A man starts walking from point A to point B at 4 km/hr. After 30 minutes, a woman starts from point A at 6 km/hr. If the woman reaches point B 20 minutes earlier than the man, then the distance between A and B in km is _________

Let ABCD be a cyclic quadrilateral with \(AB = 15\), \(BC = 20\), \(CD = 24\) and \(AC = 25\). Then \(AD\) equals _________

If \(x, y\) are real numbers and equations \(x^2 - 12x + 35 = 0\) and \(x^2 + ax + 105 = 0\) have at least one common root, then the minimum possible value of \(y^2 + 4y - 5a\) is _________

Ram purchased 3 oranges at Rs. 20 each and 5 mangoes at Rs. 38 each and then sold them by offering discounts of 25% and 20% on the fixed marked prices of oranges and mangoes, respectively. If he earned a profit of 50% on selling the oranges alone, and a total profit of 32% on sel…

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

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 _______

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 _________

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…