MCA Entrance Previous Year Question Bank

The probability that a relation $R$ from $\{x,y\}$ to $\{x,y\}$ is both symmetric and transitive, is equal to:

The probability that a randomly chosen $2\times 2$ matrix with all the entries from the set of first $10$ primes, is singular, is equal to:

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5 then the sum of cubes of the remaining two observations is:

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0,60]$ is less than or equal to $a$. If $P(A)=\frac{11}{36}$, then $a$ is equal to ________.

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is:

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is $p$. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$. If $p:q=m:n$, where $m$ and $n$ are coprime, then $m+n$ is equal to ________.

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :

Let $S=\{w_1,w_2,\dots \}$ be the sample space associated to a random experiment. Let $P(w_n)=\frac{P(w_{n-1})}{2},n\ge 2$. Let $A=\{2k+3l:k,l\in \mathbb{N}\}$ and $B=\{w_n:n\in A\}$. Then $P(B)$ is equal to:

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and ${\sigma }^2$ represent mean and variance of $X$, respectively, then $10({\mu }^2+{\sigma }^2)$ is equal to

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is: