1
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+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
$${{7} \over {105}}$$
2
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
$${3 \over 4}$$
4
JEE Advanced 2014 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1
Given that for each $$a \in \left( {0,1} \right),\,\,\,\mathop {\lim }\limits_{h \to {0^ + }} \,\int\limits_h^{1 - h} {{t^{ - a}}{{\left( {1 - t} \right)}^{a - 1}}dt} $$ exists. Let this limit be $$g(a).$$ In addition, it is given that the function $$g(a)$$ is differentiable on $$(0,1).$$

The value of $$g'\left( {{1 \over 2}} \right)$$ is

A
$${\pi \over 2}$$
B
$$\pi $$
C
$$-{\pi \over 2}$$
D
$$0$$
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