JEE Main 2026 · 4 Apr · Shift 2 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 75

Let $\alpha=\dfrac14+\dfrac18+\dfrac1{16}+\dots\infty$ and $\beta=\dfrac13+\dfrac19+\dfrac1{27}+\dots\infty$ . Then the value of $(0.2)^{\log_{\sqrt5}(\alpha)}+(0.04)^{\log_5(\beta)}$ is equal to:

Answer and worked solution

Official answer: C

Sums. $\alpha=\frac{1/4}{1-1/2}=\frac12$ and $\beta=\frac{1/3}{1-1/3}=\frac12$ .

First term. $(0.2)^{\log_{\sqrt5}(1/2)}=5^{-2\log_5(1/2)}=4$ .

Second term. $(0.04)^{\log_5(1/2)}=5^{-2\log_5(1/2)}=4$ .

Sum 8.

(C)

Topics:Logarithms Geometric progression

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JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 7