1
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.

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2
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.

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3
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let $$\vec{v}=\alpha \hat{i}+2 \hat{j}-3 \hat{k}, \vec{w}=2 \alpha \hat{i}+\hat{j}-\hat{k}$$ and $$\vec{u}$$ be a vector such that $$|\vec{u}|=\alpha>0$$. If the minimum value of the scalar triple product $$\left[ {\matrix{ {\overrightarrow u } & {\overrightarrow v } & {\overrightarrow w } \cr } } \right]$$ is $$-\alpha \sqrt{3401}$$, and $$|\vec{u} \cdot \hat{i}|^{2}=\frac{m}{n}$$ where $$m$$ and $$n$$ are coprime natural numbers, then $$m+n$$ is equal to ____________.

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4
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language

Let $$A$$ be the area bounded by the curve $$y=x|x-3|$$, the $$x$$-axis and the ordinates $$x=-1$$ and $$x=2$$. Then $$12 A$$ is equal to ____________.

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