For what value of do the simultaneous equations 2x+3y=1,

If a relation R on the set of integers Z is defined as
a R b ⇔ a - b ∈ Q,
then the relation is:

From a group of 7 men and 4 women, in how many ways can a committee of 4 be formed such that it includes at least one woman?

For A = [[2,3],[-1,4]], find det(2A).

A sum increases by 40% in 4 years at simple interest. What will be the compound interest on Rs 14000 at the same rate after 3 years? 

Let f: [3, ∞) → R be defined by f(x) = x² – 6x + 11. The range of f is:

A cone has a height of 12 cm and a base radius of 5 cm. A sphere with the same volume as the cone is constructed. What is the radius of the sphere?

The equation of the plane passing through the point (2,−1,3) and having direction ratios (1,4,−2) is: