There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

• 3

• 36

• 66

• 66

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

• 1/3

• 2/7

• 1/21

• 1/21

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ..., 20}.

Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1 85.
Statement-2: If the four chosen numbers form an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends,3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

• 484

• 485

• 468

• 468

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one–by–one, with replacement, then the variance of the number of green balls drawn is

• 6/25

• 12/5

• 6

• 6

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is

• less than 500

• at least 500 but less than 750

• at least 750 but less than 1000

• at least 750 but less than 1000

In a binomial distribution B(n, n= 1/4) , if the probability of at least one success is greater than or equal to 9/10 , then n is greater than 

It is given that the events A and B are such that  then P(B) is 

• 1/6

• 1/3

• 2/3

• 2/3

In a shop, there are five types of ice-creams available. A child buys six ice-creams.
Statement -1: The number of different ways the child can buy the six ice-creams is ¹⁰C₅.
Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

• 1/729

• 8/9

• 8/729

• 8/729