CUET Mathematics Mock Test - 1

A toy manufacturing firm has its variable cost $C(x)={\alpha }^{2}x(\beta \sqrt{x}+\alpha \beta )$, where $x$ is the number of toys produced. The cost of storage and other fixed expenses are $Rs.4500$. If the marginal cost is $40$ when $144$ toys have been produced and $\alpha \beta =1$, find the possible values of $\alpha$.

The function $f(x)={\tan }^{-1}x-x$ is monotonically decreasing in the set:

Find the rate of change of the volume of a cube when the side of the cube is $10\text{cm}$, given that the side is changing at a rate of $4\text{cm/s}$.

If $y+{\sin }^{-1}(1-x^2)=e^x$, then $\frac{dy}{dx}$ is:

Let $f(x)=|x^2-3x-4|$ defined for $-1\le x\le 4$. Which of the following is correct?