Sets — MATHS STD 11 Science — Question

1. If $\text{A } \cap \text{B}=\phi$ then either $ \text{A}=\phi$ or $ \text{B}=\phi$
   
2. For $ \text{a} ≠ \text{b}, \ ({\text{a}},\text{b})=(\text{b}, \text{a})$ and $ \text{a} ≠ \text{b}$
   
3. If $\text{A}\subseteq \text{B}$, then $ \text{A } \times\text{A }\subseteq ( \text{A } \times\text{B })\ \cap ( \text{B} \times\text{A })$
   
4. If $\text{A}\subseteq \text{B}$ and $\text{C}\subseteq \text{D}$, then $ \text{A } \times\text{C }\subseteq ( \text{B} \times\text{D }) $ Which of these is/are correct?
   

A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is:

1. $\frac{1}{3}$

2. $\frac{4}{11}$

3. $\frac{2}{11}$

4. $\frac{3}{11}$

If $\sin\theta+\text{cosec}\theta=2,$ then $\sin^2\theta+\text{cosec}^2\theta$ is equal to:

1. 1
2. 4
3. 2
4. None of these