Match all the possible combinations between Column X (Cement compounds) and Column Y (Cement properties) :
| Column X | Column Y |
|---|---|
| (i) $${C_3}S$$ | (P) Early age strength |
| (ii) $${C_2}S$$ | (Q) Later age strength |
| (iii) $${C_3}A$$ | (R) Flash setting |
| (S) Highest heat of hydration | |
| (T) Lowest heat of hydration |
Which one of the following combinations is correct?
Let y be a non-zero vector of size 2022 $$\times$$ 1. Which of the following statements is/are TRUE?
A pair of six-faced dice is rolled twice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is _________ (round off to three decimal places).
Consider the polynomial f(x) = x3 $$-$$ 6x2 + 11x $$-$$ 6 on the domain S, given by 1 $$\le$$ x $$\le$$ 3. The first and second derivatives are f'(x) and f''(x).
Consider the following statements :
I. The given polynomial is zero at the boundary points x = 1 and x = 3.
II. There exists one local maxima of f(x) within the domain S.
III. The second derivative f''(x) > 0 throughout the domains S.
IV. There exists one local minima f(x) within the domain S.