Question

For what value of λ are the vectors $\stackrel{\wedge}{i}+2λ \stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -3\stackrel{\wedge}{k}$ perpendicular ?

What is the range of the function f(x) = $\textstyle{\frac{|x-1|}{x-1}}$, x ≠ 1?

Find $|\stackrel{\rightarrow}{x}|\$, if for a unit vector $\stackrel{\rightarrow}{a}\$ and ($\stackrel{\rightarrow}{x}\$ + $\stackrel{\rightarrow}{a}\$ )($\stackrel{\rightarrow}{x}\$ -$\stackrel{\rightarrow}{a}\$ ) = 15.

If R = {(x, y) : x + 2y = 8} is a relation on N, writethe range of R.

If f : R → R and g : R → R are given by f(x) = sin x and g(x) = 5x² then find gof(x)

Determine the value of the constant ‘k’ so that the function

Find : $\textstyle\int{\frac{\sin^{2}\!x-\cos^{2}\!x}{\sin^{2}\!x\cos^{2}\!x}}\,d x$