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ANSWER

Show that one and only one out of n, n+2, n+4 is divisible by 3, where n is any positive integer.

Posted by Stuti Singla 4 years, 6 months ago (10112350)

CBSE > Class 10 > Mathematics

2 answers

Adicherla Sathvik 4 years, 6 months ago (9440131)

We know that any positive integer is of the form 3q or 3q + 1 or 3q + 2 for some integer q & one and only one of these possibilities can occur Case I : When n = 3q In this case, we have, n = 3q, which is divisible by 3 n = 3q = adding 2 on both sides n + 2 = 3q + 2 n + 2 leaves a remainder 2 when divided by 3 Therefore, n + 2 is not divisible by 3 n = 3q n + 4 = 3q + 4 = 3(q + 1) + 1 n + 4 leaves a remainder 1 when divided by 3 n + 4 is not divisible by 3 Thus, n is divisible by 3 but n + 2 and n + 4 are not divisible by 3 Case II : When n = 3q + 1 In this case, we have n = 3q +1 n leaves a reaminder 1 when divided by 3 n is not divisible by 3 n = 3q + 1 n + 2 = (3q + 1) + 2 = 3(q + 1) n + 2 is divisible by 3 n = 3q + 1 n + 4 = 3q + 1 + 4 = 3q + 5 = 3(q + 1) + 2 n + 4 leaves a remainder 2 when divided by 3 n + 4 is not divisible by 3 Thus, n + 2 is divisible by 3 but n and n + 4 are not divisible by 3 Case III : When n = 3q + 2 In this case, we have n = 3q + 2 n leaves remainder 2 when divided by 3 n is not divisible by 3 n = 3q + 2 n + 2 = 3q + 2 + 2 = 3(q + 1) + 1 n + 2 leaves remainder 1 when divided by 3 n + 2 is not divsible by 3 n = 3q + 2 n + 4 = 3q + 2 + 4 = 3(q + 2) n + 4 is divisible by 3 Thus, n + 4 is divisible by 3 but n and n + 2 are not divisible by 3 . Thanks I HOPE YOU UNDERSTAND?

Sia ? 4 years, 6 months ago (6945213)

We know that any positive integer is of the form 3q or 3q + 1 or 3q + 2 for some integer q & one and only one of these possibilities can occur
Case I : When n = 3q
In this case, we have,
n = 3q, which is divisible by 3
n = 3q
= adding 2 on both sides
n + 2 = 3q + 2
n + 2 leaves a remainder 2 when divided by 3
Therefore, n + 2 is not divisible by 3
n = 3q
n + 4 = 3q + 4 = 3(q + 1) + 1
n + 4 leaves a remainder 1 when divided by 3
n + 4 is not divisible by 3
Thus, n is divisible by 3 but n + 2 and n + 4 are not divisible by 3
Case II : When n = 3q + 1
In this case, we have
n = 3q +1
n leaves a reaminder 1 when divided by 3
n is not divisible by 3
n = 3q + 1
n + 2 = (3q + 1) + 2 = 3(q + 1)
n + 2 is divisible by 3
n = 3q + 1
n + 4 = 3q + 1 + 4 = 3q + 5 = 3(q + 1) + 2
n + 4 leaves a remainder 2 when divided by 3
n + 4 is not divisible by 3
Thus, n + 2 is divisible by 3 but n and n + 4 are not divisible by 3
Case III : When n = 3q + 2
In this case, we have
n = 3q + 2
n leaves remainder 2 when divided by 3
n is not divisible by 3
n = 3q + 2
n + 2 = 3q + 2 + 2 = 3(q + 1) + 1
n + 2 leaves remainder 1 when divided by 3
n + 2 is not divsible by 3
n = 3q + 2
n + 4 = 3q + 2 + 4 = 3(q + 2)
n + 4 is divisible by 3
Thus, n + 4 is divisible by 3 but n and n + 2 are not divisible by 3 .

ANSWER

Which is the primary objective of economic planning in india

Posted by R K 4 years, 6 months ago (11263791)

CBSE > Class 12 > Economics

1 answers

Sia ? 4 years, 6 months ago (6945213)

The main objective of Indian planning is to achieve the goal of economic development economic development is necessary for under developed countries because they can solve the problems of general poverty, unemployment and backwardness through it.

ANSWER

1 +1

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CBSE > Class 10 > Mathematics

5 answers

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Html is a hyper text markup language and it is used for making web page. It is used for making web page In html we create a any form , we any type of image, video etc by the help of html we link any website .

Sia ? 4 years, 6 months ago (6945213)

html is hyper text markup language and is used for making web pages
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CBSE > Class 11 > Biology

1 answers

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5 answers

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ANSWER

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Posted by Priya Tudu 4 years, 6 months ago (11257134)

CBSE > Class 11 > Business Studies

1 answers

Sia ? 4 years, 6 months ago (6945213)

Objectives of Business – Profitability, Growth, Stability, Efficiency and Survival. Business means busy in some activities. Business means conducting activities such as – sale, purchase and manufacturing etc for profit and growth.

ANSWER

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ANSWER

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Posted by Ishika Kasana 4 years, 6 months ago (4455566)

CBSE > Class 10 > Science

3 answers

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CBSE > Class 10 > Science

5 answers

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CBSE > Class 12 > Political Science

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CBSE > Class 12 > Political Science

1 answers

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ANSWER

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CBSE > Class 12 > Political Science

1 answers

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ANSWER

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CBSE > Class 12 > Political Science

1 answers

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CBSE > Class 12 > Political Science

1 answers

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CBSE > Class 07 > Mathematics

2 answers

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CBSE > Class 07 > Mathematics

3 answers

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ANSWER

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CBSE > Class 07 > Mathematics

2 answers

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