Question : If $a-b=-7$ and $a^2+b^2=85$, then find $ab$.

Option 1: 18

Option 2: –30

Option 3: –44

Option 4: –60

Question : If $a =\cot A+\cos A$ and $b =\cot A-\cos A$, then find the value of $a^2-b^2-4 \sqrt{ab}$.

Option 1: 0

Option 2: –1

Option 3: 1

Option 4: –4

Question : If A + B = – 5 and AB = 6, then find the value of A³ + B³.

Option 1: 35

Option 2: 45

Option 3: –35

Option 4: 215

Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a³ + b³ + c³?

Option 1: 1

Option 2: 5

Option 3: 3

Option 4: 2

Question : In right angled triangle ABC, if $\angle \mathrm{A}=30^{\circ}$, find the value of $3 \sin \mathrm{A}-4 \sin ^3 \mathrm{~A}$.

Option 1: 2

Option 2: –1

Option 3: –2

Option 4: 1

Question : Directions: If × means ÷, – means +, ÷ means × and + means –, then 84 × 7 ÷ 4 – 16 × 8 ÷ 2 + 14 = ?

Option 1: 36

Option 2: 38

Option 3: 44

Option 4: 24