CUET UG 2024 — Mathematics Algebra

If f(x) = 2x + 3, then f⁻¹(x) is:

If a random variable $X$ has the following probability distribution: | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | k | 2k | 3k | k² | 6k² | , then Match List-I with List-II | List-I | List-II | |---|---| | (A) k | (I) 3/7 | | (B) $P(X < 2)$ | (II) 6/49 | | (C) $P(X > 3)$ | (III) 1/7 | | (D) $P(2 \leq X \leq 3)$ | (IV) 22/49 | Choose the correct answer from the options given below:

If the roots of the equation x² - 5x + k = 0 are in the ratio 2:3, then the value of k is:

It is known that 3% of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is:

If R and S are two equivalence relations on a set A, then