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

If the mean and variance of the frequency distribution

$$x_i$$ 2 4 6 8 10 12 14 16
$$f_i$$ 4 4 $$\alpha$$ 15 8 $$\beta$$ 4 5

are 9 and 15.08 respectively, then the value of $$\alpha^2+\beta^2-\alpha\beta$$ is ___________.

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

Let the eccentricity of an ellipse $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ is reciprocal to that of the hyperbola $$2 x^{2}-2 y^{2}=1$$. If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is ___________.

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3
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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4
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 __________.

Your input ____
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