4. For all positive integers, let k* be defined by k* = (k-1)(k+2) . Which of the following is equal to 3*+4*?4*5*6*7*

For all positive integers, let k* be defined by k* = (k-1)(k+2) . Which of the following is equal to 3*+4*?

If X(k) is the N-point DFT of a sequence x(n), then what is the DFT of x*(n)?Select one:1. X(N-k)2. None of the mentioned3. X*(k)4. X*(N-k)

Let k be an integer. When can we claim the following?k2 =kXi=1kExperiment with that expression for several values of k before answer-ing the question.

Fill in the blanks: 3 = __i + k__ * __ j; where, i=-1, j=2, k=1.

3. (i) For any integer a, what is (–1) × a equal to?(ii) Determine the integer whose product with (–1) is(a) –22 (b) 37 (c) 04. Starting from (–1) × 5, write various products showing some pattern to show(–1) × (–1) = 1.5. Find the product, using suitable properties:(a) 26 × (– 48) + (– 48) × (–36) (b) 8 × 53 × (–125)(c) 15 × (–25) × (– 4) × (–10) (d) (– 41) × 102(e) 625 × (–35) + (– 625) × 65 (f) 7 × (50 – 2)(g) (–17) × (–29) (h) (–57) × (–19) + 576. A certain freezing process requires that room temperature be lowered from 40°C atthe rate of 5°C every hour. What will be the room temperature 10 hours after theprocess begins?