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a) How many equivalence relations on {a, b, c, d, e, f} have
b) How many arrangements are there of
c) How many triangles are resolute by the vertices of a regular polygon with
1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.
compare: 643,251: 633,512: 633,893. The answer is 633,512.
trigonometric ratios of sum and difference of two angles
A 'woman was trying to teach her three-year-old child the numbers from 1to 5 from a children's book on numbers. Each number was illustrated by the same number of trees drawn next t
how you divide 100 by 10 and then x by 10
[3+tan20+tan80]/tan20+tan80
Round 14.851 to the nearest tenth? The tenths place is the ?rst number to the right of the decimal. Here the number 8 is in the tenths place. To decide whether to round up or
Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) . Solution Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do i
Calculate the area and perimeter of a parallelogram: Calculate the area and perimeter of a parallelogram with base (b) = 4´, height (h) = 3´, a = 5´ and b = 4´. Be sure to in
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