1
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is __________.

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2
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

The value of $$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$$ is __________.

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3
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

For $$\alpha, \beta, z \in \mathbb{C}$$ and $$\lambda > 1$$, if $$\sqrt{\lambda-1}$$ is the radius of the circle $$|z-\alpha|^{2}+|z-\beta|^{2}=2 \lambda$$, then $$|\alpha-\beta|$$ is equal to __________.

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4
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1
Change Language

If the lines $$\frac{x-1}{2}=\frac{2-y}{-3}=\frac{z-3}{\alpha}$$ and $$\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{\beta}$$ intersect, then the magnitude of the minimum value of $$8 \alpha \beta$$ is _____________.

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