1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

A
$${2 \over 7}$$
B
$${1 \over 18}$$
C
$${1 \over 7}$$
D
$${1 \over 9}$$
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
A
$${1 \over {10}}$$
B
$${1 \over {15}}$$
C
$${1 \over {5}}$$
D
$${1 \over {30}}$$
3
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :
A
$${1 \over 8}$$
B
$${5 \over 8}$$
C
$${5 \over 16}$$
D
1
4
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face occurs with probability $${1 \over 6} + x$$. All other faces occur with probability $${1 \over 6}$$. Note that opposite faces sum to 7 in any die. If 0 < x < $${1 \over 6}$$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is $${13 \over 96}$$, then the value of x is :
A
$${1 \over 16}$$
B
$${1 \over 8}$$
C
$${1 \over 9}$$
D
$${1 \over 12}$$
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