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

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:

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 :

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:

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?

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:

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

A solid brass sphere of radius 21 cm is converted into a right circular cylindrical rod of length 28 cm. The ratio of total surface areas of the rod to sphere is:

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: