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1
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 ___________.
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2
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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3
JEE Main 2021 (Online) 24th February Evening Slot
Numerical
+4
-1
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If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.
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4
JEE Main 2020 (Online) 6th September Evening Slot
Numerical
+4
-0
Consider the data on x taking the values
0, 2, 4, 8,....., 2n with frequencies
nC0 , nC1 , nC2 ,...., nCn respectively. If the
mean of this data is $${{728} \over {{2^n}}}$$, then n is equal to _________ .
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