CUET Mathematics Mock Test - 1

Given that $x\sim B(n=10,p)$, if the expectation $E(x)=8$, find the value of $p$.

Let $Z$ denote the number of hours you study on a Monday. It is known that $P(Z=0)=0.4$, $P(Z=1\text{ or }2)=kz$ (where $k$ is constant), and $P(Z)=0$ otherwise. What is the probability that you study at least two hours?

If $P(A)=0.4$, $P(B)=0.8$, and $P(B|A)=0.6$, then $P(A\cup B)$ is equal to:

If $A=\left(\begin{array}{cc}2& 2\\ 9& 4\end{array}\right)$ and $I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$, then $10A^{-1}$ is equal to:

The differential equation representing the family of curves $y=a\sin (\lambda x+\alpha )$ is: