Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is

The number of solutions of the equation \(x_1 + x_2 + x_3 + x_4 = 50\), where \(x_1, x_2, x_3, x_4\) are integers with \(x_1 \ge 1, x_2 \ge 2, x_3 \ge 0, x_4 \ge 0\) is

A fruit seller had a certain number of apples, bananas and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of apples, 60% of bananas, and 50% of…

The number of values of x for which \(C^{17-x}_{3x+1}\) is defined as an integer is

The terms of a geometric progression are real and positive. If the \(p^{th}\) term of the progression is q and the \(q^{th}\) term is p, then the logarithm of the first term is

The greatest number among \(2^{300}\), \(3^{200}\), \(4^{100}\), \(2^{100} + 3^{100}\) is

The number of real solutions of the equation \(x^2 - 10|x| - 56 = 0\) is

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of n for which the sum of its first n terms is closest to 100, is

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is