1
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

A
$$\frac{5}{11}$$
B
$$\frac{5}{6}$$
C
$$\frac{1}{6}$$
D
$$\frac{6}{11}$$
2
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

In an A.P., the sixth term $$a_6=2$$. If the product $$a_1 a_4 a_5$$ is the greatest, then the common difference of the A.P. is equal to

A
$$\frac{2}{3}$$
B
$$\frac{5}{8}$$
C
$$\frac{3}{2}$$
D
$$\frac{8}{5}$$
3
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\text { Let } A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{array}\right] \text { and }|2 \mathrm{~A}|^3=2^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }$$

A
9
B
17
C
3
D
5
4
JEE Main 2024 (Online) 29th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$R$$ be a relation on $$Z \times Z$$ defined by $$(a, b) R(c, d)$$ if and only if $$a d-b c$$ is divisible by 5. Then $$R$$ is

A
Reflexive and transitive but not symmetric
B
Reflexive and symmetric but not transitive
C
Reflexive but neither symmetric nor transitive
D
Reflexive, symmetric and transitive
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