Question

If $\begin{vmatrix} 2x & x+3 \\ 2(x+1) & x+1 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, write the value of x.

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.

If Δ = $\begin{vmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{vmatrix}$ , write the minor of the element $a_{23}.$

Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].

If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.

Find a unit vector in the direction of $\stackrel{\rightarrow}{A}$ = $3\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +6\stackrel{\wedge}{k}$

Evaluate $\textstyle\int{\frac{\cos{\sqrt{x}}}{\sqrt{x}}}\,d x\ .$