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1
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1
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The remainder, when $$7^{103}$$ is divided by 17, is __________

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2
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
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Let $$\alpha$$ be the constant term in the binomial expansion of $$\left(\sqrt{x}-\frac{6}{x^{\frac{3}{2}}}\right)^{n}, n \leq 15$$. If the sum of the coefficients of the remaining terms in the expansion is 649 and the coefficient of $$x^{-n}$$ is $$\lambda \alpha$$, then $$\lambda$$ is equal to _____________.

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