List of top Mathematics Questions on Elementary Operation (Transformation) of a Matrix

If the lines \( \frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \) and \( \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-7} \) are perpendicular to each other, find the value of \( k \) and hence write the vector equation of a line perpendicular to these two lines passing through the point \( (3, -4, 7) \).
The probability distribution of a random variable \( X \) is: \[ \begin{array}{c|c|c|c|c|c} X & 0 & 1 & 2 & 3 & 4 \\ \hline P(X) & 0.1 & k & 2k & k & 0.1 \\ \end{array} \] where \( k \) is some unknown constant. The probability that the random variable \( X \) takes the value 2 is:

ASSERTION-REASON BASED QUESTIONS:-
Questions number 19 and 20 are Assertion and Reason based questions. 
Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). 
Select the correct answer from the codes (A), (B), (C) and (D) as given below.