Algebra-33

Answer the following questions on the basis of the information given below:

f₁(x)= x for 0 ≤ x ≤ 1

     = 1 for x = 1

     = 0 otherwise

f₂(x)= f₁(-x) for all x

f₃(x)= -f₂(x) for all x

f₄(x)= f₃(-x) for all x

Q1) How many of the following products are necessarily zero for every x
f₁(x)f₂(x), f₂(x)f₃(x), f₂(x)f₄(x)?

(1)0     (2)1     (3)2     (4)3

Q2) Which of the following is necessarily true?

(1)f₄(x) = f₁(x) for all x          (2)f₁(x) = -f₃(-x) for all x

(3)f₂(-x) = f₄(x) for all x         (4)f₁ (x) + f₃(x) = 0 for all x

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Puzzle-33

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

(A)  2         (B)    3        (C)   4           (D)   8
Solution follows here: