) and \(c\) are real numbers such that \(a + b + c = 0\) and \(abc \neq 0\). If \(\det M = 0\), then the maximum possible value of \(\frac{a^2 + b^2}{c^2}\) 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 ______

In a company, initially the ratio of the foreign and domestic workers was 5 : 8. When some foreign and 12 domestic workers left the company, this ratio became 2 : 3. Later, when 10 more foreign workers were replaced by 10 new domestic workers, this ratio became 3 : 7. The initial…

The remainder when \(7^{103} + 7^{101}\) is divided by 9 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 _______