CUET Mathematics 2025 22 May Shift 1 PYQs

The probability distribution function of a normal variate with mean $\mu$ and variance $\sigma^2$ is given by:

$f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, $-\infty < x < \infty$, $-\infty < \mu < \infty$, $\sigma > 0$

If $y = f(x)$ be the normal probability curve, then which of the following is correct?

(A) The normal curve is symmetrical about the line $x = \mu$.

(B) Mean, median and mode of the distribution coincide.

(C) Y- axis is an asymptote to the normal curve.

(D) If x increases numerically, $f(x)$ decreases rapidly.

Choose the correct answer from the options given below:

Bag A contains 2 unbiased and 3 biased coins whereas Bag B contains 3 unbiased and 2 biased coins. A bag is selected at random and 2 coins are taken out simultaneously. The probability, that both coins are unbiased is:

If the random variable X has the following probability distribution:

then K is equal to