Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that $a^{2} - b^{2}$ is divisible by 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B

$G_{1} : 3, 6, 9......3 n G_{2} : 1, 4, 7..... (3 n - 2) G_{3} : 2, 5, 8.... (3 n - 1) a^{2} - b^{2} = (a - b) (a + b)$
Either a-b is divisible by 3 (or) a + b is divisible by 3 (or) both
$n c_{2} + n c_{2} + n c_{2} + n c_{1} . n c_{1} 3 \frac{n (n - 1)}{2} + n^{2}$

Suggest Corrections

Similar questions

Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that $a^{2} - b^{2}$ is divisible by 3

Q. Two numbers x and y are chosen at random from the set {1,2,3........3n}. The probability that

x^{2} - y^{2}

is divisible by 3 is

Q. Two numbers

a

and

b

are chosen at random from the set of first

30

natural numbers. Find the probability that

a^{2} - b^{2}

is divisible by

3

Q. Out of

3 n

consecutive numbers, the number of ways in which

3

numbers can be selected such that their sums is divisible by

3

Q. Two numbers a and b are selected from the set of natural number then the probability that

a^{2} + b^{2}

is divisible by

5

is?

Join BYJU'S Learning Program

Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that a2−b2 is divisible by 3

The correct option is B G1:3,6,9......3nG2:1,4,7.....(3n−2)G3:2,5,8....(3n−1)a2−b2=(a−b)(a+b) Either a-b is divisible by 3 (or) a + b is divisible by 3 (or) both nc2+nc2+nc2+nc1.nc13n(n−1)2+n2

Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that $a^{2} - b^{2}$ is divisible by 3

The correct option is B

$G_{1} : 3, 6, 9......3 n G_{2} : 1, 4, 7..... (3 n - 2) G_{3} : 2, 5, 8.... (3 n - 1) a^{2} - b^{2} = (a - b) (a + b)$
Either a-b is divisible by 3 (or) a + b is divisible by 3 (or) both
$n c_{2} + n c_{2} + n c_{2} + n c_{1} . n c_{1} 3 \frac{n (n - 1)}{2} + n^{2}$