Lower Limit

Q. From a group of 4 men and 3 women, 2 persons are selected at random, Find the probability at least one man is selected.

1. $\frac{7}{6}$
2. $\frac{6}{7}$
3. $\frac{5}{6}$
4. $\frac{11}{21}$
5. $\frac{12}{21}$

Q.

A four-digit number is formed by using digits 1, 2, 3, 4 without repetition. What is the probability that the number is divisible by 4?

1. None of these

2. 1/4

3. 1/2

4. 3/5

5. 4/5

Q.

A five digit number is formed with the digits 0, 1, 2, 3 and 4 without repetition. Find the chance that the number is divisible by 5.

1. None of these
2. $\frac{3}{4}$
3. $\frac{1}{4}$
4. $\frac{2}{4}$
5. $\frac{4}{5}$

Q.

'A' is the set of natural numbers less than 100. 'B' is the subset of 'A' such that 'B' contains two digit numbers from set 'A' which are divisible by exactly two numbers. 'C' is the subset of 'B' such that 'C' contains numbers whose sum of digits is divisible by 2. 'D' is the subset of 'C' such that 'D' contains numbers whose sum of digits is a perfect square or a perfect cube. Then find the median of the set 'D'?

Type the answer in the blank below:
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Q.

In a class, there are 14 boys and 11 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

1. none

2. 21/46

3. 10/11

4. 7/8

5. 21/23

Q.

If a two digit number is selected at random, then what is the probability that it will be a multiple of '3' and not a multiple of '5'?

1. 

2. 

3. None of these

4. 

Q. Two squares are chosen at random from the small squares drawn on a chessboard. What is the chance that the two squares chosen have exactly one corner in common?

1. 0.042
2. 0.048
3. 0.052
4. 0.075

Q.

A four-digit number is formed by using digits 1, 2, 3, 4 without repetition. What is the probability that the number is divisible by 4?

1. None of these

2. 

3. 

4. 

Q. A Number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

1. 
2. 
3. 
4. 

Q.

$x_1$, $x_2$, $x_3$, ..., $x_{40}$ are forty real numbers such that $x_r$$<$$x_{r+1}$ for r = 1, 2, 3... 39. Five numbers out of these are picked up at random. The probability that the five numbers have $x_{20}$ as the middle number is:

1. ()/()

2. ()/()

3. ()/()

4. ()/()

Q. When a two digit number is rotated by ${180}^{\circ }$ a different two digit number is obtained. What is the probability of such an occurrence?

1. 
2. 
3. 
4. 
5. 

Q. If $10$ things are distributed among $3$ persons, the chance of a particular person having more than $5$ of them is $\frac{1507}{19683}$.

Q. In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lies in the same row or column?

1. $896$
2. $56$
3. $60$
4. $768$

Q. Two squares are chosen from the squares of an ordinary chess board. It is given that the selected squares do not belong to the same row or column. The probability that they have a side in common

1. $\frac{25}{49}$
2. $\frac{32}{49}$
3. $\frac{1}{18}$
4. $\frac{1}{2}$