CUET Mathematics - The probability distribution function of a normal variate with mean and variance ^2 is given by: f(x) = 1(2)e^-1/2(x-/)^2, -∞ < x < ∞, -∞ < < ∞, > 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 = . (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: | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 2

Algebra

Medium

applied

(A) and (D) only

(A), (B) and (D) only

(A), (B), (C) and (D)

(B) and (C) only

✅ Correct Option: 2

Related questions:

CUET Mathematics 2024 Slot 1

Let $X$ denote the number of hours you play during a randomly selected day. The probability that $X$ can take values $x$ has the following form, where $c$ is some constant.

$\mathrm{P}(\mathrm{X}=\mathrm{x})=\left\{\begin{array}{lll} 0.1, & \text { if } \mathrm{x}=0 \\ \mathrm{cx}, & \text { if } \mathrm{x}=1 \text { or } \mathrm{x}=2 \\ \mathrm{c}(5-\mathrm{x}), & \text { if } \mathrm{x}=3 \text { or } \mathrm{x}=4 \\ 0, & \text { otherwise } \end{array}\right.$

Match List-I with List-II :

List-I	List-II
(A) $c$	(I) 0.75
(B) $P(X \leq 2)$	(II) 0.3
(C) $P(X = 2)$	(III) 0.55
(D) $P(X \geq 2)$	(IV) 0.15

15 May Shift 1

In a game, a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise, when a fair dice is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. The expected value of the amount(in Rs.) he wins or loses is:

15 May Shift 1

Let x denote the number of doublets in three throws of a pair of dice with the following probability distribution.

x	0	1	2	3
P(x)	$\frac{25}{72}k$	$\frac{15}{72}k$	$\frac{1}{4}k$	$\frac{1}{36}k$

If value of k is equal to $\frac{m}{n} \cdot \gcd(m,n) = 1$ , then $m + n$ is equal to

CUET Mathematics 2025 21 May Shift 2 PYQs

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