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दिवाली आशा, विश्वास और जीत का त्योहार है। यह दिवाली आपको अपने सपनों और जुनून को पूरा करने के लिए प्रेरित करे। आपको अपने शिक्षकों और गुरुओं का मार्गदर्शन और समर्थन हमेशा मिलता रहे। आप अपनी उपलब्धियों से अपने माता-पिता और दोस्तों को गौरवान्वित महसूस कराएं। आपको और सभी विद्यार्थियों को दीपावली की शुभकामनाएँ!

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JRF STUDY In this **Quora **space, You can also ask me any doubts or queries related to

The function f(x) is bounded due to its continuity on the compact interval [0, 1]. This is a valid conclusion from the fact that f is continuous and f(x) = f(x + 1) for all x ∈ ℝ, which implies the periodicity of the function with a period of 1.
[IIT JAM 2021]

a function is periodic with period 1 if its values repeat every 1 unit along the x-axis. This means that the function's behavior within any 1-unit interval is the same as in any other 1-unit interval[IIT JAM 2021]

Let f : ℝ → ℝ be a continuous function satisfying f(x) = f(x+1) for all x ∈ ℝ. Then
A. f is bounded.
SOL. Let f : ℝ → ℝ be a continuous function satisfying f(x) = f(x+1) for all x ∈ ℝ.

The periodicity of f tells us that the image of f is f([0, 1]) . Since f is continuous and [0, 1] compact, it is bounded.
[ IIT JAM 2021]

What does the partition function p(n) count?
a. Number of non-isomorphic groups
b. Number of non-cyclic groups
c. Number of possible partitions of n into positive integers
d. Number of elements in a cyclic group