1
JEE Advanced 2014 Paper 2 Offline
+3
-1
Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is
A
$${1 \over 2}$$
B
$${1 \over 3}$$
C
$${2 \over 3}$$
D
$${3 \over 4}$$
2
JEE Advanced 2014 Paper 2 Offline
+3
-1
Box $$1$$ contains three cards bearing numbers $$1,2,3;$$ box $$2$$ contains five cards bearing numbers $$1,2,3,4,5;$$ and box $$3$$ contains seven cards bearing numbers $$1,2,3,4,5,6,7.$$ A card is drawn from each of the boxes. Let $${x_i}$$ be number on the card drawn from the $${i^{th}}$$ box, $$i=1,2,3.$$

The probability that $${x_1} + {x_2} + {x_3}$$ is odd, is

A
$${{29} \over {105}}$$
B
$${{53} \over {105}}$$
C
$${{57} \over {105}}$$
D
$${{1} \over {2}}$$
3
JEE Advanced 2014 Paper 2 Offline
+3
-1
Box $$1$$ contains three cards bearing numbers $$1,2,3;$$ box $$2$$ contains five cards bearing numbers $$1,2,3,4,5;$$ and box $$3$$ contains seven cards bearing numbers $$1,2,3,4,5,6,7.$$ A card is drawn from each of the boxes. Let $${x_i}$$ be number on the card drawn from the $${i^{th}}$$ box, $$i=1,2,3.$$

The probability that $${x_1},$$, $${x_2},$$ $${x_3}$$ are in an arithmetic progression, is

A
$${{9} \over {105}}$$
B
$${{10} \over {105}}$$
C
$${{11} \over {105}}$$
D
$${{7} \over {105}}$$
4
JEE Advanced 2013 Paper 2 Offline
+4
-1
A box $${B_1}$$ contains $$1$$ white ball, $$3$$ red balls and $$2$$ black balls. Another box $${B_2}$$ contains $$2$$ white balls, $$3$$ red balls and $$4$$ black balls. A third box $${B_3}$$ contains $$3$$ white balls, $$4$$ red balls and $$5$$ black balls.

If $$2$$ balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these $$2$$ balls are drawn from box $${B_2}$$ is

A
$${{116} \over {181}}$$
B
$${{126} \over {181}}$$
C
$${{65} \over {181}}$$
D
$${{55} \over {181}}$$
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