CUET Mathematics Mock Test - 4

Let $f:(0,+\infty )\to \mathbb{R}$ and $F(x)={\int }_0^{x}f(t)dt$. If $F(x^2)=x^2(1+x)$, then $f(4)$ equals:

If $A$ is a skew-symmetric matrix, then its transpose $A^T$ is equal to:

Correct evaluation of $\int \frac{x}{(x-2)(x-1)}dx$ (where $p$ is an arbitrary constant) is:

If ${\lim }_{n\to \infty }{\sum }_{k=1}^n\left[{\left(\frac{3k}{n}\right)}^2+2\right]\frac{3}{n}={\int }_0^{6}f(x)dx$, then:

A coin is tossed twice. If $E$ and $F$ denote the occurrence of a head on the first toss and second toss respectively, then what is $P(E\cup F)$ equal to?