Class 12 Mathematics 2024 Board Exam

If $x=at$, $y=\frac{a}{t}$, then $\frac{dy}{dx}$ is :

A function $f:{\mathbb{R}}^{+}\to \mathbb{R}$ (where ${\mathbb{R}}^{+}$ is the set of all non-negative real numbers) defined by $f(x)=4x+3$ is :

If $y={\cos }^{-1}(e^x)$, then $\frac{dy}{dx}$ is :

If the sum of all the elements of a $3\times 3$ scalar matrix is $9$, then the product of all its elements is :

The number of solutions of differential equation $\frac{dy}{dx}-y=1$, given that $y(0)=1$, is :

The integrating factor of the differential equation $x\frac{dy}{dx}-y=x^4-3x$ is :

Let $f:{\mathbb{R}}^{+}\to [-5,\infty )$ be defined as $f(x)=9x^2+6x-5$, where ${\mathbb{R}}^{+}$ is the set of all non-negative real numbers. Then, $f$ is :

If a matrix has $36$ elements, the number of possible orders it can have, is :

The solution of the differential equation $\frac{dy}{dx}=\frac{1}{\log y}$ is :

The degree and order of differential equation $(y^{\prime \prime }{)}^2+\log (y^{\prime })=x^5$ respectively are :