Which of the following is/are not true ?
I) If 1 is not a prime number, then 2 is not a prime number.
II) e is a vowel and $12\times 3 = 36$
III) It is not true that 14 is a composite number and 3 is even number.
IV) $\sqrt{5}$ is an irrational number, but $3+\sqrt{5}$ is a complex number.

Question

If $ x \neq 0 $, then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]

Answer 1

Step 1: Evaluate every statement as true or false:
I: $F$ (implication with true hypothesis, false conclusion). II: T and T gives T. III: $\sim(T \land F) = \sim F = T$. IV: T "but" T gives T.

Step 2: Pick the false ones:
The question asks for those that are not true. Only I is false.

Step 3: Option check:
Option (B) "Only I" is the match.

Final Answer:
Only I is not true, option (B). \[ \boxed{\text{Only I}} \]

Which of the following is/are not true ?
I) If 1 is not a prime number, then 2 is not a prime number.
II) e is a vowel and \(12\times 3 = 36\)
III) It is not true that 14 is a composite number and 3 is even number.
IV) \(\sqrt{5}\) is an irrational number, but \(3+\sqrt{5}\) is a complex number.

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on Statements

Questions Asked in MHT CET exam

Which of the following is/are not true ?I) If 1 is not a prime number, then 2 is not a prime number.II) e is a vowel and \(12\times 3 = 36\)III) It is not true that 14 is a composite number and 3 is even number.IV) \(\sqrt{5}\) is an irrational number, but \(3+\sqrt{5}\) is a complex number.