CUET Mathematics Mock Test - 3

What is the area bounded by the curves $|y|=1-x^2$?

If $I_1=\int \frac{e^x}{e^x+e^{-x}}dx$ and $I_2=\int \frac{dx}{e^{2x}+1}$, then what is $I_1+I_2$ equal to?

If $f(x)=2\ln (e^{x/2})$, what is the area bounded by $f(x)$ for the interval $[0,2]$ on the x-axis?

Find the area of the parabola $y^2=4ax$ bounded by its latus rectum.

Ram is a fruit seller. Apples cost Rs 80/kg and Mangoes Rs 120/kg. Profits are Rs 10/kg and Rs 12/kg respectively. Let $x$ be kgs of apples and $y$ be kgs of mangoes. If Ram wants to maximize profit, the objective function $Z$ is: