In the expansion of (1 + x)^p (1 + x)^q, if the coefficient of x³ is 35, then what is the value of (p + q)? 

If p times the pth term of an AP is equal to q times the qth term (p ≠ q), then what is the (p + q)th term equal to? 

Let p = ln(x), q = ln(x³) and r = ln(x⁵), where x > 1. Which of the following statements is/are correct? 

I. p, q and r are in AP.

Il. p, q and r can never be in GP.

Select the answer using the code given below.  

If $\rm z=\frac{1}{3}\begin{vmatrix}i&2i&1\\\ 2i&3i&2\\\ 3&1&3\end{vmatrix}=x+iy;i=\sqrt{-1}$ then what is modulus of Z equal to?