JEE MAIN 2023 ONLINE 31ST JANUARY MORNING SHIFT

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Identify X, Y and Z in the following reaction. (Equation not balanced)

Let a differentiable function \(f\) satisfy \(f(x)+\int_\limits{3}^{x} \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3\). Then \(12 f(8)\) is equal to :

The amplitude of \(15 \sin (1000 \pi \mathrm{t})\) is modulated by \(10 \sin (4 \pi \mathrm{t})\) signal. The amplitude modulated signal contains frequency (ies) of

A. \(500 \mathrm{~Hz}\)

B. \(2 \mathrm{~Hz}\)

C. \(250 \mathrm{~Hz}\)

D. \(498 \mathrm{~Hz}\)

E. \(502 \mathrm{~Hz}\)

Choose the correct answer from the options given below:

Adding surfactants in non polar solvent, the micelles structure will look like

Let \(\mathrm{y}=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y=-\frac{1}{2}\). Then

\(S=\left\{x \in \mathbb{R}: \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}\) :