The function $f(x) = x^3 - 27x + 4$, $1 \leq x \leq 6$ has
Consider two Ordinary Differential Equations (ODEs):
P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $
Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $
Which one of the following options is CORRECT?
In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is
Three vectors $\overrightarrow{p}$, $\overrightarrow{q}$, and $\overrightarrow{r}$ are given as
$ \overrightarrow{p} = \hat{i} + \hat{j} + \hat{k}$
$ \overrightarrow{q} = \hat{i} + 2\hat{j} + 3\hat{k}$
$ \overrightarrow{r} = 2\hat{i} + 3\hat{j} + 4\hat{k}$
Which of the following is/are CORRECT?