1
JEE Main 2021 (Online) 18th March Morning Shift
Numerical
+4
-1
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is _________.
2
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to __________.
3
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
Consider the statistics of two sets of observations as follows :

Size Mean Variance
Observation I 10 2 2
Observation II n 3 1

If the variance of the combined set of these two observations is $${{17} \over 9}$$, then the value of n is equal to ___________.
4
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Let X1, X2, ......., X18 be eighteen observations such
that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90$$, where $$\alpha$$ and $$\beta$$ are distinct real numbers. If the standard deviation of these observations is 1, then the value of | $$\alpha$$ $$-$$ $$\beta$$ | is ____________.
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