CUET Mathematics Mock Test - 4

What is the probability that the roots of the equation $x^2+x+n=0$ are real, where $n\in \mathbb{N}$ and $n<4$?

Five coins are tossed at a time. The probability of obtaining at least one head is:

$X$ is a random variable with probability density function:
$$f(x)=\{\begin{array}{ll}\frac{1}{2\pi }& -\pi \le x\le \pi \\ 0& \text{elsewhere}\end{array}$$
Then $E[\sin x]$ is:

If the lines $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$ and $\frac{x-x_2}{p}=\frac{y-y_2}{q}=\frac{z-z_2}{r}$ lie on the same plane, then:

Let $X$ be a random variable that is uniformly chosen from the set of positive odd numbers less than $100$. The expectation $E[X]$ is: