MHTCET 20 Apr 2026 Shift 1 Paper

Concept:This problem checks the truth values of compound statements formed using implication, conjunction, and negation.Explanation:Statement I: Let $p$ be "1 is not a prime number" and $q$ be "2 is not a prime number".Here, $p$ is true, but $q$ is false because 2 is the smallest prime number.An implication $p \rightarrow q$ is false only when $p$ is true and $q$ is false.So statement I is not true.Statement II: $e$ is a vowel is true, and $12 \times 3 = 36$ is also true.Since both parts are true, the conjunction is true.Statement III: Inside the statement, "14 is a composite number and 3 is an even number" is false, because 14 is composite but 3 is not even.The negation of a false statement is true, so statement III is true.Statement IV: $\sqrt{5}$ is an irrational number is true.Also, $3+\sqrt{5}$ is a real number, and every real number is a complex number with imaginary part 0.We can write $3+\sqrt{5} = (3+\sqrt{5}) + 0i$, so $3+\sqrt{5}$ is a complex number.Thus statement IV is true.Therefore, only statement I is not true.Answer:Option B: Only I.