A boy has a collection of blue and green marbles. The number of blue marbles belong to the set `{2,3,4,…..,13}`. If two marbles are chosen simultaneou

Monjur Alahi

A boy has a collection of blue and green marbles. The number of blue marbles belong to the set `{2,3,4,…..,13}`. If two marbles are chosen simultaneously and at random from his collection, then the probability that they have different coloursis `(1)/(2)`. Possible number of the blue marbles is
A. `3`
B. `6`
C. `10`
D. `12`


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Correct Answer - A::B::C
`(a,b,c)` Let the no. of blue marbles is `a` and no. of green marbles is `b` .
`:.(ab)/("^(a+b)C_(2))=(1)/(2)`
`implies(a+b)(a+b-1)=4ab`
`impliesb^(2)-(2a+1)b+a^(2)-a=0`
but `b in R implies D=(2a+1)^(2)-4(a^(2)-a)=8a+1`
`:. 8a+1` must be a perfect square.
Hence possible values of `a` are `3,6,10`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
If two distinct numbers m and n are chosen at random form the set {1, 2, 3, …, 100}, then find the probability that `2^(m) + 2^(n) + 1` is divisible b

Correct Answer - `(49)/(198)` `2^(m) + 2^(n) + 1 = (3 - 1)^(m) + (3 - 1)^(n) + 1` `=3k + (-1)^(m) + (-1)^(n) + 1` This is divisible by 3...

2 Answers 1 views
Two number `aa n db` aer chosen at random from the set of first 30 natural numbers. Find the probability that `a^2-b^2` is divisible by 3.

Correct Answer - `(47)/(87)` The total number of ways of choosing two numbers out of 1, 2, 3, …, 30 is `.^(30)C_(2)` = 435. Now, 30 natural numbers are categorized as...

2 Answers 1 views
If a and b are chosen randomly from the set consisting of number 1, 2, 3, 4, 5, 6 with replacement. Then the probability that `lim_(x to 0)[(a^(x)+b^(

Correct Answer - C Given limit, `underset(x rarr 0)(lim)((a^(x) + b^(x))/(2))^((2)/(x))` `=(underset(xrarr0)lim(1+(a^(x) + b^(x) - 2)/(2))^((2)/(a^(x) + b^(x) - 2)))^(underset(xrarr0)lim((a^(x) -1 + b^(2)-1)/(x))` `= e^(log ab) = ab = 6`

2 Answers 1 views
There are two red, two blue, two white, and certain number (greater than 0) of green socks n a drawer. If two socks are taken at random from the drawe

Correct Answer - D Let the number of green socks be `x gt 0`. E: Two socks drawn are of the same color implies P(E) = P(R R or B B...

2 Answers 1 views
A boy hits a baseball with a bat and imparts and impulse J to the ball. And if the boy hits the ball again with the same force, except that the ball a

Correct Answer - `J=F Deltat`

2 Answers 1 views
There are two urns `Aa n dB` . Urn `A` contains 5 red, 3 blue and 2 white balls, urn `B` contains 4 re3d, 3 blue, and 3 white balls. An urn is chosen

Correct Answer - D Let A nad B, respectively, be the events that urn A and urn B are selected.Let R be the event that the selected ball is red. Since...

2 Answers 1 views
Number of ways in which 7 green bottles and 8 blue bottles can be arranged in a row if exactly 1 pair of green bottles is side by side, is (Assume all

Correct Answer - C `(c )` First arrange `8` blue alike bottles `to ` number of ways `=1` Now select one gap out of `9` gaps created to put two green...

2 Answers 3 views
If `a` and `b` are randomly chosen from the set `{1,2,3,4,5,6,7,8,9}`, then the probability that the expression `ax^(4)+bx^(3)+(a+1)x^(2)+bx+1` has po

Correct Answer - C `(c )` The expression `ax^(4)+ax^(2)+bx^(3)+bx+x^(2)+1` `=(x^(2)+1)(ax^(2)+bx+1)` `:.x^(2)+1` is positive for all real `x` For `ax^(2)+bx=1` to be positive for all real `x` `a gt 0`, `b^(2)-4a lt...

2 Answers 1 views
Which of the following collections is not a set ? `(i)` The collection of natural numbers between `2` and `20` `(ii)` The collection of numbers which

Correct Answer - `(iv)`

2 Answers 1 views
Amar ,Bhuvan and Chetan have some marble with them. Bhuvan has 20% more marbles than Amar and Chetan has 10% less marbles than Bhuvan . If the total n

Correct Answer - `120`

2 Answers 1 views
X