MHT CET 2024 2ND MAY MORNING SHIFT

In a process 605 J heat is absorbed by the system and 380 J work is done by the system on surrounding. What is the value of $\Delta$U?

The number of real solutions of

$\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

An annular ring has mass 10 kg and inner and outer radii are 10 m and 5 m respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

What is the ratio of concentration of salt to concentration of weak acid in buffer solution to maintain its pH value $7.2\left(\mathrm{pK}_{\mathrm{a}}=6.2\right)$.

For a suitable chosen real constant a, let a function $f: \mathbb{R}-\{-\mathrm{a}\} \rightarrow \mathbb{R}$ be defined by $f(x)=\frac{a-x}{a+x}$. Further suppose that for any real number $x \neq-\mathrm{a}$ and $\mathrm{f}(x) \neq-\mathrm{a}$, (fof) $(x)=x$. Then $f\left(-\frac{1}{5}\right)$ is equal to

A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with frequency 4 Hz . The acceleration of the particle in $\mathrm{m} / \mathrm{s}^2$ is