Give brief answer of the following questions. a) Find (A B) , where A = pmatrix 3 & 2 & 6 \\ 4 & 5 & 7 pmatrix and B = pmatrix 1 & 3 & 6 \\ 3 & 2 & 5 pmatrix . b) Find the value of determinant:…

Give brief answer of the following questions. a) Find $\gamma (A-B)$, where $A=\left(\begin{array}{ccc}3& 2& 6\\ 4& 5& 7\end{array}\right)$ and $B=\left(\begin{array}{ccc}1& 3& 6\\ -3& 2& 5\end{array}\right)$. b) Find the value of determinant: $$\left|\begin{array}{ccc}1& 2& 2\\ 2& 3& 2\\ 3& 4& 3\end{array}\right|$$ c) Evaluate: ${\lim }_{x\to \infty }\frac{7x^{2+5}x-2}{2x^{3+5}x-5}$

d) Find the area of curve bounded by x-axis and ordinates of y=3x² from x₁=1 and x₂=2. e) Solve the following differential equation: $)\frac{dy}{dx}=3x+1$

f) If $A=\{a,b,c,d,e,f,g,h\},B=\{e,f,g,h,i,j,k\}$ then find A ∪ B and A ∩ B.

g) Express the following complex number into polar form $Z=1+i\sqrt{3}$

h) Rewrite the following absolute value sign -5 ≤ x ≤ 11

i) Show that the following pair of vectors are orthogonal −5⁴ + 4j⁷ -k, 5⁴ + 7j⁷ + 3k where i, j and k are the vectors.

j) Find the derivative of $y=3x^2+e^x-\frac{1}{x}+logx$