Anindita invests a total of 1 lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of 10%, 8% and 12% per annum, respectively, each compounded annually. If the initial investment amount in scheme A is 30000 rupees and the total interest earned from all the three schemes during the first year is 10600 rupees, then the total interest earned, in rupees, from all the three schemes for the second year is _________

Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ______

Let \(S_1 = \{100, 105, 110, 115, \ldots\}\) and \(S_2 = \{100, 95, 90, 85, \ldots\}\) be two series in arithmetic progression. If \(a_k\) and \(b_k\) are the \(k\)-th terms of \(S_1\) and \(S_2\), respectively, then \(\sum_{k=1}^{20} a_k b_k\) equals

If the sum of the first 21 terms of the sequence \(\ln\frac{a}{b}\), \(\ln\frac{a}{b\sqrt{b}}\), \(\ln\frac{a}{b^2}\), \(\ln\frac{a}{b^2\sqrt{b}}\), ....... is \(\ln\frac{a^m}{b^n}\), then the value of m + n is _____________.

If \(8x^2 - 2kx + k = 0\) is a quadratic equation in \(x\), such that one of its roots is \(p\) times the other, and \(p, k\) are positive real numbers, then \(k\) equals

A circle of radius 13 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 18 cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is___________.

Let \(P(x)\) be a quadratic polynomial such that \(\begin{vmatrix} P(0) & P(1) \\ P(0) & P(2) \end{vmatrix} = 0\). Let \(P(0) = 2\) and \(P(1) + P(2) + P(3) = 14\). Then \(P(4)\) equals

If a, b, c are three distinct natural number, all less than 100, such that |a - b| + |b - c| = |c - a|, then the maximum possible value of b is______________.

If \(\log_{25}\left[5\log_3\left(1+\log_3\left(1+2\log_2 x\right)\right)\right] = \frac{1}{2}\) then \(x\) is