15. What is the correct piecewise parametrization of a path C created by starting from C₁ of equation y = x + 3 from x = 0 to x = 4, then C₂ with an equation y = x² from y = 7 to the origin and a vertical line C3 that connects the two previous curves head to tail? t+3 0st≤4 4-t² 451≤4+√7 t+4+√7 4+√7≤t≤7+√7 t+3 0st≤4 (4-t)² 451≤4+√7 0 t+4+√7 4+√7 ≤t≤7+√7 t+3 t = { ₁ + √7 - 1 -t (4+√7-t)² t-4-√7 t A. r(t)=4-t 0 t B. r(t)=4-t C. r(t)=4+1 (t t+3 t² t 0st≤3 D. r(t) = t 0 0st≤4 0sts √7 0st≤4 4st≤4+√7 4+√7≤t≤7+√7
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Choose the correct answer/s. Choose E if none of the choices is correct. Show your solution
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