AIEEE 2003 (Maths) Mock Test

In an experiment with 15 observations on $x$, the following results were available: $\sum x^2=2830$, $\sum x=170$. One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is:

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is:

Events $A,B,C$ are mutually exclusive events such that $P(A)=\frac{3x+1}{3}$, $P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2x}{2}$. The set of possible values of $x$ are in the interval:

The mean and variance of a random variable having a binomial distribution are 4 and 2 respectively, then $P(X=1)$ is:

The resultant of forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled then $\vec{R}$ is doubled. If the direction of $\vec{Q}$ is reversed, then $\vec{R}$ is again doubled. Then $P^2:Q^2:R^2$ is: