1
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1 Let $$x_{1}, x_{2}, x_{3}, \ldots, x_{20}$$ be in geometric progression with $$x_{1}=3$$ and the common ratio $$\frac{1}{2}$$. A new data is constructed replacing each $$x_{i}$$ by $$\left(x_{i}-i\right)^{2}$$. If $$\bar{x}$$ is the mean of new data, then the greatest integer less than or equal to $$\bar{x}$$ is ____________.

2
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1 The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _____________.

3
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1 The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $$\sigma$$ is the standard deviation of the data after omitting the two wrong observations from the data, then $$38 \sigma^{2}$$ is equal to ___________.

4
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1 Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is _________.

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