CUET and UG exam WB JEE Mock Test Series 2025 Mathematical Science Analysis Continuity & Differentiability
Let \(f: \mathbb{R}\rightarrow (0, 1)\) be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval \((0, 1)\)?
1
\(f(x) + \int_0^{\frac{\pi}{2}}f(t) \sin \, t \, dt\)
2
\(e^x-\int_0^xf(t) \sin \, t\, dt\)
3
\(x-\int_0^{\frac{\pi}{2}-x} f(t) \cos \, t\, dt\)
4
\(x^9-f(x)\)