The value of ‘c’ in Rolle’s theorem for  on [-1,1]

For such questions, we should know the properties of Rolle's theorem.

To verify Lagrange’s mean value theorem, there exists at least one point c(a,b) such that

Rolle’s Theorem is not applicable for?

To verify Rolle’s Theorem there exists at least one point c(a, b) such that

Let P(x)be a real polynomial of degree 4 having extreme values at x=1 and x=2 if  then p(4) is equal to

40 mL of 0.05M Na₂C0₃. NaHC0₃ 2H₂0 (sesquicarbonate) is titrated against 0.05 M HCL X mL of HCI is used when phenolphthalein is the indicator and y mL HCI is used when methyl orange is the indicator in two separate titrations; hence (y - x) is:

Identify X and Y in the given figure 

Identify p, q, r, s, t and u p q r s t u