Algebra
1.If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to?

Explanation:

Solution:
$\begin{array}{rl}& 3\ast 5+5\ast 3\\ & ⇒3\ast 5=2×3-3×5+3×5\\ & ⇒3\ast 5=6-15+15\\ & ⇒3\ast 5=6\\ & ⇒5\ast 3=2×5-3×3+3×5\\ & ⇒5\ast 3=10-9+15\\ & ⇒5\ast 3=16\\ & \therefore 3\ast 5+5\ast 3\\ & ⇒6+16\\ & ⇒22\end{array}$

2.If
$p×q=p+q+\frac{p}{q}\text{,}$
then the value of 8 × 2 is?

Explanation:

Solution:
$\begin{array}{rl}& \text{8}×\text{2}\\ & =8+2+\frac{8}{2}\\ & =10+4\\ & =14\end{array}$

3.The value of

is?

Explanation:

Solution:

4.If
$\frac{2a+b}{a+4b}=3\text{,}$
then find the value of
$\frac{a+b}{a+2b}=?$

Explanation:

Solution:

5.If a * b = a + b + ab, then 3 * 4 - 2 * 3 is equal to?

Explanation:

Solution:

6.If a : b = 2 : 3 and b : c = 4 : 5, find a2 : b2 : bc = ?

Explanation:

Solution:

7.If
$\text{A}:\text{B}=\frac{1}{2}:\frac{3}{8}\text{,}$

$\text{B}:\text{C}=\frac{1}{3}:\frac{5}{9}$
and
$\text{C}:\text{D}=\frac{5}{6}:\frac{3}{4}\text{,}$
then find the ratio of A : B : C : D = ?

Explanation:

Solution:

8.If
$\frac{144}{0.144}=\frac{14.4}{x}\text{,}$
then the value of x is?

Explanation:

Solution:
$\begin{array}{rl}& \frac{144}{0.144}=\frac{14.4}{x}\\ & ⇒\frac{144×1000}{144}=\frac{144}{x×10}\\ & ⇒1000=\frac{144}{10x}\\ & ⇒x=\frac{144}{1000×10}\\ & ⇒x=\frac{144}{10000}\\ & ⇒x=0.0144\end{array}$

9.If 1 < x < 2, then the value of

Explanation:

Solution:

10.If a ⊕ b = (a × b) + b, then 5 ⊕ 7 equals to?

$\begin{array}{rl}& a\oplus b=\left(a×b\right)+b\\ & ⇒5\oplus 7\\ & =\left(5×7\right)+7\\ & =35+7\\ & =42\end{array}$