The value of \(999\frac{1}{7} + 999\frac{2}{7} + 999\frac{3}{7} + 999\frac{4}{7} + 999\frac{5}{7} + 999\frac{6}{7}\) is equal to :

If \(\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 3\), then value of \(\sin^4\theta - \cos^4\theta\) is

Cost price of article A is ₹ 200 more than the cost price of article B. Article A was sold at 10% loss and article B was sold at 25% profit. If the overall profit earned after selling both the articles is 4%, then what is the cost price of article B?

The ratios of copper to zinc in alloys A and B are 3:4 and 5:9, respectively. If A and B are taken in ratio 2:3 and melted to form new alloy C, then the ratio of copper to zinc in C is:

If \(x^3 + y^3 = 468\) and \(x + y = 12\), then value of \(x^4 + y^4\) will be

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots (4, 3). Alok made a mistake in writing down coefficient of \(x\) to get roots (3, 2). The correct roots of the equation are:

P's income is ₹ 140 more than Q's income and R's income is ₹ 80 more than S's. If the ratio of P's and R's incomes is 2:3 and the ratio of Q's and S's incomes is 1:2, then the incomes of P, Q, R and S are, respectively:

Let \(x\) be median of the data 13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14. If 8 is replaced by 18, then the median of data is y, then the sum of x and y is equal to:

The difference between compound and simple interests on a certain sum of money at the interest rate of 10% per annum for \(1\frac{1}{2}\) years is ₹ 183, when the interest is compounded semi-annually, then the sum of money is