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

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

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

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…

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both 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…

If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle 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