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Find the remainder when 7^103 is divided by 24 Solution) we know by the concept of mod that..... 49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is divisible by 24) so 7^2congruent to 1 mod 24 so 7^102congruent to 1 mod 24(raising to the power 51) hence the remainder when 7^102 is divided by 24 is 1 i.e. 7^102=24m+1 so multipling by 7 both sides we have....7^103=24.7m+ 7hence 7^103=24n + 7so remainder is 7 (ans)
Discrete Uniform Distribution Acme Limited is a car manufacturer. The company can paint the car in 3 possible colors: White, Black and Blue. Until the population is sampled, th
solve for y 3x+4y=7
sin (5pi/12)
Q) In 3D-geometry give + and - signs for x,y,z, in all eight octants Ans) There is no specific hard rule for numbering the octants. So, it makes no real sense to ask which octan
An engineer has 200 resistors that he keeps in one box. Resistors are colored to help their identification, and in this box there are 30 white resistors, 50 black resistors, 80 red
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev
Need two equal fractions multiply and divide 1/6 3/4 5/15 2/7 20/25 24/36 4/9
Hypergeometric Distribution Consider the previous example of the batch of light bulbs. Suppose the Bernoulli experiment is repeated without replacement. That is, once a bulb is
(1) Prove that Zorn's lemma is equivalent to axiom of choice. (2) Use Zorn's Lemma to prove the existence of E.
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