Question : If $AD, BE$ and $CF$ are medians of $\triangle ABC$, then which of the following statement is correct?

Option 1: $(AD + BE + CF) > (AB + BC + CA)$

Option 2: $(AD + BE + CF) < (AB + BC + CA)$

Option 3: $(AD + BE + CF ) =  (AB + BC + CA)$

Option 4: $(AD + BE + CF ) = \sqrt2(AB+BC+CA)$

Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:

Option 1: Isosceles triangle

Option 2: Right-angled triangle

Option 3: Equilateral triangle

Option 4: Right isosceles triangle

Question : In a $\triangle ABC$, the median AD, BE, and CF meet at G, then which of the following is true?

Option 1: 4(AD + BE + CF) > 3(AB + BC + AC)

Option 2: 2(AD + BE + CF) > (AB + BC + AC)

Option 3: 3(AD + BE + CF) > 4(AB + BC + AC)

Option 4: AB + BC + AC > AD + BE + CF

Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:

Option 1: Equilateral

Option 2: Isosceles

Option 3: Right–angled

Option 4: Scalene

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