Question

Find a vector $\stackrel{\rightarrow}{a}\$ of magnitude ${\mathfrak{5}}{\sqrt{2}}$ making an angle of $\frac{\pi}{4}$ with x-axis, $\frac{\pi}{2}$ with y-axis and an acute angle θ with z-axis.

Simplify : cosθ $\left(\begin{array}{l l }cosθ & sinθ \\ -sinθ & cosθ\end{array}\right)$ + sinθ $\left(\begin{array}{l l }sinθ & -cosθ \\ cosθ & sinθ\end{array}\right)$

The contentment obtained after eating x-units of a new dish at a trial function is given by the function $f(x)=x^{3}+6x^{2}+5x+3.$. If the marginal contentment is defined as the rate of change of f(x) with respect to the number of units consumed at an instant, then find the marginal contentment when three units of dish are consumed.

Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.

Write the degree of the differential equation $x^{3}\left(\frac{d^{2}y}{d x^{2}}\right)^{2}+x\left(\frac{d y}{d x}\right)^{4}=0$

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Write the value of $\stackrel{\rightarrow}{p}\$ for which the vectors $3\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} +9\stackrel{\wedge}{k}$ and $\stackrel{\wedge}{i}-2p\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are parallel vectors.