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
Out of Syllabus
Change Language

Let a curve $$y=f(x), x \in(0, \infty)$$ pass through the points $$P\left(1, \frac{3}{2}\right)$$ and $$Q\left(a, \frac{1}{2}\right)$$. If the tangent at any point $$R(b, f(b))$$ to the given curve cuts the $$\mathrm{y}$$-axis at the point $$S(0, c)$$ such that $$b c=3$$, then $$(P Q)^{2}$$ is equal to __________.

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3
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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4
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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