If the mean of a, b, and c is M; ab + bc + ca = 0; and the mean of a^2, b^2 and c^2 is KM^2, then K is equal to Option 1: 3 Option 2: 9 Option 3: 6 Option 4: 4

Answer: 3. Solution: From mean of a, b, and c: (a + b + c)/3 = M a + b + c = 3M ...(1) Given: ab + bc + ca = 0 ...(2) Mean of squares: (a^2 + b^2 + c^2)/3 = KM^2 a^2 + b^2 + c^2 = 3KM^2 ...(3) From (1): squaring both sides (a + b + c)^2 = 9M^2 a^2 + b^2 + c^2 + 2(ab + bc + ca) = 9M^2 From (2): a^2 + b^2 + c^2 = 9M^2 From (3): 3KM^2 = 9M^2 K = 3

Arithmetic

Averages

Medium

If the mean of $a$ , $b$ , and $c$ is $M$ ; $ab + bc + ca = 0$ ; and the mean of $a^2$ , $b^2$ and $c^2$ is $KM^2$ , then $K$ is equal to

✅ Correct Option: 1

From mean of $a$ , $b$ , and $c$ :

$\frac{a + b + c}{3} = M$

$a + b + c = 3M$ ...(1)

Given: $ab + bc + ca = 0$ ...(2)

Mean of squares:

$\frac{a^2 + b^2 + c^2}{3} = KM^2$

$a^2 + b^2 + c^2 = 3KM^2$ ...(3)

From (1): squaring both sides

$(a + b + c)^2 = 9M^2$

$a^2 + b^2 + c^2 + 2(ab + bc + ca) = 9M^2$

From (2):

$a^2 + b^2 + c^2 = 9M^2$

From (3):

$3KM^2 = 9M^2$

$\boxed{K = 3}$

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Choose the correct answer from the options given below:

If the mean of aaa, bbb, and ccc is MMM; ab+bc+ca=0ab + bc + ca = 0ab+bc+ca=0; and the mean of a2a^2a2, b2b^2b2 and c2c^2c2 is KM2KM^2KM2, then KKK is equal to

Solution

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JIPMAT Past Year Questions (Topic-Wise)

If the mean of $a$ , $b$ , and $c$ is $M$ ; $ab + bc + ca = 0$ ; and the mean of $a^2$ , $b^2$ and $c^2$ is $KM^2$ , then $K$ is equal to