1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :
A
$$\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )$$
B
$$\left[ { - {1 \over 2},0} \right) \cup [1,\infty )$$
C
$$\left( { - {1 \over 2},\infty } \right) - \{ 0\} $$
D
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\} $$
2
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probability P(x $$\ge$$ 5 | x > 2) is :
A
$${{125} \over {216}}$$
B
$${{11} \over {36}}$$
C
$${{5} \over {6}}$$
D
$${{25} \over {36}}$$
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $$, then the value of tan p is :
A
$${{101} \over {102}}$$
B
$${{50} \over {51}}$$
C
100
D
$${{51} \over {50}}$$
4
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equations

x + y + z = 5

x + 2y + 3z = $$\mu$$

x + 3y + $$\lambda$$z = 1

is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :
A
$$p = {1 \over 6}$$ and $$q = {1 \over 36}$$
B
$$p = {5 \over 6}$$ and $$q = {5 \over 36}$$
C
$$p = {5 \over 6}$$ and $$q = {1 \over 36}$$
D
$$p = {1 \over 6}$$ and $$q = {5 \over 36}$$
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