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(a) Given a norm jj jj on Rn, express the closed ball in Rn of radius r with center c as a set. (b) Given a set A and a vector v, all contained in Rn, express the translate of A by
Five cards - the ten, jack, queen, king and ace, are well shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is
Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov
Advantages and disadvantages of operation researchs
lcm method of 648
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
Find the sum of all 3 digit numbers which leave remainder 3 when divided by 5. Ans: 103, 108..........998 a + (n-1)d = 998
use only the digits 1,2,3 and 4 in any order to write an expression for the numbers 1 to 100. you may only use each digit once. You may use exponents of 1,2,3 and 4 in some of th
7 is what percent of 105?.
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