1
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

The mean of the coefficients of $$x, x^{2}, \ldots, x^{7}$$ in the binomial expansion of $$(2+x)^{9}$$ is ___________.

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2
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

If $$a$$ and $$b$$ are the roots of the equation $$x^{2}-7 x-1=0$$, then the value of $$\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}$$ is equal to _____________.

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3
JEE Main 2023 (Online) 11th April Morning Shift
Numerical
+4
-1
Change Language

The number of integral terms in the expansion of $$\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}$$ is equal to ___________.

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4
JEE Main 2023 (Online) 11th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Given below are two statements :

Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II : $$\mathrm{Au} < \mathrm{Parsec} (\mathrm{Pc}) < \mathrm{ly}$$

In the light of the above statements, choose the most appropriate answer from the options given below:

A
Both Statements I and Statements II are incorrect.
B
Both Statements I and Statements II are correct,
C
Statements I is incorrect but Statements II is correct.
D
Statements I is correct but Statements II is incorrect.
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