JEE MAIN - Mathematics (2018 - 15th April Morning Slot - No. 12)
The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then each of them is decreased by 25, their mean remains the same. Then $$\lambda $$ is equal to :
$${1 \over 3}$$
$${2 \over 3}$$
$${4 \over 3}$$
$${10 \over 3}$$
Explanation
As mean is a linear operation, so if each observation is multiplied by $$\lambda $$ and decreased by 25 then the mean becomes 75$$\lambda $$$$-$$25.
According to the question,
75$$\lambda $$ $$-$$ 25 = 75 $$ \Rightarrow $$ $$\lambda $$ = $${4 \over 3}$$.
According to the question,
75$$\lambda $$ $$-$$ 25 = 75 $$ \Rightarrow $$ $$\lambda $$ = $${4 \over 3}$$.
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