1
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

If the term without $$x$$ in the expansion of $$\left(x^{\frac{2}{3}}+\frac{\alpha}{x^{3}}\right)^{22}$$ is 7315 , then $$|\alpha|$$ is equal to ___________.

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

The remainder, when $$19^{200}+23^{200}$$ is divided by 49 , is ___________.

3
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
The coefficient of $x^{-6}$, in the

expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}$, is
4
JEE Main 2023 (Online) 31st January Evening Shift
Numerical
+4
-1
If the constant term in the binomial expansion of $\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^{\alpha} \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to ________.
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