The mean of $10$ terms is $3$. If the first term is increased by $1$,the second by $2$,and so on,then the new mean is:

An anti-aircraft gun takes a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first,second,third,and fourth shot are $0.4, 0.3, 0.2$,and $0.1$ respectively. The probability that the gun hits the plane is

The possible values of $x$ if the standard deviation $(SD)$ of the numbers $2, 3, 2x$,and $11$ is $3.5$ are equal to:

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1, 3, 5, 7, 11, 13, 17, 19, 23$,then $3(\sigma^2 - M) = $

The mean and standard deviation of $20$ observations were calculated as $10$ and $2.5$ respectively. It was found that by mistake one data value was taken as $25$ instead of $35$. If $\alpha$ and $\sqrt{\beta}$ are the mean and standard deviation respectively for the correct data,then $(\alpha, \beta)$ is:

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum_{i=1}^{11}(x_i-4)=22$ and $\sum_{i=1}^{11}(x_i-4)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$,then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is