The roots α and β of a quadratic equation, satisfy the relations α + β = α² + β² and αβ = α²β². What is the number of such quadratic equations ?

• 0

• 2

• 3

• 4

If p², q² and r² (where p, q, r > 0) are in GP, then which of the following is/are correct ?

1) p, q and r are in GP.

2) ln(p), ln(q) and ln(r) are in AP

Select the correct answer using the code given below :

• 1 only

• 2 only

• Both 1 and 2

• Neither 1 nor 2

What is the modulus of the complex number $\frac{\cos \left(\mathrm{\theta }\right) + \mathrm{isin}\left(\mathrm{\theta }\right)}{\cos \left(\mathrm{\theta }\right) - \mathrm{isin}\left(\mathrm{\theta }\right)} \mathrm{where}, \mathrm{i} = \sqrt{ - 1} ?$

• $\frac{1}{2}$

• 1

• $\frac{3}{2}$

• 2