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 _________

From the passage: Five friends A, B, C, D, and E go on a trip together. Each of them lik...

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…

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 ______

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 _______

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 _______

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…

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…