1
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1
Change Language

$$\mathrm{r}=\mathrm{k}[\mathrm{A}]$$ for a reaction, $$50 \%$$ of $$\mathrm{A}$$ is decomposed in 120 minutes. The time taken for $$90 \%$$ decomposition of $$\mathrm{A}$$ is _________ minutes.

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2
JEE Main 2024 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

A
130
B
136
C
142
D
406
3
JEE Main 2024 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

A
$$\frac{1}{9}$$
B
$$\frac{2}{9}$$
C
$$\frac{1}{27}$$
D
$$\frac{2}{27}$$
4
JEE Main 2024 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A$$ be a $$3 \times 3$$ real matrix such that

$$A\left(\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right)=2\left(\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right), A\left(\begin{array}{l} -1 \\ 0 \\ 1 \end{array}\right)=4\left(\begin{array}{l} -1 \\ 0 \\ 1 \end{array}\right), A\left(\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right)=2\left(\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right) \text {. }$$

Then, the system $$(A-3 I)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)$$ has :

A
exactly two solutions
B
infinitely many solutions
C
unique solution
D
no solution
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