AIEEE 2004 (Maths) Mock Test

In a series of $2n$ observations, half of them equal $a$ and remaining half equal $-a.$ If the standard deviation of the observations is $2,$ then $|a|$ equals

The probability that $A$ speaks truth is $\frac{4}{5},$ while this probability for $B$ is $\frac{3}{4}.$ The probability that they contradict each other when asked to speak on a fact is

A random variable $X$ has the probability distribution:

For the events $E=\{X\text{ is a prime number}\}$ and $F=\{X<4\},$ the probability $P(E\cup F)$ is

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of $2$ successes is

With two forces acting at a point, the maximum effect is obtained when their resultant is $4\text{N}.$ If they act at right angles, then their resultant is $3\text{N}.$ Then the forces are