Find which of the binary operations are commutative and which are associative. State whether the following statements are true or false. Justify For an arbitrary binary operation * on a set N, a*a=a .

* being a binary operation on N, is defined as a*a=a . Hence operation * is not defined, therefore, the given statement is false.

Find which of the binary operations are commutative and which are…

If $A$ is an invertible matrix of order $2,$ then det $(A^{–1})$ is equal to

→

Find $\int \frac{x^{2}+1}{x^{2}-5 x+6} d x$

→

For all real values of $x,$ the minimum value of $\frac{1-x+x^{2}}{1+x+x^{2}}$ is

→

Find the absolute maximum and minimum values of a function $f$ given by
$f (x) = 2x^3 – 15x^2 + 36x +1$ on the interval $[1, 5]$.

→

Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.

→

What is the cosine of the angle which the vector$\sqrt{2}\hat{\text{ i}}+\hat{\text{j}}+\hat{\text{k}}$ .

→

Find the angle between the lines $\text{2x = 3y = – z and 6x = – y = – 4z.}$

→

Evaluate:$\int\limits_0^1\frac{\text{2x}}{\text{1 + x}^{2}}\text{dx}$.

→

Show that the vectors $2\hat{i}-3\hat{j}+4\hat{k}\ \text{and}\ -4\hat{i}+6\hat{j}-8\hat{k}$ are collinear.

→

Classify the following measures as scalars and vectors. $20 \ m/s^2$

→